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Testing for structure in a multi-product industry with price expectations : the Canadian cattle industry Gordon, Daniel Vernon 1984

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TESTING FOR STRUCTURE IN A MULTI-PRODUCT INDUSTRY WITH PRICE EXPECTATIONS: THE CANADIAN CATTLE INDUSTRY by DANIEL VERNON GORDON B.A. The University of Lethbridge, 1977 M.A. The University of Saskatchewan, 1980  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Economics  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1984 ©DANIEL VERNON GORDON, 1984  In  presenting  requirements British freely  this for  an  Columbia, I available  permission  for  thesis  advanced  agree  for  in  that  reference  extensive  partial degree the  at  this  I  of  the  the U n i v e r s i t y  Library  and s t u d y .  c o p y i n g of  fulfilment  shall  further  thesis  make agree  for  of it that  scholarly  p u r p o s e s may be g r a n t e d by t h e Head of my D e p a r t m e n t or by or her  representatives.  publication  of  allowed without  Department  of  this  It thesis  my w r i t t e n  understood for  August 20,  1984  financial  permission.  Economics  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date:  is  Columbia  that gain  copying shall  not  his or be  i i ABSTRACT  The aim of profit  The  model  r e s p o n s e and  model of  of  the  the  short  run s u p p l y  have  argued  elasticity  this  a  a  consistent  from the  is  carried  cow-calf of  out  farmers.  in  profit  negative the  sign  of  the  industry;  production  short of  ii)  and cattle  a prediction  from  s i g n of  the  elasticity  transformation technological  for  transformation  coefficients certain  function  the  theory.  unknown and w i l l  of a  of  the  profit  characteristics It  structure by  economic  in  depend  producers.  function.  defined  the  prices.  not  test  i)  production  is  The e s t i m a t e d  run  substitution  supply e l a s t i c i t y  of  supply  short  run n e g a t i v e  is  studies  factors:  the  of  determine  run  the  today  expectations  to  (Past  s u p p l y depends on t h r e e  farmers'  expectations  is  run  consistent  derived  to  producers.  short  industry the  of  model,  cattle  and i i i )  Consequently,  analysis  existence  between  Canada  is  then  short  cattle  to provide  are  response  In  of  to  of  equations  possibilities  used  used here  and  dynamic  The model  structure  on p r i c e  the  behaviour  theoretical  farm  industry.  technological  Rather  is  static  the  elasticities.)  .cow-calf  cow-calf  a  farm m o d e l .  A comparative  tomorrow;  develop  empirically  duality  cow-calf  to  a  investment  estimated  maximizing  is  of  and t o e s t i m a t e  theory  that  research  maximizing  determine supply  this  is  cow-calf  the  determined production  non-homothetic,  subject  of  function  to decreasing  are  underlying that in  the  western  non-homogeneous returns  to  scale  and j o i n t  p r o d u c t i o n between  Other  characteristics  determined  by  elasticities supply  relationship  of  determined  there  that  is  cattle  non-postive cattle  no  of  cattle  takes  of  industry choice.  expectations slopes, slopes,  are These  with  output  derived  input  and a  s u p p l y and  fluctuations, cattle  for  the  evidence  on  substitute  end-of-period  to  z e r o or  also  only  of  the  effect  cattle  in current of  indicate  that  less.  calculated. the of  effect changing  supply.  It  is  in expectations cattle  cattle  s t r o n g enough t o d e c r e a s e  supply  is  adjustments  elasticity to  not  but a l s o  prices  accounting  supply  account  c a u s e d by c h a n g e s  decrease  significantly of  measure  of  prices  always  a priori  between  elasticity  price  expectations  cattle  cow-calf  demand.  elasticity cattle  the  non-negative  having  predicted  The t o t a l This  having  cattle.  elasticities  conform to a l l  functions  inventory  of  calculating  functions  demand  c r o p s and  prices  supply. this  short  run  of  will  However,  tendency  is  elasticities  TABLE OF CONTENTS  ABSTRACT  .  i i  TABLE OF CONTENTS  iv  L I S T OF TABLES  vi  L I S T OF FIGURES  .  ACKNOWLEDGEMENTS  viii ix  Chapter 1.  INTRODUCTION  1  1 .1  Objectives  7  1.2  Existing Literature  7  1.3  Thesis Outline  9  Footnotes 2.  12  THE CANADIAN CATTLE INDUSTRY 2.1  Introduction  2.2  Some C h a r a c t e r i s t i c s  2.3  Alternative  Production  t o Cow-Calf  Producers  2.4  14  Existing Theoretical Industry  of  the C a t t l e Strategies  Industry  A THEORETICAL  14  Available 30  M o d e l s of  the  Cow-Calf  Footnotes 3.  —  34 43  MODEL OF THE COW-CALF INDUSTRY  3.1  Introduction  44  3.2  A Single  Output P r o f i t  Cow-Calf  Producer  Function  for  a 45  3.3  Separability  as a M a i n t a i n e d H y p o t h e s i s  3.4  A g g r e g a t i o n Over  3.5  A S i n g l e Output P r o f i t F u n c t i o n f o r R e p r e s e n t a t i v e Cow-Calf Producer  3.6  Some C o m p a r a t i v e  Farms  Statics  57 59  a  65 68  3.7  A M u l t i - O u t p u t , M u l t i - I n p u t Model of R e p r e s e n t a t i v e Cow-Calf Producer  3.8  C h a r a c t e r i z i n g the  3.9  Testing for Multi-Input Footnotes  Structure  of  a  74  Production  ....  Structure using a Multi-Output, Variable Profit Function  79 82  ..  85  VARIABLE SPECIFICATION AND FUNCTIONAL  FORMS  4.1  Introduction  87  4.2  Price  91  4.3  Data  4.4  Stochastic Specification Techniques  Expectations  98 and  Estimation  111  Footnotes PARAMETER  122  ESTIMATES AND SUMMARY  STATISTICS  5.1  Introduction  125  5.2  Empirical Results P r o f i t Function  using a Translog  5.3  Empirical  using Time-Series  Results  Variable  125  Data  151  Footnotes  166  SUMMARY AND CONCLUSIONS  167  BIBLIOGRAPHY  176  .  APPENDIX A.  Farm E x p e n d i t u r e  Survey  Questionnaire,  B.  C r o s s - S e c t i o n a l Data  C.  Time-Series  D.  R e g r e s s i o n R e s u l t s u s i n g Cobb-Douglas and T r a n s l o g F u n c t i o n a l F o r m s : Almon Lag Price Predictions *  232  E.  Estimated  246  F.  Price  by S o i l  Zone  Data  ...  184 206 228  Parameters:  Predictions:  1981  ARIMA M o d e l s  ARIMA M o d e l s  253  vi L I S T OF  TABLES  2.1  C a n a d i a n Farm C a s h R e c e i p t s  2.2  C a n a d i a n E x p o r t s and I m p o r t s  2.3  Value  2.4  Canadian T a r i f f  4.1  E s t i m a t e d C o e f f i c i e n t s ARIMA(2,1,0)  of  Cattle  and C a l v e s  and D r e s s e d Beef Live of  of  and V e a l  of  Live  Animals  Structure  A n i m a l s and Meat  Calves, FES  for D i f f e r e n t  Products  Cows and H e i f e r s ,  D e f i n i t i o n of V a r i a b l e s  (Translog)  4.4  D e f i n i t i o n of V a r i a b l e s  (Time-Series  4.5  Testing for  Profit  Function  Categories  Calgary  4.3  Share  17 18  Data  Structure  15  20  Model,  Summary of  on t h e  of  Products  4.2  5.1  Sale  C a n a d i a n E x p o r t s and I m p o r t s  A n i m a l s and Meat  Steers,  from t h e  97 101  with Linear  107 Data)  109  Restrictions  Equations  117  Regression Coefficients-Translog  126  5.2  G o o d n e s s of  Fit  5.3  Testing for  Structure  5.4 5.5  H e s s i a n C o e f f i c i e n t s and E i g e n v a l u e s E i g e n v a l u e s f o r H e s s i a n M a t r i x at each Observation  132  5.6  Returns  136  5.7  Elasticities  5.8  Summary of Price  Statistics  130  133  to Scale of  Choice  Cross Price  (Translog)  138  and Own  Elasticities  141  5.9  Summary C l a s s i f i c a t i o n of  5.10  C l a s s i f i c a t i o n of  5.11  129  I n p u t Use  C l a s s i f i c a t i o n of  O u t p u t Use  Farm I n p u t s  Outputs with respect Inputs with respect  144 to to  147 148  vi i 5.12  Regression C o e f f i c i e n t s , Profit  Quadratic  Function of  153  5.13  Elasticities  Choice  5.14  Summary of Own E l a s t i c i t i e s  5.15  Total Elasticities  5.16  Summary of  D.1  Estimated Price  Cattle  of  (Quadratic) of  Cattle  Supply  156  Supply  158  Supply  ..  Elasticities  Prediction  Equations  164 using a  P o l y n o m i a l D i s t r i b u t e d Lag  234  D.2  Example of  D.3 D.4  R e g r e s s i o n R e s u l t s : T r a n s l o g P r i c e Index O u t p u t S u p p l y and C r o s s P r i c e Elasticities H o l d i n g T o t a l O u t p u t C o n s t a n t , Means of t h e Exogeneous V a r i a b l e s J o i n t E s t i m a t i o n : N o r m a l i z e d Cobb-Douglas P r o f i t  D.5 D.6  Predicted  F u n c t i o n and Net  161  Prices,  Steer  Equation  ......  I n p u t Demand E q u a t i o n s  235 239 239 241  Own P r i c e E l a s t i c i t i e s , C r o s s P r i c e E l a s t i c i t i e s , and E l a s t i c i t i e s W i t h R e s p e c t To t h e Fixed Factor  242  D.7  Total  242  D.8  Estimated  D. 9  Price E l a s t i c i t i e s , Cross Price Elasticities T r a n s l o g P r o f i t F u n c t i o n , Means of E x o g e n e o u s V a r i a b l e s 1981, Almon Lag P r i c e E x p e c t a t i o n s  245  E. 1  Estimated  248  E.2  Plots  Supply  Elasticities:  Parameters  Almon L a g P r i c e  the  of  O u t p u t Component  Translog Profit  Expectations  Parameters:  ARIMA(2,1,0)  the A u t o c o r r e l a t i o n F u n c t i o n  Residuals  Function,  of  244  249  viii L I S T OF FIGURES  2.1  Choice Steer  Calgary  Prices  and Omaha  in Canadian  2.2  A g g r e g a t e Demand F a c i n g  2.3  Inventories  of Beef  Inventories  o f Cows and H e i f e r s  2.4  Cattle  Producers  Farms,  Canada  Western  and E a s t e r n  and Female  Funds  21  Canadian  23  Cows and H e i f e r s  2.5  Steer  2.6  Female S l a u g h t e r a s a P e r c e n t a g e S l a u g h t e r , Canada  2.7  Flow  3.1  Dynamic  4.1  P l o t of A u t o c o r r e l a t i o n and P a r t i a l A u t o c o r r e l a t i o n Functions, Steer P r i c e s ,  4.2  P l o t of A u t o c o r r e l a t i o n and P a r t i a l Functions, First Differeneced  D i a g r a m of C a t t l e  Steer  Behavior  Prices,  Cattle  Supply  5.1  Supply  Function  27  Canada  Production  of a Cow-Calf  Calgary  4.3  25  on F a r m s ,  Canada  Slaughter,  on  o f f Farms  28  of  Steer  29  Decisions  32  Producer  47 Calgary  . . . 94  Autocorrelation 96 103  Cross-Sectional  Versus Time-Series  156  ix ACKNOWLEDGEMENTS  I  would  Barichello, their  like  of  study.  individuals. John  Graham,  constructive  criticisms  Tim  grateful  departments providing  and B i l l  their  of an  I  from would  Hazledine,  Lymer,  and  Rick  Schworm over  for the  assistance,  this  discussions  with  like  to  Cameron  Economics  members  and  excellent  Erwin  Klein,  Ray  and  Ralph  for  their  Bollman  for  data. students  Agricultural  environment  thank  Short  in o b t a i n i n g the  the  to  Kurt  and c o o p e r a t i o n and  comments and a s s i s t a n c e am  to  encouragements  benefited  Specifically,  Rick  I  and  Without  also  Lattimore,  his  appreciation  would not have been c o m p l e t e d .  This dissertation  Diewert,  my  John C r a g g ,  suggestions,  this  dissertation  other  express  Chuck B l a c k o r b y ,  comments,  course  to  in  in  Economics which  to  the for study  economics. Finally,  I  would l i k e  me t o c o n t i n u e my e d u c a t i o n and of  to  thank  and my w i f e ,  c o n t i n u e d s u p p o r t d u r i n g many, graduate  studies.  my p a r e n t s  for  f o r her  love  sometimes t u r b u l e n t ,  years  This dissertation  Gloria,  encouraging  is  dedicated to  her.  1 1.  A number of and  INTRODUCTION  economic s t u d i e s  characteristics  of  the Canadian cow-calf  decision-making behavior Tryfos 1978,  1974, Pugh  need f o r  economists  this  characteristics  gradually  Nelson  and  of  1)  price  investment  d e c i s i o n s and  animal the  is  heifers more  input  (i.e.,  be r e t a i n e d  animals:  i n the  short  over  a  Three  into  the  i n the  of  lower  brought  to  increase  market).  is  negative  and  put in  period  1971,  and  forward the  (i.e.,  changes 2)  requires  the  that  output);  reproduction  cows  to  in beef  herd  and  as and  produce  and 3) (i.e.,  reproduction process their  to  cattle  producers  initiate  current  in the  are  cattle  output  of  lag  there  p r o d u c t i o n p r o c e s s as w e l l  existence  animals  the  structural  adjustment  inventories);  of c a t t l e  to  by  that  1969, Y v e r  will  characteristics  when p r o d u c e r s d e c i d e  all  suggests  breeding herd in order  implies  time  long  responses  biological  a  is  reasons are  supply  cattle  the  which  run  1966, J a r v i s  additional  this  of  Second,  and e m p i r i c a l ,  expectations  b o t h an  output  parameters.  expectations  changing  first  The  t h e c o n s e q u e n c e s of  run  the p r i c e  others).  determine  1978).  short  and M a c A u l a y  to  1964, R e u t l i n g e r  explain negative  generated  1968,  of  positive  Spreen  and  the  knowledge  other  supply  is  (Kerr  1  Martin,  1983,  and  have  order  becomes  and  industry:  to  both t h e o r e t i c a l  elasticity  (Marshall  Canada  structure  industry  producers  1976, H a a c k ,  industry  in  in p o l i c y  evidence, the  cattle  1978, A g r i c u l t u r e in  changes  of  Kulshreshtha  interest  have a n a l y z e d t h e  the the  between  when  new  2  Existing  studies  however,  have  m o d e l l i n g and p r e d i c t i n g t h e d y n a m i c and i n v e s t m e n t in  behavior  describing  these  have p r o b a b l y had realistic the  of  problems,  more  industry  In  previous  have still  short-run  supply  exists  (Jarvis  existence  of  relation  importance not  negative of  explicitly  theoretical price factor 2)  generating  Empirical  investment  studies  are  t h e model  of  It  good  static  in order  consistently  the dynamic  cattle the  producers.  econometric  of  beef  in  is  This will  allow  and  the  the  study  that  causal  short  run.  industry  are  simultaneously  3)  Most  structure  empirical  appended  elements  into  required  to  model  behavior  more  to the  improved s p e c i f i c a t i o n  presumably  do  their  major  are  good.  the  to  in  this  animals  analysis  a  p r o d u c e r s but  cow-calf  dynamic  of  demonstrate  the  lag  a  These  response a l l u d e  be shown  output  "and  Theoretical  expectations  model  cattle  cattle".  cattle  of  (1978)  the  1)  and  any  specification  r e s p o n s e and i n v e s t m e n t  equations  for  results,  in  introduce  Intertemporal  than  supply responses  an  analysis.  beef  which  of  w i t h some f o r m o f to  meaningful  the  that  and  workers  producers are  to  fact  "Research  factors.  of  will  cattle  negative  response (1961),  slaughter  run s u p p l y  in  Knight  studies  1971)  account  attempts  c o m p l i c a t e d by t h e an  Yver  analysis.  expectations  for  expectations  take  for  the p r o p e r  to three  short  price  that  contradictory  about  1969,  run s u p p l y  deriving  empirical  p r o b l e m s can be a t t r i b u t e d studies  stated  problems  a d d i t i o n , N e l s o n and S p r e e n  generated  controversy  some  producers.  elasticities  commodities".  have a r g u e d t h a t  short  difficulty  supply-price  other  cattle  had  of of  accurate  3 results. The 1968,  development  and McFadden  of  1978)  duality offers  theory  the  which  to  supply  r e s p o n s e s and i n v e s t m e n t duality  regularity  theory  conditions  .maximization,  the  with  the  r e l a t i o n s h i p between t h i s  profit  function  function allows either  t o be d e r i v e d  other.  therefore,  Theoretically,  the  cow-calf  estimating or  the  industry  can  transformation  indirectly  by  the  (the  profit  profit  to a  farm  function." A  dual  transformation  knowledge of  be r e c o v e r e d e i t h e r  estimating  of  technological  function  certain  available  from t h e  the  under  and a  run  producers.  assumption  c h a r a c t e r i z e d by a p r o f i t  with  short  cattle  that  production p o s s i b i l i t i e s  can be c o m p l e t e l y  of  of  demonstrates  and  3  tools  m o d e l l i n g dynamic  behavior  2  1953, Gorman  e c o n o m i s t new  a p p r o a c h the problem of  Generally,  (Shepard  the  parameters directly  primal  by  approach)  function  (the  dual  approach). There are the  transformation  vector the and this  of  farm,  inputs  unlikely case,  techniques,  will  several  in  to  the  be  be m u l t i c o l l i n e a r ,  regression otherwise  coefficients would  be  in  used,  c a u s i n g the to the  error  standard  be l a r g e r absence  (or of  model  would  In be  econometric  w o u l d be  likely  the  c h o s e n by  structure.  regression  is  If  econometric  variables, it  estimating  1976).  and more c o m p l i c a t e d  instrumental are  the  squares  to  f u n c t i o n are  e n d o g e n o u s i n an  least  data  (Woodland  transformation  and a l t e r n a t i v e  such as  5  independent of  ordinary  time-series  disadvantages  function d i r e c t l y  such i n p u t s are  inappropriate  If  however,  that  required. the  errors  smaller)  inputs of  the  than  they  multicollinearity.  4 Finally,  if  the  farm m a x i m i z e s p r o f i t s ,  used in e s t i m a t i n g modelled  the  transformation  one  is  willing  price-taking behavior,  order  equations conditions  involved  in  very  function By  in  function.  (e.g.,  However,  unless  it  is  functional  many of  the  of  the  (optimal) necessity  of  solving  Certain  function  to  "well-behaved" Besides conditions,  it  circumventing  theory  derived  that  are  two  other  demand and o u t p u t  w i t h farm p r o f i t  output p r i c e s .  need  in a p p l i e d economics  input  differentiating  satisfies  the  the p r o f i t B e c a u s e of  forced  the  transformation  parameters  can  with be  thereby  the  direct  overcome.  avoids  an the  in a maximizing on  the  the  profit  c o n d i t i o n s of  (Diewert to  of  m a x i m i z a t i o n and  solve  principal  first  order  advantages  (Diewert  1974).  be  of  First,  supply equations  in d e r i v i n g  a  1973).  function with respect ease  to  approach s p e c i f i e s  m a x i m i z a t i o n can  the  the  is  imposed  function  to  one  conditions  are  first  difficulty  profit  and  transformation  there  function  order  subject  associated  directly  first  the  the  the  dual  output  6  recover  the  restrictions  ensure  profits  forms f o r  a s s u m p t i o n s of  conditions,  to  b e c a u s e of  problems  transformation  function  problem.  consistent  the  maintained  profit  solutions  C.E.S.).  using a dual approach to  m a x i m i z i n g and  demand and  order c o n d i t i o n s ,  C o b b - D o u g l a s or  p r i c e - t a k i n g market  the  as  factor  t h e m a x i m i z a t i o n of  restrictive  estimation  duality  not  function  then e m p i r i c a l  solving f i r s t  technology,  Under  is  t o assume b o t h p r o f i t  can be d e r i v e d  transformation  posit  behavior  directly.  If  supply  this  that  are  obtained  by  to  input  input  and  demand  5 and  output  supply  and c o n s i s t e n t the  equations,  r e l a t i o n s h i p between  econometric model.  easily  be  and  supply  theory  the  from t h e  allows  theoretical  Second, comparative  generated  and o u t p u t  duality  static  estimated derived  recent  production  have e n h a n c e d and e x t e n d e d t h e  in  empirical  functional  forms  Jorgensen,  and L a u  previous  test  restrictive to the  work.  The  (FFF)  by  (1973)  allowed  FFF  for  technology.  This  of  outputs  generalization  production  Finally,  and  (Lau  duality inputs  takes  account  short  some  factors  optimizing  with  existence  respect  of of  or  FFF  on  use of  duality  of  flexible,  away  fact, of  need t o  certain  the  the  can more  approximation  the  priori  the  or  to  allow to  produce  In  a  1973).  associate  8  certain addition,  statistically.  restrictive  profit  notion that  (i.e.,  quantity  test  researcher  and  outputs.  on  underlying  and F F F  c a n be t e s t e d  variable  from  FFF  1973, and D i e w e r t  the M a r s h a l l i a n  to  cost  can be u s e d t o  inputs  variable  are  of  restrictions  theory  of  the  possibilities  functions  In  enables  1972, H a l l  eliminates  the development  run,  demand  and C h r i s t e n s e n ,  forms.  restrictions  e x p e n s e s w i t h t h e p r o d u c t i o n of joint  can  f u n c t i o n and do n o t a  Moreover,  7  these  outputs  the  model f i r m s w h i c h employ a number number  results  generalizations  for  The e x t e n s i o n of  multiple  and  theory  (1971)  separability,  elasticities.  statistically  the  p r o v i d e a second order  homotheticity,  substitution  model  input  introduction  functional  statistically  forms.  to  Diewert  underlying transformation  impose  for  contributions  more r e s t r i c t i v e  be u s e d t o  direct  equations.  A number of  theory  a  the  in  the  farm  is  e m p l o y e d of  each  6 variable farm  input)  may  whereas o t h e r  not  be  employed of  these  procedure,  the  in fixed  factors)  shadow  respect  to  There are dual profit  and o u t p u t  If  prices  can  Additionally, profit  allows these  be many  be  noted  i n d e p e n d e n t of it  is  across  likely  error  types  of  less  linear  that  in  a  indicate  FFF  structure  coefficients  be  with  a  in  their  the  of  serious  error  system  of  the  input  used to  from t h e d e r i v e d  be  in  the  and  this  estimating independent  or p r i c e  problem.  ratios,  Finally,  expect p r i c e s  it  to  be  equation,  restrictions  imposed  correlated  across  and o u t p u t  used  factors.  approximate  equations.  a s y s t e m s method w h i c h a c c o u n t s should  of  coefficients.  prices  is  form  econometric  i n an e c o n o m e t r i c  structure  demand  reduced  fixed  techniques  symmetry  the  functions  any  because  structure of  as  the  of  input  coefficients  a l t h o u g h one m i g h t  because  to using  are  the  that are  However,  error  that  can  function  complicated  regression  be  of  estimate  linear  that  the  equations,  equations would  to  can  functions  quantities  are monotonic t r a n s f o r m s  multicollinearity should  used  coefficients.  variables  this  factor  from t h e d e r i v e d  These  exogenous,  use of  quantities  The c o e f f i c i e n t s  and t h e q u a n t i t y  f u n c t i o n are  the  FFF.  and i n p u t  prices  are  techniques  the  with  supply equations.  and i n p u t  fixed profit  the  Using  econometric advantages  c a n be e s t i m a t e d  equations with output output  to  1968).  each  variable  (i.e.,  factor.  combined  function  of  the  a number of  approach  fixed  (Gorman  price  by d i f f e r e n t i a t i n g fixed  are  e q u i l i b r i u m with respect  derived  the  factors  when  i n p u t demand and  This  for  this  estimating output  the  supply  7 equations.  9  OBJECTIVES  1.1  The profit  aim  of  this  maximizing  determine supply  and  model  to  usinga  of  processing); of  generating  the  determine beef  technology  iii)  s u p p l y and  of  the  input  exogenous  variables;  statistics  of  run e l a s t i c i t y of  1.2  output of  substitutability  of  cattle as  producers.  follows:  model  iv)  the  as  a  result  to  generate  other  production  expectations  s u p p l y and i n p u t  and about  of  the  a  over  the  comparative  o p t i m a l v a l u e s of  a  in  demand e q u a t i o n s  function  of  and the  process  parameters  flexibility  o u t p u t s and of  industry  expectations  to undertake  the  to  theoretically  price  in  i)  (ignoring  feedlot  transformation  and i n p u t  output  run  s u p p l y and i n p u t  changes  v)  short  producers'  recover  region;  demand  t h e dynamic  supply adjustment  cattle  output  relevant  to  Canadian cow-calf  s u c h as  the  to  the  then  are  the  theoretical  and  of  producers'  empirically  farm  demonstrate  t i m e p a t h of  analysis  of  to  cattle  uniquely define  static  behavior  industry,  u s i n g the  economically  cow-calf  intertemporal  ii)  prices;  to develop a  empirically  structure  beef  is  objectives  time,  the  importance  that  the  the  discrete  sectors  future  a  r e s p o n s e and i n v e s t m e n t  characterize  to  of  estimate  Specifically,  meat  research  changes number  output in  of  summary  i n c l u d i n g the demand and  the  short  measures  inputs.  EXISTING LITERATURE The  present  study  differs  from p r e v i o u s  studies  of  the  8 cow-calf  industry  (Jarvis  1969 and Y v e r  of  cattle  v a l u e of  in  four  ways.  1971)  have d e v e l o p e d t h e o r e t i c a l  birth  The e n d o g e n o u s v a r i a b l e s , slaughter  age,  parameters.  that  are  the  the  domestic to  calf  demand. provide  industry.  complicated  they  the  models do n o t  the  average  theory  functions  duality more  theory  easily,  estimated  than  before.  equations  are  derived  from  fully  equations of  equations  are  weight,  and e x p o r t  and used  model of  the  cow-  one  to  manage  t e c h n o l o g y of and  consistent the  the  is  detail  The model i s  not  duality  allows  p r o d u c t i o n can be m o d e l l e d i n g r e a t e r precision  of  the  exogenous  slaughter  a r i g o r o u s and c o n s i s t e n t  Because  the  optimal  functions  in each c a t e g o r y ,  contrast,  and  include  as  models  lifetime.  do  estimated  to determine  slaughtered In  f u n c t i o n s of  studies  discounted  remaining  empirical  Rather,  present  input q u a n t i t i e s as  results:  specified  animals  its  endogenous v a r i a b l e s  exogenous v a r i a b l e s .  number of  for  optimal  the  theoretical  arbitrarily  or  specified  However,  represent  here  previous  p r o d u c t i o n which maximize the net an a n i m a l a t  reflect  First,  cattle  with  more  in that  profit  the  maximizing  farm m o d e l . Second, accurate is  Reutlinger  results  necessary  equations assumed  equations costs  when e s t i m a t i n g  to  estimate  to  (Tryfos  or be  have  to  of  These  that  to achieve  be  more  production models,  s u p p l y and c a t t l e  arbitrarily  functions 1974).  cattle  Previous  inventories  1967)  argued  output  simultaneously. cattle  Thompson  (1966)  studies exogenous  inventory  have  studies  either  (Langemeir  specified  expected beef  it  prices  generally  and  inventory and  feed allow  9 inventories  to  adjustment cattle  process  inventories  The  Elam  demonstrate  is  ( O s p i n a and Shumway  1978).  of  price  that  price  However,  the  the  short  the  this  study,  in  the  cattle  literature  little  the  a third will  innovation be  (Marshall  been  done  to  importance  of  adjustment  adopted  of  this  introduced  The c o n s e q u e n c e s of r u n r e s p o n s e of  has  theoretical  t i m e p a t h of  expectations  model.  dynamic  for  Therefore,  theoretical  partial  In  expectations  i n a r i g o r o u s manner  producers.  using a  determined endogenously.  1975).  expectations  cattle  level  are  an  has been w e l l documented i n  and  price  optimal  importance  industry 1964  approach  price  cattle  study  into  the  expectations  producers  by  will  for be  determined. Finally, inventory, the  existing  investment,  studies or  demands by p r o d u c e r s  Wilson  1972,  output  supply  derived  and  slaughter for  Ospina  demand  information  structural  1.3  potentially  THESIS  more u s e f u l  of  characteristics  described importance  inputs  n.d.).  will  estimation  parameters to p o l i c y  of  ignored  (Kulshreshtha  inventory  the  estimating  this  In  this  study  equations, be  and  and  estimated  will  provide  industry  making  makers.  OUTLINE  The r e m a i n d e r The  of  on  e q u a t i o n s b u t have  equations  The r e s u l t s  it  focused  Shumway  cattle  simultaneously. on  factor and  equations,  input  have  in  Chapter of  cattle  this of  thesis the  Two.  is  organized  Canadian This  cattle  discussion  production within  as  follows.  industry  are  indicates  the  Canadian  agriculture  10  and t h e free  implications  for  international  Canadian c a t t l e  trade  This chapter  includes  model c a t t l e  production. .  In  Three,  of  a  Chapter cow-calf  simplifying focus  on  on  dynamic  A comparative elasticity  static  model a r e  Data  the  required  input  include  to  demand e q u a t i o n s  the  quantity  of  to  the model  multi-input  different  inputs  u s e d on f a r m s and  inventories  data,  in  for  of  order  empirical  cattle to  the  be  and  to  is  production  postulated. a  number  of  multi-input  output  prices,  the  Four.  produced  input  by of  prices,  The t r a n s f o r m a t i o n appropriate  in t h i s  and  the q u a n t i t y  associated  obtain  supply  in Chapter  outputs  on f a r m s .  analysis  output  reported  different  and a s s o c i a t e d  required  order  expectations  multi-output,  are  farms  the  of  p r o d u c t i o n and  model c a n  estimate  cow-calf  and t h e  model  discussed.  The d a t a derived  in  price  undertaken  to  a number  Subsequently,  is  for  model  of  a multi-output,  measurements  attempts  Initially  cattle  implications  an e c o n o m e t r i c  products.  maximizing  imposed on t h e  analysis  relatively  theoretical  developed.  of  of  and meat  profit  behavior.  for  from w h i c h  past  elements  supply  extended to account technology  is  theoretical  run  animals  a theoretical  assumptions are  the  short  a r e v i e w of  producer  the  determine  i n beef  prices  of  variables  dissertation,  are  also  a discussion  of  the  described. Additionally, issues  involved  function specified  model.  Chapter  Four  in e s t i m a t i n g Functional  and t h e  includes the  forms  estimating  coefficients  for  the  equations  profit  are  of  the  profit  function  derived.  are  Finally,  11  the  econometric  methodology used t o  equations  is  detailed  stochastic  framework  The r e s u l t s Chapter  Five.  measurements in Chapter  are  of  of the  In  as the  addition,  Six.  system  assumptions  about  of the  and t h e  analyses a  are  number  hypotheses  reported of  to  be  in  elasticity postulated  tested.  The main c o n c l u s i o n s Chapter  the  the  equations.  regression  presented  Three are  are  estimate  of  the  study  are  summarized  in  1 2 FOOTNOTES TO CHAPTER ONE  1  A cattle  producer  is  d e f i n e d as a farmer  cow b r e e d i n g h e r d and p r o d u c e s c a l v e s producer heavier  may  also  animals  at  available Chapter 2  to  the  The i n v e s t m e n t  These  a  later cattle  for  calves  on  date.  The  producer  owns  sale. the  a  The  cattle  farm and  economic  will  beef  sell  choices  be d i s c u s s e d  in  Two.  e x p a n s i o n or 3  retain  who  behavior  that  r e d u c t i o n of  regularity  is  the  of  interest  here  is  the  breeding herd.  conditions  will  be d i s c u s s e d i n  Chapter  Three. 4  Diewert rests  (1974)  5  6  set  its  in R  these  functions.  These  functional impose  elasticities can  Diewert if  essence  duality  c a n be c h a r a c t e r i z e d as  n  forms  apply  are  of  substitution two  equally  restrictive  homotheticity,  distinguish  theory  "every  the  closed  intersection  parameters  of  make t h e v a l u e s  of  equal  first  to  the  its  the  on t h e types  and  of  the  approximation,  or  that  constant  function.  form i s  order  where  the  to  derivatives  derivatives  point;  the  flexible  form c a n be c h o s e n  second order some  sense  of  approximation: i)  and s e c o n d  f u n c t i o n being approximated at series  in  estimating  functional  first  to estimation  separability,  a p p r o x i m a t i o n , where a f u n c t i o n a l  the  Taylor  of  t h e o r e m by M i n k o w s k i :  disadvantages  profit  One  the  supporting half spaces".  Some of  they  7  that  on a m a t h e m a t i c a l  convex of  states  and  of  ii)  function  the the is  13 approximated with a Taylor point.  See  300 f o r 8  Primont,  expansion  and R u s s e l l  the d i s t i n c t i o n  between  the  Given  the m u l t i - p r o d u c t  nature  of  this  extension  calf at 9  Blackorby,  series  It  will  industry.  two  (1963)  be  e c o n o m i c s has applied  noted gained  duality  markets  for  Caves  and Swanson  (1981), and  Woodland  (1975),  all  sectoral  Fuss,  of  Vlastium  manufacturing). industry-level  (1977).  studies  (i.e., This data  (1980),  (1982),  Woodland  these  data  use of  (1977),  study  series  is  duality For  and  will  attempt  in  applied  examples  of  non-agricultural  (1979), Caves,  Lopez  Binswanger Christensen,  (1980),  McKay,  S i d h u and B a a n a n t e  (1981),  One  common  t h e use of  total  cow-  functions.  and Waverman  Fuss  agriculture,  initial  popularity.  and C h r i s t e n s e n  Lawrence,  almost  wide  the  pp.290-  definitions.  an  in both a g r i c u l t u r a l  see B e r n d t ,  (1974),  that  some  i n m o d e l l i n g the  modelling multi-product production should  (1978)  Canadian  prove v a l u a b l e  See Mundlak  around  feature  highly  agriculture use a  to estimate  more the  of  aggregated or  total  disaggregated  model.  14 2.  2.1  THE CANADIAN CATTLE INDUSTRY  INTRODUCTION The C a n a d i a n c a t t l e  number  of  are  d i s c u s s e d in  Section  (2.2)  are  outlined  receipts  of  industry  production  years  this  the  in  and  industry  The  when  Section  cow-calf  cattle  cattle  chapter.  producers  is  an  in Canada.  between  sale  1970 t o  period represent  cash r e c e i p t s ,  this  live  economic  determining  (2.3). past  Finally, attempts  to  sector  of  producers.  OF THE CATTLE INDUSTRY  f o r Canada from t h e  selected  in of  large  i n p r o d u c t i o n , and  an e x a m i n a t i o n of  economic b e h a v i o r  agricultural  of  cow-calf  c o n s i s t s of  cattle  trends  trade  to  SOME CHARACTERISTICS The  c h a r a c t e r i z e d by a  characteristics  Section  strategy  (2.4)  model t h e  for  international  available  production  2.2  for  T h e s e and o t h e r  options  is  small producers, c y c l i c a l  an open market beef.  industry  from  second only  of  important Table  2.1  cattle  1982.  lists and  Cattle  18.4% t o 3 4 . 9 %  to the  grains  farm  cash  calves  for  and c a l f of  (wheat,  sales  total  farm  barley,  etc.)  industry. In  1982, t h e  accounted for receipts  Another cattle  30.5%,  for  respectively.  receipts 12.6%,  from t h e and  Alberta,  sale  17.6%  of of  cattle  and  total  farm  Saskatchewan,  and  calves cash  Manitoba  1  indication  industry  is  and meat p r o d u c t s has  of  that  the  importance  international  of  trade  increased s i g n i f i c a n t l y  the  Canadian  i n beef in  recent  animals years.  15 TABLE 2.1 Canadian Farm Cash Receipts from the Sale of Cattle and Calves Year  1970  1975  Receipts from the Sale of Cattle and Calves ($ m i l l i o n )  1,469.6  1,873.9  Total Farm CAsh Receipts ($ m i l l i o n )  4,208.4  34.9  Receipts from the Sale of Cattle and Calves as a Percentage of Total Receipts  Source:  1980  1981  1982  3,665.0  3,537.0  3,586.0  10,142.4  15,837.0  18,835.0  18,840.0  18.4  23.0  18.8  19.0  S t a t i s t i c s Canada, Farm Cash Receipts, Cat. No. 21-001, Ottawa, Queen's P r i n t e r , annual.  16 Table  2.2  lists  d r e s s e d beef between this  the  and v e a l  1970 t o  period,  and t h a t  numbers of  1982.  This table  e x p o r t s have  rate  than  imports.  Canada  was a n e t  importer  in  ' 7 0 ' s and e a r l y this  trade 2.3  category  lists,  live  this  period,  the  value  rate  value  than  of  Canada e x p o r t s imports  of  i m p o r t s of  this  products  value  of  i n c r e a s e d at figures  beef  has  products  is  Canada's  accounting  and c a l v e s  Canada's  of  Table  exports  Throughout imports  a significantly  greater  represent low  the  quality Finally,  2  exceeded  recent  fact  that  beef  and  in  1977-78  exports  years,  but  the v a l u e  i n c r e a s e d t o more t h a n t w i c e  for  largest  and 85% o f  success  in  trading partners. import  3  Except  restrictions  trading  approximately total  for were  partner  90% of  total  d r e s s e d beef  international  and meat p r o d u c t s depends on low  or  value  in  e x p o r t s exceeded  products In  the  exporter  demonstrated  from the U . S .  meat  exports  of  in  international  products.  animal  1975  of the  imports.  The U . S .  cattle  of  and meat  live  but  net  animals  has c h a n g e d s i g n i f i c a n t l y .  meat  is  and  and v e a l  the  quantities  quality  value  industry  animals  significantly  1970  The s i g n i f i c a n c e  These  high  a  in  d r e s s e d beef  live  dollars,  imports  large  of  i n c r e a s i n g at  years  throughout  of  of  exports.  that  Canada c h a n g e d t o a  in m i l l i o n s  of  the  of  as w e l l .  imports  the  and pounds of selected  exporter  Furthermore,  '80's,  and  but  been  to the Canadian c a t t l e  which  indicates  has been a net  greater  late  and c a l v e s  e x p o r t e d and i m p o r t e d f o r  Canada  these  cattle  trade  trade  and  in  barriers  beef  beef  exports  of  veal.  live  animals  with i t s  a few p e r i o d s where imposed,  in  high  major tariffs  producers  have  17 TABLE  2.2  C a n a d i a n E x p o r t s and I m p o r t s o f L i v e and D r e s s e d Beef and V e a l Year  1970  1975  C a t t l e and Calves ( t h o u s a n d Head)  247.0  223.6  D r e s s e d Beef and V e a l (million lbs.)  119.1  45.1  53.3  157.4  1980  Animals  1981  1982  EXPORTS  357.8  353.0 .  504.9  114.3  174.7  183.5  92.6  52.7  171.1  83.9  139.8  129.7  133.8  140.6  IMPORTS C a t t l e and Calves ( t h o u s a n d head) D r e s s e d Beef and V e a l (million lbs.)  Sources:  S t a t i s t i c s C a n a d a , L i v e s t o c k and A n i m a l P r o d u c t s Statistics, Cat. No. 23-203, Ottawa, Queen's Printer, annual. Agriculture Canada, Livestock Market Ottawa, Queen's P r i n t e r , annual.  Review,  18 TABLE 2.3 Value of Canadian Exports and Imports of Live Animals and Meat Products Year  .  1977  1978  1979  1980  1981  1982  EXPORTS ($ million) Live Animals  135. 0  196. 0  224. 0  229. 0  201 . 0  299.0  Meat Products  222. 0  309. 0  428. 0  514. 0  620. 0  776.0  IMPORTS ($ million) Live Animals  30. 0  57. 0  48. 0  88. 0  170. 0  105.0  Meat Products  295. 0  331 . 0  332. 0  287. 0  301 . 0  297.0  Source:  S t a t i s t i c s Canada, Selected Agriculture S t a t i s t i c s Canada and the Provinces, Ottawa, Queen's Printer, 1983.  19 enjoyed  relatively  an example o f  the  Canada and i t s of  animals  different  maj'or  tariff  i n beef  tariff  trading  meat  categories are  trade  1982  and  countries U.S.  free  structure  partners  products.  of  price  per  live  animals  $.02  p e r pound  pound.  for  and d r e s s e d b e e f  market  and  beef  Because  of  the v i r t u a l  the  the  two  Figure  choice  Calgary  and Omaha, f o r  supply  or  demand  Canadian p r i c e s  the  will  and  if  cattle  2.1  per  pound. 10%  of  categories  tariff  transportation costs,  which  relationship between  is  period  of  $.01  and  for  beef  2.2,  to  price  DD'  1982.  between  the  related  to  relationship funds,  in in  i n Canada r e s u l t  in  than U.S.  cattle  cattle is  U.S.  If.changes  decreasing  price  costs  this  higher  in U.S.  t h a t U.S.  between  cattle  American  the  Canadian  1977 t o  Canadian import  variations  beef  entering  Canadian  would be  greater  include a small  Figure  North  closely  in  Canada and t h e U . S . In  total  illustrates  prices  the Canadian beef  simple diagram.*  are  consequently  t o Canada  of  the  i n beef  prices  result  One would e x p e c t  The  trade  steer  prices.  transaction  $.02  for  different  s i z e and p r o x i m i t y of  conditions  arbitrage  plus  tariffs  from z e r o to  10% of  becoming s i g n i f i c a n t l y  Canadian market  price  categories  for  important  and v e a l ,  free  Canadian beef  prices.  with quarterly  prices,  for  respectively.  two c o u n t r i e s , U.S.  presented  and meat and  Canada p r o d u c e s a p p r o x i m a t e l y output.  2.4,  import  z e r o or a p p r o x i m a t e l y  But  Table  different  on C a n a d i a n p r o d u c t s v a r i e s  the  beef  for  In  is  Canadian  livestock  either  products.  than  beef  imported the  markets  U.S. plus  tariff. and  shipments  c a n be r e p r e s e n t e d represents  the  the.  in a  Canadian  20 TABLE  2.4  Canadian T a r i f f S t r u c t u r e for D i f f e r e n t C a t e g o r i e s of A n i m a l s and Meat P r o d u c t s British  Commodity  Australia New Z e a l a n d  M.F.N.* U.S.  U . S . T a r i f f on C a n d i a n Goods  Breeding Animals  Free  Free  Free  Free  Live Cattle (excludes d a i r y cows)  Free  Free  $.01/lb  $.01/Ib  Beef and V e a l F r e s h and Frozen  $.02/lb  $.02/lb  $.02/lb  $.02/lb  P r i m e or Prepared Retail  $.02/lb  $.02/lb  $.02/lb  4.0%  Choice for  Beef  Prepared  and P r e s e r v e d  Free  Free  $.01/lb  $.02 o r 10.0%**  Beef  Canned  15.0%  Free  15.0%  3.0%  Beef Salted in Barrels  Free  Free  Free  $.022 o r 10.0%***  Cattle  Free  Free  Free  Free  * ** ***  Hides  Most F a v o r i t e N a t i o n $ . 0 2 / l b when p r i c e i s $ . 3 0 / l b o r l e s s ; 10.0% when p r i c e i s over $ . 3 0 / l b . $ . 0 2 2 / l b when p r i c e i s $ . 3 0 / l b o r l e s s ; 1 0 . 0 % when p r i c e i s over $ . 3 0 / l b .  Source:  A g r i c u l t u r e Canada, L i v e s t o c k Market O t t a w a , Q u e e n ' s P r i n t e r , 1982.  Review,  21 FIGURE 2.1 Choice Steer Prices, in Canadian Funds, Calgary and Omaha  $/CWT 90.0  Omaha  85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0  Calgary 1977  Source:  1978  1979  1980  1981  1982  Agriculture Canada, Canadian Livestock and Meat Trade Report, Ottawa, Queen's Printer, annual.  22 domestic  demand  ceiling price the U.S. small  function  (P )  represents  1  plus  of  beef  to U.S. the  range  that  of  market  less  in which  beef  relative  to  the  domestic  range  demand.  Canadian  beef  relevant  P ' If  plus  to  becomes  U.S.  U.S.  beef  that  markets.  P  1  A  price  reduced to P .  P  demand c u r v e  First,  has  if  is  to  only variations  vary  P ,  is  then  E  the  domestic  indicate will  not  on  is the  affect  Canadian p r i c e s  rise  Canadian  s u p p l y below Oq would  relevant price  P  1  f a c i n g Canadian beef  three  prices  T h i s demand  t h e C a n a d i a n market the  curve  the  competitive  h o r i z o n t a l at  r e p r e s e n t e d a s ABCE i n F i g u r e  study.  hand,  demand  m a r k e t s and  to the U.S.  in Canadian beef  is  CE)  U.S.  number of  below  in U.S.  (segment  E  Consequently,  Canadian producers  diagram  fall  to  demand c u r v e  Canadian b e e f .  becomes  entering  1  This  prices  other  beef  reduction beef  relevant  for Canadian producers  , U.S.  being  the  the  the a  total  costs  relative  of  has  the  represent  E  change  Canadian  competitive  On t h e  in U.S.  Therefore,  ,  Canadian exports  result  for  E  demand f o r  prices.  above p r i c e  P  and P  size  the  If  plus a  transportation  market  in  represents  E  will  shape of  Canadian  drawn as h o r i z o n t a l a t assumption  the  import  products  (P )  P'  The l a r g e  producers.  demand c u r v e  demand  less  Canadian  for  beef  price  import d u t y .  price.  implications  the  floor  the Canadian p r i c e  f a c i n g Canadian c a t t l e within  of  The  to Canadian markets  the U.S.  U.S.  the U.S.  important  in  products.  price  costs  The e x p o r t  products  markets  beef  the  transportation  import d u t y .  price  for  and  prices  demand  curve  (segment  AB).  producers  is  2.2. important within  implications  a certain  for  output  this range  23 FIGURE  2.2  A g g r e g a t e Demand F a c i n g C a n a d i a n C a t t l e Producers  Price  Import  Ceiling  Quantity  24 in  the q u a n t i t y  of  beef  alter  the  output  s u p p l y have no e f f e c t  Canadian  price  s u p p l i e d by  beef  of  beef  prices  demand and s u p p l y a r e exogenously are  by  independent  Finally,  one  can  only  farm  industry  level.  This  known as Figure  over  the 2.3  Canada  for  cyclical  the  r e a c h e d a peak  in  again  in  representing feed  barley  ratio  is  precede  the  ratio the  reflects  biological  the  plans  estimated  cattle  since  determined functions  separately.  beef  prices  choice period  of  as  is  low in  steer  large  T h i s has  become  represented  inventory  1945):  Figure  2.3  is  inventories  the  but  changes  such p l a n s are  of  price prices  years.  in  prices  farmers  reflected  and  curve  the p r i c e  by s e v e r a l  when c o w - c a l f  a  a  they  1968,  Generally,  in  at  in  movements,  following  were  point  to  in  on f a r m s  peak was  prices  1950-82.  Canadian  is  inventories  previous  not  model.  cows and h e i f e r s  l a g between when  the  industry  cycle  Female  inventories  and  largely  production.  of  t u r n i n g p o i n t s of l a g of  in  which'Canadian  econometric  Included  of  at  exogenous a t  The b e e f  1950 (the  1975.  The r e s p o n s e  production  the  1950-82.  in  Second,  Canadian  the  in c a t t l e  reciprocal  the  be  1965, a r e l a t i v e  over  the  of  inventories  low p o i n t  peaked  feature  period  changes  demand and s u p p l y  but a l s o  cycle".  by t h e  are  will  can be assumed t o be exogenous  simplifies  time  "beef  but  treat  level  One d i s t i n c t i v e variations  prices  and may  such p r i c e s  the  not  market,  predetermined, at  prices.  the  producers  Otherwise,  on b e e f  equalized  functions  because  in Canada.  are  the U.S.  Canadian  in  make herd  size. A better  d e s c r i p t i o n of  the  beef  cycle  is  gained  from  Number o f Animals (,000)  Figure Inventories  of  Beef  Cows  and  2.3 Heifers  on  Farms,  Canada  Price  of  Steers  Price  of  Barley 50.0  6,600.0 6,200.0  _  5,800.0  _  5,400.0 5,000.0 4,600.0 4,200.0  _  3,800.0 3,400.0  _  3,000.0  _  2,600.0  _  2,200.0  _  1,800.0  _  1,400.0  _  Statistics Cat.  No.  Statistics Cat.  No.  Canada,  23-203,  Canada,  21-516,  Livestock  Ottawa,  Handbook  Part  1,  and A n i m a l  Queen's of  Product  Printer,  Agricultural  Ottawa,  Queen's  Statistics,  annual. Statistics,  Printer,  annual.  26 examining western 2.4 for  changes  changes  the p e r i o d  trends  in  variations 80  western  occur  in the  percent  of  are  herd in western To g a i n consider  than  (say  from  the  between  the  the d e c l i n e  farmers  reducing  for  in  their  significantly contractionary  in  the  in  fact in  beef  the  beef  less  than  industry  by t h e  slaughter  steer of  the  1975,  cycle,  herd  were  held  slaughter.  female  cows  ratio  of  the  can ratio  for  during  1975,  the  cycle,  slaughter  whereas after  and  cycle  f e m a l e s as a  female  with  slaughter. a  this  to the  coincides  along  slaughter  the  p e r i o d of  (culling  shows  more  breeding herd  1975  of  is  as  steer  in a large  and  female  that  during this  beef  1970  and  slaughter  herds  2.6  cycle,  steer  in the  after  breeding  beef  female a n i m a l s  retained  is  the  indicates  1975),  Figure  than  phase  the  Canadian  D u r i n g an e x p a n s i o n a r y phase  less  pronounced  changes  c a u s e s of  This  resulting  between  cyclical  breeding herd i s  Steer  the h e r d  slaughter.  example  regions  some more  in  Figure  two  This reflects  illustrates  and  be i d e n t i f i e d  1960-82.  the  1960-82.  slaughter  The p o s i t i o n of  the  inventory  Consequently,  slaughtering heifers)  period  into  1970 and  market  However,  the  are  beef  herds  Canada.  for  changes  to  slaughter.  female  steer  herd.  Canadian  which  the p e r i o d  cycle,  of  herd,  beef  5  2.5  p r o d u c e new a n i m a l s .  generally  beef  due p r i m a r i l y  female  eastern  inventories  western  Canada.  in the  Although there  some i n s i g h t  for  in  Consequently,  Figure  slaughter  back  inventories  female  eastern  Canada.  expanded  in  1950-1982. the  production  stable  female  Canada compared t o h e r d s  shows  that  in  is a  female  Figure  2.4  I n v e n t o r i e s o f Cows and H e i f e r s on Farms, Western and E a s t e r n Canada  Number of Animals (,000) 4,500.0 _ 4,000.0 _ 3,500.0 _ 3,000.0 _ 2,500.0 _ 2,00O.O_ 1,500.0 _  Western Canada  1,00 O.c?  1,200.0 1,000.0 800.0 600.0 400.0 200.0 1950  1960 Source:  1970  S t a t i s t i c s Canada, Livestock and Animal Product S t a t i s t i c s , Cat. No. 23-203, Ottawa, Queen's Printer, annual.  1980  Figure Steer  and  Female  2.5  Slaughter,  Canada  Number o f Animals (,000) 1,900.0  1,800.0 1,700.0  1,600.0  1,500.0  1,400.0 1,300.0  1,200.0  1,100.0 1,000.0  900.0  1960  Source:  1980  1970  S t a t i s t i c s Canada, L i v e s t o c k S t a t i s t i c s , Cat. No. 23-203, Printer, annual.  and A n i m a l P r o d u c t Ottawa, Queen's  Figure  Source:  2.6  S t a t i s t i c s Canada, L i v e s t o c k S t a t i s t i c s , Cat. No. 23-203, Printer, annual.  and A n i m a l P r o d u c t Ottawa, Queen's  30 slaughter  is  ratio  female  of  significantly to  steer  an e x p a n s i o n a r y p h a s e . indicates  greater  than  slaughter  of  Conversely,  a contractionary  Both  Figure  significant  2.5  or  describes  this  less ratio  slaughter.  than  one  A  indicates  of more  than  one  phase.  and  relationship  slaughter  a  steer  2.6  suggest  between  retention  of  the  female  r e l a t i o n s h i p as  that  beef  animals.  there  cycle  is  a  and  Marshall  the  (1964)  follows:  "When t h e p r i c e of c a t t l e i s high relative to other production possibilities t h e t e n d e n c y i s t o h o l d back cows and h e i f e r s f o r b r e e d i n g . Inventories are thus a u g u m e n t e d , m a r k e t i n g s r e d u c e d and p r i c e s s t r e n g t h e n e d . As inventory numbers build up and the p r o g e n y of i n c r e a s e d cow numbers r e a c h market weight marketings increase. Eventually increased marketings reduce p r i c e s to a point that discourages further expansion and eventually some l i q u i d a t i o n of i n v e n t o r i e s t a k e s place. The f o l l o w i n g d e c l i n e i n m a r k e t i n g s r e s u l t s , i n p r i c e s i n c r e a s i n g and t h e b e g i n n i n g of a new c y c l e . " Cattle the  beef  cycle  environment chapter  2.3  as  i n which  will  decisions attempts  p r o d u c e r s have a l w a y s had t o a d j u s t  be  part  of  they  an  biological  operate.  The  e x a m i n a t i o n of  f a c e d by c o w - c a l f t o model t h i s  ALTERNATIVE  the  and r e s p o n d and  remainder  the  economic of  this  economic o p t i o n s  p r o d u c e r s and p r e v i o u s  to  and  theoretical  behavior.  PRODUCTION STRATEGIES AVAILABLE  TO  COW-CALF  PRODUCERS The c o w - c a l f reproducing activity  is  activities  farmer  animals the are  is  and  selling distinct  engaged i n selling  of  cull  from t h e  the cows  the  primary  progeny. (and  activity  of  A secondary  bulls).  s p e c i a l i z e d feeder  These operator  31 whose p r i m a r y basic  role  decision  calf  now or  decision  will  availability  point  farmer cows,  time,  weights  decisions  it  of  calves) herd, (Yver  at  second i s  in h i s  Figure  2.7  to  farmer's  management  includes produced heifers  in  cows,  any  one  (and  cow-calf bulls,  and a g e s .  is  faced  associated  numbers of  typical  plant  and  describe  producer.  decisions and year  is  different  with  optimal types  of  production decisions output  rate)  the  while  is  economic  6  cow-calf herd  The  of  number  number of  A successful  Generally, timed  a  options  reproductive  d e p e n d s on t h e  considered average.  weather c o n d i t i o n s , c a l v i n g  the  The f o c u s of  heifers.  b r e d n i n e months e a r l i e r .  85% i s  At  an animal should be sold or the purpose of p r o d u c i n g more  to  the cow-calf  bulls,  farmer.  a portfolio decision.  helps  available  of  (eg.,  weights  farmer  price  a  herd  the  1971):  s i z e of  basically  the  that  different  and t h i r d d e c i s i o n s a r e  d e t e r m i n i n g the  a  This  weights; the  of  likely  the cow-calf  d e t e r m i n i n g the o p t i m a l i n t h e h e r d ; and  first  (i.e.,  of  is  sell  and e x p e c t e d e c o n o m i c  quality;  animals  c) d e t e r m i n i n g whether retained in the herd for animals.  the  its  to  The  selling.  different  determining optimal herd s i z e levels);  b) animals  The  before  at  beef.  whether  opportunity cost  therefore,  the  is  prevailing  and  and t h e  finished  farmer  animals  pasture  heifers,  managing  major a)  of  have a v a r i e t y  steers,  three input  inputs; in  cow-calf  heavier  price of  will  In  the  depend on t h e  the  associated  t h e p r o d u c t i o n of  of  feed to  conditions:  any  is  to  calves cows  calving  b e c a u s e of take  which  place  and rate  Canadian in  the  Figure Flow Diagram of  Cull Bulls  Reproductive Herd  2.7  Cattle  Production  Decisions  Sell Calves  (300-500  lbs.)  Breeding Herd  > Calves  Retain Calves  Female  Cull  Maintain Calves, Sell Y e a r l i n g s (500-650 l b s . )  Cows  Retain Calves  Maintain Yearlings, S e l l Long Y e a r l i n g s (650-750 l b s . )  Male Bulls  >  Steers  Maintain Calves, Sell Yearlings (600-750 l b s . )  Breeding Herd  Maintain Yearlings, S e l l Long Y e a r l i n g s (750-900 l b s . )  33  early  spring.  The new calves can be sold to feedlots in the  f a l l of the year in which they are born herd  over  the  winter.  calves  can  retained  be  for  retained  the  for  retained  breeding  reproductive herd or they can become steers. sold  in the  The cow-calf farmer has available a  number of production alternatives Bull  or  calves.  within  Steers  the  can be  to feedlots as yearlings at approximately 600-750 pounds  or maintained  on pasture  and sold  approximately  750-900 pounds.  as  long  yearlings  at  (Feedlots s e l l finished steers  at approximately 1000-1100 pounds). Female calves can be kept as replacement heifers or to  feedlots.  Heifers  can  be  sold  as  sold  yearlings  at  approximately 500-650 pounds or maintained on pasture and sold as long yearlings at approximately 650-750 pounds. sell  finished  course,  the  heifers decision  (Feedlots  at approximately 850-950 pounds). Of on  whether  to  use  a  heifer  as  a  replacement can be made up to the time the animal i s s o l d . In  the  case  of  steers,  the decision of the farmer i s  quite straightforward: he must decide on and  time to s e l l the animal.  h e i f e r s , the decision i s more whether  to  (heifers),  sell or  the  optimal  In the case of b u l l s , cows, and complicated.  He must  the animal, retain i t for further  incorporate  it  weight  into  the  breeding  decide  fattening herd  for  producing calves. A  number of economic studies have attempted to model the  economic options available to cow-calf  producers.  The next  section w i l l examine two important contributions in t h i s area.  34 2.4  EXISTING THEORETICAL MODELS OF THE COW-CALF INDUSTRY There.  attempts  have to  industry.  been  model Jarvis  theoretic  a  the  number  and Yver  a p p r o a c h t o model t h i s  models  supply  elasticities.  interested cow-calf  is  in  Carvalho  capturing  the  Yver  Yver one of  price  on the J a r v i s their  although similar is  defines  the  m a x i m i z a t i o n of  the p r e s e n t  For  other  to  with  of  short  run  hand,  is  expectations studies and  of  Yver are  the  into  steers  of  feed  the  models  industry the  summarized b e l o w .  The  or  model,  the J a r v i s  inputs  is  less  model.  7  producer  used  and  equivalent  net d i s c o u n t e d v a l u e of problem  model.  on  T h i s problem i s  this  series  the c a t t l e  Jarvis of  time  p r o b l e m f a c e d by t h e c a t t l e  the a n i m a l .  birth.  emphasis  negative  on the  d i s c u s s e d in p l a c e  of  at  sale  The  approach  main r e s u l t s  d e t e r m i n i n g the q u a n t i t y  t i m e of  industry.  capital-  In  many e x i s t i n g e m p i r i c a l  c o m p l i c a t e d and  use a b a s i c  by u s i n g dynamic programming t e c h n i q u e s .  incorporate  model,  cow-calf  the  to  model,  the  of  analysis  Carvalho  theoretical  dynamic c h a r a c t e r i s t i c s  C a r v a l h o combines t h i s  based e i t h e r  (1971)  (1972)  addition,  are  of  t h e p o s s i b l e e x i s t e n c e of  industry  Because  important  characteristics  (1968)  their  o£  the  to  as the the  animal  c a n be r e p r e s e n t e d  as  follows. I **'  Vm(0)  2  where Vm(0)  is  = qW(tm)e~  the p r i c e  is  of  the  weight  feed  tm - p/ f(x)e~ 0  r x  dx,  the d i s c o u n t e d v a l u e at  respectively the  rtm  input  of  beef  the a n i m a l , at  and f e e d p e r  tm i s  any p o i n t  birth,  in  the  q  unit  slaughter  time,  and r  is  and of age, the  p  are  weight, W f(x)  is  interest  35  The f i r s t term on the right hand side of ( 2 . 1 )  rate. total to  is  the  revenue from the sale of the animal at age tin discounted  the  present.  The model assumes that the farmer knows the  price of beef (q) with c e r t a i n t y .  The  second  term  on  the  right hand side represents the cost of feeding the animal over its  lifetime,  discounted  to the present.  that the price of feed is constant over the  The model assumes lifetime  of  the  animal. If  one  assumes  that  the  throughout i t s l i f e t i m e , the f i r s t  animal order  is  fed  condition  optimally for  the  maximization of Vm(0) requires that: (2.2) 3Vm(0) "  •T  e"  r t m  [ q W (tm)-rqW(tm)-pf(tm)] = 0.  Equation ( 2 . 2 ) indicates that a steer w i l l be slaughtered when  the percentage increase  in i t s weight equals the rate of  interest plus feed costs per d o l l a r ' s worth of animal, or (2.3) 9w(tm) 9t  1  =  r+pf(tm).  W(tm)  qW(tm)  The second order condition for the maximization of  Vm(0)  is: (2.4)  9Vm(0) - e~ 3tm^  At  slaughter  rtm  [qW (tm) - rqW (tm) -pf'(tm)] < 0. f,  age tm , i t is l i k e l y that both the weight  W(tm) of the steer and feed intake f(tm) (W'(tm),  f'(tm)  > 0).  Therefore,  will  be  increasing  in order to satisfy  i t is s u f f i c i e n t that the steer be increasing in weight decreasing rate at slaughter age tm ( i . e . , W'(tm) < 0 ) .  (2.4),  at  a  36  Yver  considers  the  effect  of changes in beef and feed  prices on the optimal slaughter age of steers.  Using Equation  ( 2 . 2 ) and the i m p l i c i t function theorem, he is  able  to  show  that (2.5)  dtm = -pf(tm) ( d i n g - dlnp) , [qW'(tm) - rqW'(tm) - p f ' ( t m ) ]  where  the  condition In  denominator  is  negative  from  the  second order  (2.4).  Equation  slaughter  age  pf(tm)  (2.5),  represents  tm and i s p o s i t i v e .  feed  costs  Furthermore, the negative  sign on the right hand side is cancelled by the negative of  the  denominator.  in  this result demonstrates that a negative run.  into  will  response  is  8  female animals by  account the female animals' additional output in  the form of calves in the discounted accounting  costs  Consequently,  supply  This model can be extended to represent taking  feed  the optimal slaughter age of a steer.  expected in the short  sign  Therefore, this equation indicates that  an increase in beef prices or a decline increase  at  for  value  this additional factor,  function.  After  Yver is again able to  show a negative supply response in the short  run  for  female  animals. In  addition,  Yver  reaches a number of conclusions with  regard to changes in the c a p i t a l price of c a t t l e  and  changes  in beef and feed p r i c e s .  The algebra used in generating these  conclusions  and  is  tedious  will  not  be  presented here.  However, the conclusions can be summarized as follows: 1 ) The e l a s t i c i t y of c a p i t a l price with respect  to  beef  37 price  is: i)  positive  and  monotonically  towards  unity  the  optimum s l a u g h t e r  ii)  larger  The  2) price  highest  for  of  as  birth,  the  declining  animal  approaches  age;  females  elasticity  at  than  f o r male  capital  price  animals.  with respect  to  feed  is: i)  negative  declining  and l a r g e s t monotonically  approaches the ii)  in absolute  larger  toward  zero  optimum s l a u g h t e r  in absolute value  value as  at  birth,  the  animal  age;  for  female  than  for  male  in  feed  price  animals. An  3) will  increase  increase  i n beef  price  or a d e c l i n e  t h e optimum s l a u g h t e r  age of  all  animals  in  the  indicate  that  herd. To s u m m a r i z e , t h e Y v e r an  increase  future) thereby  in  increases  For  of  the  beef  the  animals  steers,  fattening  cattle in  to  implies either breeding,  the  animals  the  short  run,  in  the  slaughter of  this of  all  beef  will  to p e r s i s t  keeping  to  the  these  profitable  animal  the  animal,  Under  9  it  into  may have been  the  to  sold.  longer  heifers  and  heavier  weights  (heifers)  or  the a g g r e g a t e  and  indicates  that  animals.  In  In  there the  be p o s i t i v e  will  be a  long run, due t o t h e  the  cows,  and  For  to obtain c a l v e s .  will  age. find  otherwise  weights.  fattening  in  elasticities  producer  implies  heavier  (expected  slaughter  the herd t h a t  this  results  m a r g i n a l v a l u e p r o d u c t of  i n c r e a s i n g the o p t i m a l  conditions retain  the p r i c e  (and J a r v i s )  it  decrease supply  increase  in  38 h e r d s i z e and a v e r a g e The Y v e r the  and J a r v i s m o d e l s were  cattle  industry  justification obtained  for  in  primarily  profit  two  maximizing is  maximizer  over  operation. retires.  from  retiring.  I 1j,  animals  all  animals  in  the  the  future;  for  and d i d  factors  time  farmer  has  period j over  in  notion  one y e a r  (2)  calves.  of  into  age  the  to  cattle from  s y s t e m of  quasi-rational  during  which  of  prices.  is  a  profit is  in  farm f o r m p e r i o d s  and  the  farmer  animals  one  n  periods  a c c o r d i n g to be  year  sold of  in  age  market  categories:  cattle  he  is  in period j .  three  feeder  of  farmer  which cannot than  price  t o be d e r i v e d  the  his  k i n d s of  the  attempted  expectations  time,  as  the maximizing p r o b l e m .  w h i c h can be s o l d a t  c a n be d i v i d e d  and (3)  the  operates  less  breeding herd;  (1972)  An e c o n o m e t r i c  periods  three  animals  such  i m p o r t a n c e of  Carvalho  farmers'  born in p e r i o d j  D  b e g i n n i n g of  industry  the  and t h e  behavior.  At any p o i n t  farm  I j , animals period;  in  model assumes t h a t  1 0  all  The  then  The  focused  relationship  introduced  Carvalho  elasticities  models  important  a dynamic  to account  theoretical  i n an e c o n o m i c model of  farmer  he  some  t o model  These  o b t a i n e d as a s o l u t i o n t o  addition,  The  work.  industry  factors  attempts  run s u p p l y  run b e h a v i o r  the  by a l l o w i n g  expectations  and  of  short  in decision-making.  these  equations In  short  initial  provide  negative  empirical  the  nature  industry  to  f o r a number of  expectations include  and  the  past  on  not a c c o u n t dynamic  weights.  this at  price In (1)  age:  the CJ;  addition, animals  t o be s o l d now or  in  39  C a r v a l h o assumes t h a t total  time  p e r i o d n,  the  farm i s  by a q u a d r a t i c  V(S ,£. ,V ,C |K ,F ,I n  n  n  n  n  n  n  +aE [V(S _ n  subject  n  =  F  n+1  +  K  n+1  + S,  K  n  =  1  On  =  1  In  =  K & V  n+1  I  n  X  C  a  l  i  v  n  9  S  = number o f  feeder  j = number o f n  c V(.) are  n  n  is  n  feeder  calves  n  n  n  n  of  culls,  = price  of  feeders,  = price  of  calves,  left  until  n  2  n  n  2  f  = maintenance  n n  +& -V ] n  2  sold, slaughter,  next  period  when  there  retirement,  .5a[K  n  n  value of p r o f i t s  = total  n  2  ),  the e x p e c t e d p r e s e n t  n n  n  i n the b r e e d i n g h e r d ,  q V +P S +c C ^ n n  " )  n  sold for  = price  n periods  -v  -C -S ) -.5g(F -S )  animals  (= F +1 -C -6 -S  P  n  from t h e h e r d ,  = number o f c a l v e s  n  & n  &  added t o t h e h e r d ,  on f e e d ,  q  -  +  '  = animals  F  i n  n  rate),  F „  n  I  n  '  culled  C  n +  n  S  = animals  n  in  n+1 " n + 1 ~ n+1 '  = new a n i m a l s  n  n  n  = number o f a n i m a l s  n  the  identities:  _£<  c  0n+1  n  n  V  K  over  , C _ , | K . , . F _ , , I - , , n-1)]  M  n+1 " n + 1  ^ n  P S +c C - . 5a (K  2  , V  1  +  n  ) -.5f(F  0 n  to the f o l l o w i n g F  where:  n  generated  function as: n  2  n  profits  i n o p e r a t i o n c a n be a p p r o x i m a t e d ,  ,n) = q V  -.5b(K -V ) -.5d(l n  the  revenue, cost  of a n i m a l s  kept  in  stock, ,5b[K -V ] n  n  2  =  aging cost of animals kept in stock,  40 .5d[I  3  Q n  • 5 f ( F +1 -& -C -S ) n In n n n  = v a l u e of  n  Using a quadratic by  the  well,  global  the  dynamic  function  convexity  simplicity  satisfies  animals  animals  of  the  on  at  periods  profit  of  p e r i o d n,  conditions  for  and  profits.  this  or  also  minimum  function.  function allows  Carvalho  feed,  feed,  e n s u r e s a maximum  or c o n c a v i t y  the  on  rate,  operator  next  programming t e c h n i q u e s .  function  of  = expectation  n  [V(. _i |. _i] n  for  calves,  = one p e r i o d d i s c o u n t  a  E  producing  = aging cost  2  n  of  = feeding cost  2  .5g(F -S ) n  = cost  2  As  solution  shows  that  first-period  by  this  certainty  equivalence. The m a x i m i z i n g s o l u t i o n last it  year  before  retirement,  in each p e r i o d  manner s  the  until  following  requires then,  the  general  solving  t h e model  working backwards,  solutions solutions  converge.  are  in  the  solving In  this  obtained:  = <i/g)P -(i/g)c -(i/g)a E (p _ )+F , n  n  2  n  n  n  2  n  &n = ( l / b ) g - [ ( l / a + A a d ) + ( l / b ) ] c n + ( l / a + A a d ) a E ( q - i ) 2  n  2  n  n  ( l / a + A a d ) a E ( c _ ) + [ 1/a+A a d) + 1/d) ] a E ( P _ ) , 2  V  n  C  n  "  2  n  d/b)q -(l/b)c n  n  n +  2  2  2  n  n  2  K , n  = [ d / a + A a d ) + (l/b) + (l/f ) + ( 1 / g ) ] c - ( l / g ) P - ( 1 / b ) q 2  n  n  n  -(1/f ) a E ( P _ ) - ( 1 / a + A a d ) E ( q _ ) n  n  2  l  a  -(l/a + X 2 a d ) a E ( c _ ) - [ ( l / a 2  a A in  the  2 E  n( n-2) p  number  + I  of  n  n  A  2  n  a  l  d ) + ( l / b ) + ( l / f ) + ( 1/g)]  lnfuture  solution equations.  conditional  2  n  expectations  prices  appear  These from  as e x o g e n o u s  prices past  are prices  variables  generated according  as to  41 expectations (Nerlove that  formed by a  1972).  quasi-rational  Generally,  anticipated  values  of  expectation  quasi-rational  variables  process  expectations  imply  may be r e p l a c e d by  their  maximum-mean-square-error p r e d i c t i o n s . The  solution equations  form the  b a s i s of  the  econometric  model. Carvalho provides cients  in  study at change of  these  1)  steer  increase  provided heifer  sales  as  this  are  will  of  cows  for  a given  derived to  the  supply  will  actual  increase 3)  or  if  if  is  If  decrease.  increases total  one  for  price  overwhelms price  4)  Cow s a l e s  the  expected  steers  as  in and  and  steer  the  price  need t o be  sold  revenue. of  the  Carvalho  model  need  not  be  satisfied  some  form  of  distributed  from a p r o f i t model,  behavior  sales  increase  heifer  fewer h e i f e r s  number  increases,  for  increase  the  expected  Heifer  heifers  prices,  to  a large  of  will  coeffi-  the  2)  expectations  and t h e r e f o r e  dynamic  Yver  there  the  pertinent  increase  h i g h compared t o a c t u a l  incorporating account  sales  increases  the  The c o n t r i b u t i o n First,  of  r e a c h i n g n i n e months of a g e .  prices.  heifers  Steer  prices  young s t e e r s  will  interpretations  s o l u t i o n e q u a t i o n s which a r e  hand.  in  useful  elements.  Carvalho  depends  on  with  Instead,  maximizing model. is  able  price  is  static  lag the  models  structure  to  d y n a m i c s can  be  Second, to  twofold.  in  contrast  show t h a t  expectations  short of  run  cattle  producers. There model.  are  First,  however, it  two main d e f i c i e n c i e s  concentrates  on g e n e r a t i n g  in  the  output  Carvalho  supply  and  42 inventory producers  equations for  complexity the  of  importance  short  run  associated the of  the  manner.  the  interpretation  next  chapter,  problems industry.  an  ignores inputs.  the This  derived is  p r i m a l model u s e d i n  supply  theoretical  but  effect  of  price  response  is  not  Rather, of  the  attempt  by u s i n g the  it  necessary  the a n a l y s i s .  determined  ex  in a  of  be  made  duality  to  on  the  rigorous  post,  from In  overcome  t o model t h e  the  Second,  expectations developed  by  due t o  regression c o e f f i c i e n t s .  will  theory  is  demand  the  these  cow-calf  43  FOOTNOTES TO CHAPTER  1  Statistics and t h e  2  Canada  Provinces,  Alberta  420/10,  C a n a d a ' s major are  Ottawa,  Agriculture,  Agdex N o . 3  , Selected  the U . S . ,  4  See M a r t i n  5  Because  of  this features  of  A heifer  7  The J a r v i s model a l l o w s  models are  to  be  Manual,  Edmonton,  and a n i m a l  products  and E n g l a n d .  the  one  for  can  capture  Canadian cow-calf  its  the  industry  by  production.  first  calf  the q u a n t i t y  of  is  born.  inputs  an endogenous v a r i a b l e :  fed  to  otherwise  both  results  and  identical.  s h o u l d be n o t e d t h a t  run  in beef  New Z e a l a n d ,  becomes a cow a f t e r  animal  lists  Canada  p.4.  Canadian cow-calf  6  It  Cow-Calf  characteristic,  a n a l y z i n g western  8  Beef  trading partners Australia,  Statistics  (1981).  essential  the  Aqriculture  1983.  The  1976,  TWO  a number of supply  expectations  Yver  r e a s o n s why t h e  elasticites of  qualifies  may  farmers,  estimated  not  data  these  be  s i g n s of  short  negative  (price  p r o b l e m s , and f a c t o r  input  constra i n t s ) . 9  This  is  the  production  flexible 10 T h i s  is  true  under c e r t a i n f u n c t i o n and i f  slaughter  but  model.  See  it  does c a p t u r e  Carvalho  (1979).  reqularity the  conditions  g r a d i n g system  of  permits  weights.  a simplified version  Carvalho  Carvalho  only  of  the  model  estimated  t h e main c h a r a c t e r i t i e s  (1972)  or  Nerlove,  of  Grether,  by his and  44 3.  3.1  A THEORETICAL  INTRODUCTION The p u r p o s e of  model  which  attempt  is  the  to  short  extend  In made  the  to  output  first  of  cow-calf  the  subsequent  addressed: across  2) price  analyzing  m o d e l s by  the  output  determining  the  expectations  for  t h e model  from w h i c h a t r a c t a b l e  within  econometric  i)  examining the  In  to  but a s s u m i n g o n l y a allow  t e c h n o l o g y which  run b e h a v i o r  the  dynamic  t o be e m p h a s i z e d and w i l l of  a to  (which the  multi-output, assume  is  industry of  (3.3)  level)  inputs;  will  by  of  on t h e  from c o n s i s t e n t  single aspects  facilitate multi-input of  an  aggregating  i s s u e s must  ii)  input  be  using a  existence  two  and  address  Restrictions result  the  obtained  i m p o r t a n c e artd i n p l i c a t i o n s  hypothesis.  will  function  aggregation Section  attempt  short  order  function  initial  farmers'  development  farm l e v e l  an  This w i l l  production  farms.  maintained  profit  function.  profit  the  both  An  producers within a m u l t i -  farmers'  (3.2),  cow-calf  function.  industry from  section  variable  profit  profit  input  producer.  theoretical  function;  and 3)  framework  theoretical  derived.  model  farm-level  cow-calf  1) m o d e l l i n g  of  a  run s u p p l y and d e r i v e d  existing  profit  run s u p p l y b e h a v i o r ;  model c a n be  to develop  demand by c o w - c a l f  implications  intertemporal  is  representative  multi-input  theoretical  level  a  chapter  on t h r e e a r e a s :  and i n p u t  output,  short  of  made  concentrating supply  this  describes  demand b e h a v i o r  an  MODEL OF THE COW-CALF INDUSTRY  be  aggregation  aggregation  by  separability  as a  underlying  farm-  aggregation  from  45 the  farm l e v e l  level  will In  to  Section  for  In  the  This  restrictions  will  run b e h a v i o r other  function  (3.8).  multi-input  be  in  comparative will  (3.7),  using  in  Section  single  be e x t e n d e d t o of  output  accommodate  the  cow-calf  a description the  The  statics  the  a  producers'  be d e r i v e d  includes  for  postulated.  technology  also  function  changes  imposed on the model due t o  of  elasticity  cow-calf  Finally,  profit  measurements  production w i l l  a number of  from r e s t r i c t i o n s function,  biological  on the will  testable  theoretical  be p o s i t e d  appropriate be r e p o r t e d  of  the  nature  hypotheses,  multi-output,  in Section  describing  the  theorectical  emphasized that  a number of  industry  will  impose dynamic  existence  of  categories the  natural  restrictions  "second hand" markets of  animals,  farm l e v e l  the  reproduction  industry  characteristics  level  the  except  stock or  of  (auction  breeding animals  Section  generated multi-input  PRODUCER  model,  it  s h o u l d be  of  the  cow-calf  on the  model.  markets)  be  herd can o n l y  The  for  all  implies  that  increased  by p u r c h a s i n g a n i m a l s .  aggregate  the  (3.9).  females, can  to  in  A SINGLE OUTPUT PROFIT FUNCTION FOR A COW-CALF Before  the  will  profit  production.  technology  at  of  section  function  section  A number o f  3.2  producer  profit  producer  (3.4).  output  a s w e l l as  profit  (aggregate)  a single  following  multi-output,  industry.  of  short  representative  representative the  (3.5),  expectations  (3.6).  in Section  cow-calf  implications  this  representative  be d e t e r m i n e d  representative  price  the  by  However,  at  be i n c r e a s e d  by  1  46  natural  reproduction.  constraint  at  These  2  conditions  both the farm l e v e l  by  animals  the  this  period)  p e r i o d ' s beginning stock number of animals l e f t To  account  of  a  dynamic  (the number of replacement  h e i f e r s next p e r i o d i s determined bred  impose  and  the  animals  number  industry is  of  female  level  determined  (next by  the  over at the end of the p e r i o d ) .  for  these  dynamic  constraints  i n the  t h e o r e c t i c a l model, one assumes that the o b j e c t i v e of the cowc a l f producer period  i s to maximize  planning  horizon  expected  profits  over  a  two-  s u b j e c t to the c o n s t r a i n t that next  p e r i o d ' s beginning stock of animals i s decided t h i s p e r i o d the  basis  of  entire period  expected p r i c e next p e r i o d . i n which the farmer  on  Subsequently, the  i s i n b u s i n e s s can be viewed  as o v e r l a p p i n g two-period p l a n n i n g h o r i z o n s . The  basic  problem  facing  a  cow-calf  farmer  is  determine whether i t i s more p r o f i t a b l e t o s e l l an animal period for  at  known  price.  These  simple  i n F i q u r e 3.1.  dynamics are i l l u s t r a t e d farmer  this  ( c e r t a i n ) output p r i c e or r e t a i n the animal  s a l e i n the f u t u r e at an u n c e r t a i n  The  to  i s assumed t o have a given stock of animals at  the beginning of p e r i o d zero ( C ) . b  Moreover, the farmer  knows  o  (with  certainty)  output  p r i c e i n p e r i o d zero ( P ) and input Q  p r i c e s i n p e r i o d zero (W ). Q  does  not  know  output  But i n p e r i o d  price  be i n p e r i o d one (EgP-^) .  the  farmer  i n p e r i o d one ( P ^ ) . Rather, i n  p e r i o d z e r o , he forms some e x p e c t a t i o n of will  zero,  what  output  price  47  Figure  Dynamic  3.1  Behavior  of  TIME PERIOD 0  12  <  o C  o Y  farmer  with a vector economic and  the  valued  but  that  at  is  output  zero.  next  period  (C^)  to  In  Given  ( E  Q  P ),  the  residual  to  with a vector given  his  determines  of  farmer  variable  e x p e c t a t i o n of the  end o f  in  period stock  animals  residual  of  the m a x i m i z a t i o n p r o c e s s .  Consequently, period  is  just  the  the  again  valued at  beginning  an W ,  of  the  period  maximization  prevailing  of  stocks  next  output  period  price  output  other  (C^).  with  input  the next of  in  price  animals  This  will  stock  (C^)  Note  period (C ) 1 e  of  (Ej^), and  the  (Y-^) a g a i n as a  that  output  known o u t p u t  stock  the p r e v i o u s p e r i o d ' s  prices ( W ^ ) ,  animals  s u p p l i e d d u r i n g p e r i o d one  is  b  i n p e r i o d one  of  (Y^ )  (C ) o  farmer  end-of-period  stocks  quantity  i n p e r i o d one  the  end  purchase  (q^),  price  l  price  combines b e g i n n i n g  inputs  l  Y  ) during  expectation  end-of-period  the  (Y  v a l u e d at  farmer's  c  responding to  the  from  price  beginning-of-period stocks  p e r i o d one,  _  animals  input  at  that  of  period,  supply  to note  is  ,  Q  next  output  supply  the  P  retained  he may d e c i d e  augment  determine  price  the e x p e c t e d output  current  Then,  Q  the  important  stock  (q ).  price  animals "  a n a  Q  initial  inputs  d e f i n e d as  It  are  he  C  (which i s  process).  and,  ( )  the  about  of  l  q  with output  stock  period  period  variable  expectations  determines  zero  of  _  o  combines  environment  his  first  „  6  O  The  producer  TIME PERIOD 1  P W o o q  a Cow-Calf  price ( P - ^ .  animals  ending stock  supply  of  in  any  animals  48  p l u s any animals purchased at the beginning of the next p e r i o d  Output  supply i n any p e r i o d i s  just  the b e g i n n i n g - o f - p e r i o d  stock of animals minus the e n d - o f - p e r i o d stock of animals o r :  The  intertemporal  problem  faced  by  the farmer can be  viewed as the maximization of each p e r i o d ' s to  price  expectations  and  profits,  subject  to the dynamic c o n s t r a i n t .  This  simple model of dynamic behavior can be c h a r a c t e r i z e d using discrete,  two-period,  variable  profit  framework of Hicks (1946), Malinvaud and Diewert and Lewis Assume  (1953),  Diewert  be  a  flow  f o l l o w i n g assumptions i)  and  that  breeding  supply  of  a  observed  beef.  In  addition,  the  i n the sense  that  are employed i n the model.  (Hartman  determines the stock of period  1976).  animals  at  That the  given today's e x p e c t a t i o n of output  •period. industry  T h i s assumption given  to breed a cow on  his  is  sold.  this  The output of the  The stock of animals i s q u a s i - f i x e d  is  capital  cow  the stock i n any p e r i o d i s chosen before the output beef  the  (1972),  f o r t h i s i n i t i a l a n a l y s i s that the farm's  g i v e s r i s e to two cows next p e r i o d .  farm w i l l  in  (1981).  stock c o n s i s t s only of cows period  function  a  is  not  is,  price the  beginning  of  farmer of  next  (beef) p r i c e s next  unrealistic  in  the  cattle  that a cow-calf farmer must decide on whether to o b t a i n another animal i n the  future,  e x p e c t a t i o n s of the p r e v a i l i n g p r i c e when the  based progeny  49  ii)  In  any  period,  complete  knowledge  period.  This  employment  variable  of  output  assumption  of  variable  Consequently,  iii)  Variable  iv)  The  in  allows  -input  stock  input  farmer  price  is  are  a price  prices  farmer  output can  decisions  chosen  input  the  usage  prices  are  and  inputs after  variable  accommodate e r r o r s  inputs  be  that  adjust  are  known.  adjusted  to  1976).  known w i t h in a l l  in  to  prices  (Hartman  taker  given  certainty. output  and  input  markets. v)  There are  The d y n a m i c s of stock  of  price;  This alters  its  and above of  are  with  the  is  the  assumption r e q u i r e s stock  rate  (Brechling  1975). of  as  cattle  adjustment  costs  innocuous.  The f a r m e r  by  market. price  at  are  taker  in  it  is  all  firm  additional  costs  over  (Nickell  these  costs  the  speed  of  the  costs.  new c a p i t a l .  farm  level  can d e c r e a s e  These  or  1978, p . 2 5 ) .  appears  It  at  an  increases  assumption  of  zero  t o be  rather  his  cattle  nearest  auction  increase  he c a n a l t e r  that  retraining  adjustment  the c a t t l e  costs  assumption  increase  t o and f r o m t h e  assumed t h a t markets,  the  future  As a  that  production,  the  comment.  b a s e d on t h e  new equipment  animals.  to expected  w i t h r e o r g a n i z a t i o n and  transporting animals Because  the  of  assumption that  further  may i n c u r  of  adjustment  assumed  increasing  herd  it  purchase p r i c e  a d o p t i o n of  terms  from t h e  stock  from c o n v e x a d j u s t m e n t  costs associated  generally  In  arise  stock  the  determined with respect  capital  capital  there  is  do not  last  to a d j u s t i n g  t h e model d e r i v e  animals  they  no c o s t s  producer associated  is  a  input  50 levels  without  level  however,  industry  incurring additional this  level,  reproductive expands i t industry  assumption  the h e r d  is  will  increase  not  a  then as  industry  input  prices  will  cost  aggregate  herd  The  expand  only  as  fast  But  as  the  for  inputs.  demand  taker  demand  are  assumed either of  not  the  that the  adjustment  farm or  adjustment  the  t e c h n o l o g y of  production inputs, period  C  b  is  of  q and C , b  beginning e  can b  available  beginning  stock  s u p p l y of  indicating stocks  indicating  for  that  that  are  the (e.g., some  into  this  chapter  an  of  the  Y,  the  output f(.)  cows  of  is  C  beef  shows t h e  the m a r g i n a l  strictly  by  strictly  a  t h e more cows a v a i l a b l e  f at  is  (1980), concave  a vector e  is  of  end-ofthat  technological of  inputs  end-of-period increasing  p r o d u c t s of  positive,  at  during  vector  to determine f  factor  study.  cows,  the  be  estimation  where q i s of  such  will  and Denny  described  =  beef.  it  a significant  another  could  because  research,  for  combining of  If  size  M o d e l l i n g and  be  e  and Y i s  industry  the  and E p s t e i n  f(q,C ,C )  cows,  s t o c k s and o u t p u t  C ,  (1977)  The p r o d u c t i o n f u n c t i o n  the  not  beginning-of-period stock  possibilities with  are  levels.  farm  function  stock  period.  the  its  increases,  However,  this  be r e s e r v e d  Epstein  in  costs.  focus of  industry  as  translate  increasing  the  p.35).  costs  costs w i l l  Following  must  model d e v e l o p e d  primary  At  input markets  inputs  This  be m o d i f i e d t o h a n d l e a d j u s t m e n t costs  in a l l  for  associated with  intertemporal  industry  tenable.  its  1978,  the  less  increase.  (Nickell  At  is  allow.  price  land),  adjustment  can  potential  will  costs.  inputs  decreasing  the  end of  in and in the  51 period  ( C ) , the l e s s output s u p p l i e d e  At  any  point  in  time,  (Y) d u r i n g the p e r i o d .  c u r r e n t beef p r i c e s and f a c t o r  p r i c e s are known but next p e r i o d ' s beef p r i c e s are u n c e r t a i n . The  farmer  is  distribution to  assumed  to  have  a  subjective  probability  concerning these p r i c e s and to s e l e c t a s t r a t e g y  maximize the  expected  value  of  the  discounted  sum  of  anticipated  p r o f i t s over a two-period f u t u r e p l a n n i n g h o r i z o n  (subject  the  to  accumulation farm l e v e l ,  equation,  stock and  of  cows  ( C ^ ) , the  animal  his price expectations).  At the  the farmer can purchase cows (C^) to augment  of-period that  initial  stocks  at  price  P .  However, i t w i l l  t  farmers only purchase animals at the  period.  No animals are purchased  be assumed  beginning  i n the f i r s t  end-  period  of  each  (C^=0).  These c h a r a c t e r i s t i c s can be d e s c r i b e d as: (3.1)  Max E V  C  e  t  ,  t  j  p t  i  - i -  (1+r)  s.t.  [P f(q ,C ,C^) -  - P^] ,  b  t  t  c£ = ( l + X ) ^  + (1+X)CP,  C > 0, o b  C = 0, o P  where:  q  t  is  a v e c t o r of inputs chosen d u r i n g p e r i o d t given  that the farmer knows with c e r t a i n t y c u r r e n t output and  input  prices; W  i s a vector of f a c t o r is  the  input  end-of-period  prices;  stock  determined with respect t o the farmer's  of  animals  expectation  and of  is beef  p r i c e s next p e r i o d ; C  p  is  the number of cows purchased at the beginning of  p e r i o d t : i t i s determined a c c o r d i n g t o the  farmer's  desired  52 future  levels  of  future  profits  and b e e f  is except  the  for  beginning  animal  subject  to e x p e c t a t i o n s  b e g i n n i n g - o f - p e r i o d stock  of  cows  i n which in  stock  period  t  is  of  animals  given  is  which  period  takes  (t-1)  account  p r o d u c e news c o w s , the to  number the  of  the  0 £  X  cows a t  number of  p r o g e n y of the  of  cows  determined  P  the  is  t  function  _< 1.  the  of  represents  beef the  in  t  cows  the n  = ( 1 ) C - l + ( 1 + X)C% t  (X) of  formula  the  in  any  cows  indicates period t  last  period  bought a t  the  to  that  is  equal  plus  the  b e g i n n i n g of  progeny;  price  the  This  the  e  ability  b e g i n n i n g of  t h o s e cows p l u s any  is  formula C  reproductive  retained  p e r i o d and t h e i r P  by the  and,  (CQ > 0),  b  previous  of  prices;  period zero  stock  stocks  of  beef  stock  prices  per  price  of  but w i l l  animal's  ability  E  is  the mathematical  r  is  the  discount  hundredweight;  also  a  include  not  only  a component  t o p r o d u c e new  expectation  rate,  cow and i s  a  that  animals;  operator;  assumed c o n s t a n t  and  and known  with  certainty. After Ct  = [C  /(1 X)]-C^_  C  Equation t  The  t  farmer  being  =  °  animal  accumulation  and s u b s t i t u t i n g  1  (3.1) (  1  +  r  into  fixed  the  as  maximization  OffA)  )  optimization procedure.  views the  constraint  c a n be r e w r i t t e n a s : ,  maximization problem in Equation  as a two-stage the  the  +  b  problem, W  rearranging  number of  or p r e d e t e r m i n e d .  In  (3.2) the  cows a v a i l a b l e  can  first  i n any  He must d e c i d e  be v i e w e d stage,  period  on t h e  as  optimal  53 quantity  of  from w h i c h  inputs  he d e t e r m i n e s  period  stocks)  Optimal  inventory  output  price  the  t o combine w i t h t h e  present  and  the  he e x p e c t s  inventory  stock  carryovers  p e r i o d output are  valued  to p r e v a i l  as  the  by the  next  of  cows  (end-ofresidual.  farmer  at  the  period discounted  to  or:  t life)- V W =  second stage  determines will  current  carryovers  z  In  optimal  fixed  optimal  involve  of  the  optimization procedure,  beginning  the  stocks  purchase  of  for  the  animals  next  the  farmer  period.  t o augment  This  existing  stocks. The  first  d e f i n e d as (3.3)  "  <P »W »Z ;cj)  is  variable (1970)  profit  order  each  For for set  for  (3.2)  can  be  dual  to  of  a  its  variable  while  to e x i s t  function  the  Gorman  a dual  set  concept  (1968)  and McFadden  and  1972, and D i e w e r t  redefine  f(Y,X;v), Y  =  relationship the  variable  c o n d i t i o n s must be  i n e x p o s i t i o n of  and  profit  introduced  regularity  generality,  set  the  properties.  there  follows:  possibility  fc  (1953-54)  (Lau  ease  greater as  Equation  P f ( q ^ C ^ C * ) - w j ^ + Z C^  e  possibility  certain  function  Max q ,C  function  production  function,  maximizing  d e f i n e d as  determined  In the  =  Samuelson  3  in  follows:  n (.) f(.).  stage  1973 and  the  where  (YI,...,  satisfied  conditions  production f(.)  Ym)  is is  profit by  1974).*  regularity  the  between  an  and  possibility  the  production  M-dimensional  54 vector  denoting  dimensional is  variable  vector  outputs.  denoting variable  a J-dimensional vector  (Y,x;v)  is  X = (XI,..., inputs,  d e n o t i n g the  is  an N-  V = (V1,...,  fixed  the M+N+J-dimensional v e c t o r  Xn)  of  inputs, all  Vj)  and z =  outputs  and  inputs. The  f o l l o w i n g assumptions are  fl)  f  is  made on  a c l o s e d non-empty s u b s e t  f: of  5  M+N+J-dimensional  space, f2)  f  f3)  if  z'eT,z"  f4)  if  (Y,x;v)ef  from above An by  is  for  a convex  v  economic  Diewert  regularity  set,  < z'  then  then  z"eT,  the  components o f  interpretation  (1973 and  1974).  condition,  of  (f2)  free  disposal,  positive  prices prices  fixed  and  for  the  the  profit  that  r a t e s of  (f4)  is  a  mathematical  the  transformation,  indicates  satisfies  function  shown t h a t  variable  variable  f i x e d at  if  of  outputs.  farmer  outputs p = ( p  the  (f3)  t h a t a bounded  the  inputs w = ( w  v,  technology  l r  variable  ...,  ,p ),  ,w ),  and  1 r  ...  faces  profit  n  m  function  as: T  f  (fl)  above n o t a t i o n ,  n(P,W;V) = max [P Y - W X:  If  has  for  inputs are  c a n be d e f i n e d (3.4)  provided  i n p u t s can p r o d u c e o n l y a bounded v e c t o r  C o n t i n u i n g with the  the  each assumption i s  indicates  implies  positive  bounded  Condition  non-increasing marginal  of  are  fixed.  exhibits  vector  Y  T  conditions  satisfies  n(.)  (Y,X;V)ef], P > > Om, W > > On.  (fl)  to  Equation  satisfies  the  (f4)  (3.4),  and  the  variable  then Diewert  following conditions:  (1973)  55 111)  n-(PfW,;v)  is  p»0m,  a  non-negative  w»0n,  and any  112)  n(.)  is  nondecreasing in  p,  n3)  n(«)  is  nonincreasing  w,  Jl4)  n(.)  is  homogeneous o f  115) n ( . )  is  convex  116) n ( . )  is  concave  Condition consistent  is  11(1)  in  function  for  v,  d e g r e e one i n p and w,  i n p and w, in v for a  every  f i x e d p and w.  regularity  w i t h economic p r o f i t  condition  which  is  maximization,  n(  2)  indicates  that  if  p'>p''  then n ( p ' , w ; v ) > n ( p ' ' , w ; v ) ,  n(  3)  indicates  that  if  w'>w"  then  n(p,w' ;v) <n(p,w' ' ; v ) , and  n(  4)  indicates  that  for  X>0,  n(XPr Xw;v) = xn ( p w , ;v) .  Moreover, II(.)  f e x h i b i t s constant  is  homogeneous  Il(p, w;Xv) = XII ( p , w;v) . function  is  exists  fixed  inputs.  satisfying satisfying  of  (JI5)  ( 1973)  conditions  for  conditions  (3.4).  (II6)  to s c a l e  (f1)  that  (f4)  Thus f and n a r e  v  or  of  any  exists  profit and  that  prices  and  function  II  unique  f  a  generates  equivalent  n through  representations  t e c h n o l o g y and t h e r e f o r e n may be used t o c h a r a c t e r i z e  t e c h n o l o g y and t e s t Returning producer,  the  for  to the dual  1  Max  E  intertemporal  problem  relationship defined  1  Z (1+r)t t=o  the  structure.  be u s e d t o r e w r i t e E q u a t i o n  (3.5)  if  X > 0,  the  in p r i c e s  given  that  and o n l y  that  vector  (116), t h e r e to  if  in  ensure  each g i v e n  to  one  s m a l l changes  proves (ni)  f  degree  and  a maximum f o r  Diewert  returns  of  well-behaved  there  Equation  every  (3.2) t  as: t  the  in Equation  [n(P .w ,z ;cJ) - P c J t  of  t  (l+X)  ].  cattle  (3.3)  can  56 Generally,  the i n t e r t e m p o r a l  each p e r i o d but only of  errors  in  Furthermore,  the p l a n s  problem (3.5)  f o r t=0 a r e c a r r i e d  expectations  if  the  (Epstein  variable  profit  Equation  (3.3)  addition,  differentiable  with respect  expected  output  then E q u a t i o n  the of  satisfies  prices,  optimal quantities period  1932).  inventories  *  (3.6)  Y  t  =  * t  <?•  t  p t  t  t  n  z  <  P  t  t'W  C  w .,  and  fixed  p , fc  t  the p r o f i t  to  supply,  Lemma  respectively.  t  (Hotelling  of Y  *  of  Il(.) with  ' Q*£»  t  output  a  n  ^  t  and t h e l e v e l  c  t  supply,  demand r e s p e c t i v e l y ,  and z )  t  (3.6) e x p l i c i t l y  the  optimal animal  stock  defines  the f a r m e r . farmer  beginning  b  < - ) 7  has  stock  the f i r s t  of  b  1  1  1  stage  as the  of t h e  In t h e s e c o n d s t a g e only of  to  cows.  i n p e r i o d one i s c h o s e n  E [n(P ,w Z ;cJ) - PjCj/d+A)]. o  demand, and end  differentation  t o m a x i m i z e t h e e x p e c t e d v a l u e of p r o f i t 3  and  C ^.  optimization,  beginning  input,  are defined a s :  (p , w ,  o p t i m i z i n g problem f a c i n g  period's  input  maximizing q u a n t i t i e s  of the p r i c e s  factor  output,  ( 3 . 3 ) c a n be s o l v e d f o r  demand, and e n d - o f - p e r i o d s t o c k  Equation  the  (ni ) t o (116) and i s , i n  t>»  respect  functions  by  b  t  partial  input  defined  -n (P ,w ,z ;c ),  the  represent  1980).  b  t  where n i d e n o t e s to  Denny  n (P ,w ,z ;c ), W t  •  q  solutions  for  out because  function  conditions  of o u t p u t  and  by a p p l y i n g H o t e l l i n g ' s  These o p t i m a l  is solved  of  determine  next  Recall  that  in period  i n p e r i o d one o r :  zero  57 Next p e r i o d ' s o p t i m a l differentiating solving  the  animal  Equation  first  order  b*  stock  ( 3 . 7 ) with  condition  for  is  determined  respect Cj  t o Cj  by  and  then  or:  = En b(P ,W ,Z ;C *).(l+X).  (3.8)  c  It  is  1  1  interesting  homogeneous of  degree  function  can  be  there  constant  are  that C  in  b  variable  to  note  one  if  written  that  the  and o n l y as  returns  Equation  not d e f i n e d .  b  1  to  C  production  if  the  n(p ,w  b  ,z  t  scale  function  variable ).  ( 3 . 8 ) would v a n i s h  profit  Therefore,  in p r o d u c t i o n ,  it  is  and c o n s e q u e n t l y  function  is  strictly  concave  if  clear C  b  T h i s p r o b l e m can be a v o i d e d by a s s u m i n g t h a t  profit  is  in the  is the  fixed  input. An e c o n o m e t r i c and  (3.6)  by  (3.8),  determining  price  specifying However,  model can be p o s t u l a t e d ,  the as  estimating  expectations  stochastic  is  often  the rather  estimate  a farm l e v e l  an  than  aggregate  specifying  an  a functional of  the  farm model,  case,  level  II( .) ,  producers,  and  each  data  variables.  one must p o s t u l a t e  profit  equation.  available  relate  farm.  Equations  form f o r  for  the  equations  "representative"  aggregate  cattle  disturbances  econometric  variables  of  specifying  using  to  aggregate  Rather the  the  than  existence  However,  function,  for  before  restrictions  imposed by a g g r e g a t i o n must be e x a m i n e d .  3.3  SEPARABILITY AS A MAINTAINED HYPOTHESIS In  the  most  profit  studies  of  aggregate  and p r o d u c t i o n  technology,  functions  plays  separability  a significant  of  role.  58 Separability as  i s postulated to lessen  multicollinearity  separability defined,  c a n be  thereby  estimate  a given  Micro  and  assumed,  aggregate  reducing  the  s y s t e m of  between  by t h e l e v e l  micro pair  (i,j)  Formally,  = f (X ,  z  z  where f  the p r i c e  (3.11)  f  1  z  1  1  production  Since  f  z  function separable  n  ...  be  and  2  f  z  of  essentially  input  (k). 1947).  The 7  function; X ), z  inputs. ( X 1  Z  ,  . . . , X ) , and n  z  ..., qj. n  z  homogeneous  be homogeneous p r i c e  n  ...^X )  (3.12)  third  is  rate  ..., X ).  z  ty ,  ...,Q  1  Z  to  correspondingly as:  qm) = ( i q ,  = f ( X ,  z  Q ,  ( X ,  (i,j)  = (X , . . . ,  z  be  ( 3 . 9 ) c a n be r e w r i t t e n a s :  Now l e t and  marginal  into n subgroups:  z  vector  q = (qi,...,  Equation  and X  can  necessary  from k ( L e o n t i e f  and X i a r e m i c r o X  the  Z have a p r o d u c t i o n Z  partition  partition  if  a  separable  ...,X )  z  i s output  Next  (3.10)  firm  commodities  If  6  inputs  of use of  i s then let  two  such  estimation.  information  equations.  any  unaffected  f  facilitate  i n p u t s c a n be a g g r e g a t e d  substitution  (3.9)  to  econometric problems  ( q, x  ..., q)  quantity  aggregators  aggregators  defined  respectively.  n  Then,  over the  f u n c t i o n o f f i r m Z c a n be w r i t t e n a s : = f (V» ( X ) z  is i \p  1  z  f  increasing is  (  1  linear  Blackorby,  /( X )). n  z  i n i t s a r g u m e n t s and e a c h • homogeneous, Primont,  and  ~ f  z  is  Russell  aggregator  homothetically 1978, C h a p t e r  Three). The separable  economic  implication  production functions  of is:  assuming  homothetically  59  f /  X  z  aV That  X  Z  (—Z—i ~) 3f /3 X. 1  Z  r  =  i . J E X , re X ,  0  Z  J  is,  the  marginal  rate  of  substitution  jth  input  in  the  1th aggregator  function  rth  input  in  the  kth aggregator  function.  It  has  been shown  (Blackorby,  1982)  this  and B l a c k o r b y consistent level  if  with  profit  and o n l y  functions  are  that  if  output  price  separable  (P)  is  Primont,  treatment  in  the  micro  and o u t p u t  at  profit  the  quantity  and  profit  (Y)  and  of  the  can  1978  inputs  the  same a p p r o p r i a t e  Therefore,  8  ith  and R u s s e l l  of  aggregate  the  independent  maximizing behavior  the  c o m m o d i t i e s and p r i c e s .  between  is  aggregate production  partition  function  be w r i t t e n  of  with as:  (3.13)  n (P,q) Z  = max [ PY -  Z  Z  Z  QVq)).  1 1  AGGREGATION OVER FARMS Aggregate  production  functions  are  economic  research.  purely because  theoretical  fictitious it  fully  significantly the  T  = n (P,Q ( q) Z  3.4  q X : f ( X ) > fo ]  aggregate  industry demand  these  and  describes  the  technology  its  aggregate  level,  at  no its the  one cost.  micro  industry  in  applied are  counterpart. the  are  profit  of  of  outputs  derivd  a  function,  u s e d by a f a r m ,  supply level,  profit  functions  production  maximizes The  dual  used  aggregate  A  than  their  widely  concept.  different  inputs,  constructs  However,  or m i n i m i z e s for  functions  from  is At the and the  60 d e c i s i o n s of be p r o f i t  the  various  i n what c o n t e x t  "aggregate  production  representation types  of  and i i )  that  (Gorman  one  an  of  industry  sets  X  N-dimensional  f .  Each  z  f  negative  signs)  Z = 1...z.  and K  Let  P  the set  conditions  are  f  z  Schworm  1982b,  and  z  x  9 P  i  the  Pn)  existence  maximizing behavior, is  identical  of  Z  (X ,  farms K )  z  and i n p u t s a r e input  vector  be the  to  of  a  with the  farms c o m b i n e d . with where  z  o u t p u t s and i n p u t s  each ,  z  (outputs  d e s i g n a t e d by for  each  corresponding  the  farm  Given  firm price  e  production  the  regularity  can be d e s c r i b e d  f ] Z  is  i = l...n. 1  that  a  function:  output vector Z  has  technology  [PX/ (X,K)  Z  ^ ! f ^ l = X  1982a,  demand,  fixed  using a dual p r o f i t  o p t i m a l net  aggregation  and  of  level,  n ( P , K ) = max  where t h e  the  Two  Primont  a f u n c t i o n of  signs,  satisfied,  Z  complete  1968, B l a c k o r b y ,  consists  = f (X ,K ).  z  a  of  farms.  micro  possibility  completely  to a l l  to think  exact  that  = (P1,...,  parametric  At  is  z  i)  individual  is  z  as  all  vector  d e s i g n a t e d by p o s i t i v e  vector  appropriate  postulate  s u p p l y and i n p u t  technology a  and can  maximizing behavior  Consider  are  to  9  p r o d u c e r whose p r o f i t  regard to output  is  assumed  farm p r o d u c t i o n f u n c t i o n s ?  aggregation.  1978, and B l a c k o r b y  representative  z  it  function"  individual  aggregation  implies  profit  is  a g g r e g a t i o n c a n be c o n s i d e r e d :  Exact  1983)  of  fictitious  Russell  farms which a r e  maximizers.  Therefore, an  individual  defined  as:  61 The  question  conditions the  exact  imposed  following  (3.14)  of  on  aggregation  IKP.KCK  K )) =  1  Z  -  FY  the vector ...,K ) and Z  The  n (P,K ) =  1  Z  Z  E  m  the margin.  be of the  Russell  all  X  vector  of  fixed  factors  conditions  under  by  (1968)  1978)  only  function  f u n c t i o n of the z  z  z  Gorman  which (see  where i t i s demonstrated  i f a l l farms are  i d e n t i c a l at -quasi-  ( i . e . , Gorman Polar Form (GPF)) form: zo  z  the aggregate p r o f i t  n(p,k(io) =  function  the  farms).  operating  f u n c t i o n f o r the  i n d u s t r y must  form:  zn (p,K ) = zn (p)k (k ) + z n ( p ) . z  z  z  must  shadow  z  zo  z  (3.16)  indicate  that  each  farm's  be a f f i n e i n the f i x e d f a c t o r and of  p r i c e of the  Finally, with  z  z  farms value an e x t r a u n i t  (i.e.,  Z  i n d i c a t e s that each farm must have a  Equations (3.15) and  all  Z  ,  provided  z  profit  Z  n (p,K ) = n (p)K (K ) + n (p) z  Moreover,  (3.16)  the  sufficient  i f and  homothetic production (3.15)  tpx/(x,k) et]  x  were  holds This  with a p r o f i t  *  and  satisfied  (3.14)  Z  no e x t e r n a l economies or diseconomies.  Blackorby, Primont, and that  f o r which  [PX /(X ,K )ef ] ,  m a X  Z  of p r i c e s P,  necessary  (3.14) i s  the  - 9n(p,K(.)),  Z  n(p,K(.)) =  1  are  holds?:  Y  (K ,  what  i n d i v i d u a l farm t e c h n o l o g i e s  Z  given  is:  the  constant  the  factor  equally  f i x e d f a c t o r i s the same f o r  assumption returns  fixed  that  to  that  all  farms  s c a l e i m p l i e s that  are the  62 following  restrictions  respectively  (Gorman  are  imposed  on  (3.15)  and  (3.16)  1968):  n (p) - o zo  and  E n (P) = 0 . zo  z  The a g g r e g a t e  n  *' J  i7) X  i"  It  is  restriction factor  9P  amongst t h e  "  ±  of  but w i l l  aggregate  profit  factors  =  each  ... . N  important  farm must use the  neutral  of  fixed  effect  on  fixed factors  aggregate  output  vectors  and the  profits  What t h i s  implies  is  once  that  an  as:  JI(P)k(k) + n ° ( P ) ,  of  the  i n the d i s t r i b u t i o n farms  and  thus,  K)  is  only  n(P,  aggregate  technology  functions, n (p K) z  assuming that a l l  in t h e i r  technology  can be i d e n t i f i e d ,  sufficient  a  farms.  course,  Consequently,  H(p,K)  t o e m p h a s i z e an  a redistribution  have  underlying micro p r o f i t  the margin  point  Because  individual  Of  representation  this  to changes  amongst  determined.  at  as:  3Pi  f u n c t i o n has been d e f i n e d  n(p,k) invariant  zo  z  change the net  individual  is  z  efficiently,  farms w i l l  2  2  the GPF.  e a r n e d by  it  z  c a n now be w r i t t e n  an (p) , z 9n (p), i = I  _ Ek (k )  worthwhile  equally  profit  output v e c t o r  — an(p,k(k))  Y  W;  net  and  f  farms that  knowledge of  t o o b t a i n an e x a c t  of  the  is  completely  .an as  fixed  "exact"  l o n g as  the  identical  at  parameters  of  remain. are the  aggregate  characterization  data alone of  the  is  micro  production processes. It aggregate  is  clear can  that be  the  obtained  c o n d i t i o n s under w h i c h an are  quite  exact  restrictive.  63 Consequently, at  all  certain  conditions farm,  the v e r y  the  pertaining  to  model of  this  the  the  an  aggregate  profit  restrictions  an  exact  not  profit  siginificantly Second,  reveal  an  exact  , which  of  all  n(P,K)?  Therefore,  in t h e i r n(P,K)  some  the  structural Because  farms a r e  form  IT(p,K) are  not  farms  is  (i.e.,  aggregator,  the  functions.  and c o n s e q u e n t l y ,  margin.  specific  details  underlying micro production functions  quasi-homothetic the  all  aggregation  is  it  farm's  the  exact  properties  individual  exact,  its  permit  the  d o e s not  not  loses  of  What a r e  n(P,K)  the  to  function,-.II (P,K)  of  form of  of  would  the  from farm  producer  knowledge  not  where  significantly  only  is  industry.  because  structural  situation  a representative  aggregation).  First,  at  of  a  differ  case,  o b t a i n e d by the  fictitious  In  s u c h an a g g r e g a t o r  the p r o d u c t i o n p r o c e s s  Consider not  1968).  production  abstraction In  of  (Gorman  of  meaning.  existence  is not  identical  may  differ  technology.  does  not  technologies  convey  and  its  any  information  structural  on  form  is  uninformative. Third, it  is  amongst  an a g g r e g a t e to  individual  farms.  However,  T h e r e may e x i s t  different  different  contingent  upon  the  function n(P,R)  redistribution  distributions  of  this  of is  the not  structural  is  exact,  fixed  factors  the  case  forms of  K.  Therefore,  is  "well-behaved"  for  n(P,K)  n(P,K)  is  K.  Consequently, all  a  profit  invariant  n(P,K). for  if  even  if  n(p,K)  usual properties  of  a profit  function,  the  and  shows  aggregate  64 function  to  which  Moreoever,  there  of  factors  fixed  cannot  be  are  is  price that  conditions reason  dual paths  rationalized  regularity The  it  is  and an  contingent  initial  would  generate  by  technology  a  (Blackorby  for  also  this  quite  K.  distribution  aggregate  data  that  satisfying  and Schworm  is  upon  the  1982b).  simple.  The  aggregate  A production  function  estimated,  picks  supplied initial  and  is  up  the  obtained  aggregate  from inputs  corresponding  distribution  of  fixed  possibilities.  But  redistributed  among f a r m s ,  aggregate  factors  is  unchanged).  function, all  and f o r  it  is  in  fixed  factors  behavior The  data  is  research  the  of  aggregate  1)  he  value a marginal rely  on  generated  exact  will  unit  condition  for  of  the  a fixed or  technology (1)  of  course,  exact  data such  an  P  aggregator  However,  some i n i t i a l  who has  impose  aggregation;  on t h e  demand and s u p p l y  that  virtually  sets  relies  functions  on are  distribution  approximation  available  w i t h two c h o i c e s  can  measure are  an  provide  to  the  of of  quantities.  by a r e p r e s e n t a t i v e  separability If  of  researcher  faced  is  outputs  (given  fixed  (although  not  when  factors  aggregate  The hope  neighborhood  applied  project:  using  and t h e r e f o r e  really  is  the  a bogus f u n c t i o n .  aggregation.  useful  the  n(P,K)  really  as  farms c h a n g e s  When  empirical  fictitious  all  vectors  and a t t e m p t s  substitution  all  which,  demanded and  price  factors)  the  n(P,K)  holds  equally  that  all  and  and  (Blackorby over  all  impose  the farms  therefore  he can assume t h e  producer set  aggregate  abandoning  restriction  factor 2)  beyond  only  data  are  homothetic  1982). farms,  then  the  65 appropriate does  not  which  procedure  hold,  the  then  procedure  researcher's study  Schworm  is  exact  there  will  choice  aggregation.  is,  at  present,  generate  will  the  1982a).  The  generated  using  conditional  upon the  no way  best  depend g e n e r a l l y  and the c h a r a c t e r i s t i c s important aggregate  of  the is  data  must  to  if  it  determine  results.  on t h e  data  point  restrictions  However,  that  The  objective  (Blackorby empirical  be  of and  results  interpreted  imposed by  the  as  aggregation  procedure.  3.5  A  SINGLE-OUTPUT  COW-CALF  exists  defined  for  can  described e  of  beginning stock  of  decreasing (f4)  by  the  aggregate stock cows  cows  cattle  level  producer  e x p a n s i o n must described  as:  production This  aggregate  (q),  (C ), b  is  Assume t h a t  a  technology  representative  production  an a g g r e g a t e  F  e  quantity set  quantity  and a q u a n t i t y increasing F satisfies  in  function  i n d e x of defined index  beef for  of  i n d e x of q  farm  and  conditions  a  the  ending C  b  (fl)  but to  (3.2).  The p r o b l e m f a c e d industry  FOR A REPRESENTATIVE  production p o s s i b i l i t y  (C ). e  in Section  an  inputs  of  in C .  aggregate industry.  where Y i s  s u p p l i e d and F i s vector  an  the cow-calf  Y = F(q,C ,C ) b  FUNCTION  PRODUCER  Assume t h e r e  be  PROFIT  is  the  identical  except be  by  that  imposed.  representative to  that  f a c e d by t h e  the a d d i t i o n a l These  farm  the  individual  restriction  characteristics  at  on can  herd be  66  ( 3  '  r Y ,q ,C  1 8 )  t  t  1  t  Vo t=0  ^ 7  s.t.  C  (1+r)  variables  each v a r i a b l e , the  aggregate  the  animal  ability the  to  b  o  capacity  or  of  cows a t  predetermined.  inputs  the  stocks), Again,  leaving  last  optimal 6  t  As b e f o r e , across  the  carried revision profit t,  inventory (1+r)  the  t  +  of  the  That  because  the  output  f u n c t i o n can a g a i n  the m a x i m i z i n g b e h a v i o r  are  reduces  the  farmer  cows.  two-  t o a oneviews  the fixed  quantity  of  From t h i s  he  (end-of-period  as  valued  to  female  farm)  carryovers  period  stocks  ending  optimal of  as  industry's  any p e r i o d a s b e i n g  f i x e d stock  the  residual.  at  1  only  problem  the p l a n s  errors  p l a n s once t h e  that  farm from a  individual  is,  intertemporal  two p e r i o d s but out  period's  representative  carryovers t  the  constraint  inventory  current  except  Furthermore,  restricts  He must d e c i d e on t h e  optimal  (3.2)  industry.  b e g i n n i n g of  t o combine w i t h t h e  determines  E  beginning animal  this  of  the  Section  the  of  maximization problem.  number  t  s h o u l d now be i n t e r p r e t e d  for  stage maximization problem (for stage  in  next p e r i o d ' s  problem  t  t  constraint  Additionally,  maximization  t  lf  as d e f i n e d  representation  increase  W q :(q cJ,cJ.Y ) F],  > 0  accumulation  0  Y  where a p p l i c a b l e ,  reproductive  stocks.'  t  are  t t"  = (l+A)C*_  h  c  All  [ P  in  second  the  for  period  is  t=0 a r e  expectations  be u s e d t o of  (3.18),  solved actually  necessitate  arrives.  represent,  representative  A  i n any farm  .  dual period This  67 is  defined  (3.19)  as:  n ( P , W , Z ; C ) = max t  t  q  The  V  b  t  industry's  of-period Lemma  as:  (3.20)  Y* =  V ^ ° t  ~  )  V t  g C*.  +  t t C  supply,  input  demand, and e n d -  c a n be d e t e r m i n e d by a p p l y i n g  Equation  defined  (  o p t i m a l output  inventory  to  e  (3.19).  These  industry  Hotelling's  equations  are  n (P ,W ,Z ;C ), b  p t  q* = - n  t  w t  t  t  (P w ,z ;c t  t  t  b t  ),  t*= «t t» t» t f>-  c  n  where n i ( . ) i s to  pt,  wt,  the  level  of  z  ;c  partial  profit  demand, as  the  differential  respectively.  farm's  input  respectively, the  w  and z t  representative supply,  (p  fixed  with  n(.)  Y*t, q * t ,  respect  and C^* d e n o t e  maximizing q u a n t i t i e s  and  functions  of  of  output  end—of — period inventory  of  the  factor  C .  prices  (pt,  wt,  the  demand  and z t )  and  b  t Duality  techniques  predict  when t h e  number  of  price  of  1974)  industry  be  i n c r e a s i n g or  in  the h e r d .  The  an a n i m a l  in  the  can  differentiating  beginning-of-period (3.21 ) n b ( p ,w ,Z ;C ) c t t t t b  increase  industry's animal  will  animals  by  An  can be u s e d t o g e n e r a t e  m  in  shadow p r i c e  herd  is  be  Equation  animal shadow p r i c e herd  industry's  size greater  reducing optimal  determined  (3.19) of  with  t,W t ,Zt ;Ct) b  > price  respect  be  predicted  than  the  (flow)  an a n i m a l ,  the  (Diewert  can  of  to  shadow  stocks an a n i m a l i n t h e  or:  (3.22) ILb(P c  a formula  to  (C ), herd, b  if  price  the of  an  68 A decrease occurs.  in herd  can  has  (3.21)  model c h a r a c t e r i z e d  short  be  predicted  run  model:  interpreted  an  interesting  in Equation  consequently  subject  to  the  is  combining  the  information contained  Equation  possible  (See  (3.20).  In optimal  long  run  to  property.  The cow-  defined results  the long  in  fixed  as  a  must  be  factor.  run e s t i m a t e s  Equation  and  (3.21)  M o r r i s o n , and W a t k i n s  by  1982,  and  herd s i z e ) ,  the  1981).  equilibrium  shadow p r i c e  of  an a n i m a l  (at  optimal  must e q u a l  the  (flow)  price  can  be d e r i v e d  or:  (3.23)  n b(P ,W ,Z ;C *) = P . b  c  t  optimal  t  t  (3.24)  t  profit  s o l v i n g Equation  maximizing herd s i z e C  (3.23) g i v e n  wt,  zt,  and Pt  by  as:  b  t  t  substituting  desired changes  pt,  f c  c *= n*(P ,w ,z ,P ) , t  t  Long run c h a r a c t e r i s t i c s  3.6  of  obtain  Berndt,  Brown and C h r i s t e n s e n  by  opposite  (3.20) i s  level  it  The  the  econometric  However,  (Pt)  if  1 1  Equation calf  size  C°  into  measurements. in  price  can  SOME COMPARATIVE Using  obtained  Equation  for  changes  the  industry  Equation  (3.20)  Similarly,  the  can  be  obtained  and d e r i v i n g  response  be o b t a i n e d d i r e c t l y  of  form E q u a t i o n  C * b  the to  (3.24),  STATICS comparative  (3.20), in  the  optimal  variables  c a u s e d by a change  an a t t e m p t  to  sign  of  these  in  results,  static  levels  the the  of  results the  can  endogenous  exogenous p a r a m e t e r s . restrictions  be  implied  In by  69 duality  theory  and  imposed on t h e To  neo-classical  single  output  facilitate  production theory  profit  exposition,  will  be  model.  Equation  (3.20)  will  be  repeated: (3.20)  Y*= n  (P ,W , Z ; C ) , b  P  * = -nw (P ,w ,z ;c ), b  q  c  t  t*  =  n  <  current the  a change  in current  to pt - n  d?  n  c  t  consider  respect  where  t  p  due t o a c h a n g e  (3.25)  t  ? <' »VV t>t  First,  with  t  p  price  results t  output  (p ).  supply  (Y*t )  Differentiating  t  Y*t  in:  p (P ,W ,Z ;C ) t  in current  + H  b  t  p  .A.  (P ,W ,Z ;C ) t  z t  t  b  t  1  t  t  (.) t t price  represents  p  (pt)  the  change  holding a l l  second d e r i v a t i v e ) ,  other  (.)  n  is  i n Y*t  from a change  variables  positive  constant  by  in  (i.e.,  convexity  of  t t the  profit  function,  when c u r r e n t  price  implying  current  output  p  z  Generally,  increase  increases.  (.) r e p r e s e n t s t h e change i n Y*t from t t expected p r i c e (zt) holding a l l other v a r i a b l e s n  will  the  s i g n of n  (.)  is  a  change  in  constant.  unknown and w i l l  depend  t t on  whether  current  end-of-period  output  s t o c k of  by  the  indicates  that  in order  will  Consequently,  a substitute  animals.  imposed  animals  is  biological  be r e t a i n e d current  to  o r a complement  However, nature  of  the  in  output  the  herd at  the  restrictions  cattle  s u p p l y more c u r r e n t  with  production  output,  end o f  the  fewer period.  s u p p l y and e n d - o f - p e r i o d s t o c k  of  70 animals are s u b s t i t u t e s and the sign of n indicates  that  current  output  expected f u t u r e output p r i c e  i s negative.  pz  supply  will  This  decrease  when  increases.  3Zt  represents  the  change  in  expectations  about  f u t u r e p r i c e caused by a change i n c u r r e n t output p r i c e .  The  371  sign  of  will  price  i n r e v i s i n g h i s expectations  p o s i t i v e , negative, If  ^||.  following will  a  postive, increase If  and  may  be  = 0, t h i s i m p l i e s no change i n expected p r i c e in  current p r i c e .  determined  implying  by  the  The s i g n of  sign  of ^ P ( « ) p  that c u r r e n t output w i l l  which  t  is  i n c r e a s e given an  i n current p r i c e . 3  decrease  of the f u t u r e  or zero.  change  thus be  depend on how the farmer uses c u r r e n t  Z t  given  < 0, an  the  farmer  increase  c u r r e n t output w i l l again  expects  future  in current p r i c e .  increase because the  price  to  In t h i s  case,  positive  sign  of Hp p(.) i s r e i n f o r c e d by the p o s i t i v e s i g n o f (.) t t tt 3p Finally, i f .?... > 0, the farmer expects the f u t u r e n  P  z  t  z t  3Pt  p r i c e of animals to i n c r e a s e * p r i c e , then the sign of <* * if 3Zt > o then 9X1 £ 3Pt 3Pt Yt  9 p t  <  given  an  increase  in  current  will  be as f o l l o w s : 3zt 0 iff n >n t t t t * P  p p P  <  P  Z  d P t  3Zt  That i s , i f "gp-jT > 0, a negative supply response i s expected i n the short run i f the magnitude of It « i s smaller t t than n 3Zt *t t 3 P t p  7  It  i s of some i n t e r e s t to transform  an e l a s t i c i t y measurement:  Equation  (3.25) i n t o  71 (3.26) Total E l a s t i c i t y of Supply r8Yt 9Pt  . Ft, Yt  on t h e the  (3.26)  changes  of  of  the  in current  price,  in  that  f u n c t i o n does not an  total  elasticity  between  price  this  model,  and  cross of  elasticity of  of  in the  unknown a n d w i l l  total  rather  result,  (1969)  and Yver  supply  elasticity  holding other  cow-calf the  (1971)  by  how  in the  short  allowing  variables  d e p e n d on t h e  the  a short  s i g n of  the  it  future  constant.  Or  price  supply s i g n of  s i g n of  that of  the  negative  prediction  elasticity of  i n the  of  run  to  profit  the  not a  is  producers.  to p r e d i c t  Recall  is  the  p o s s i b l e that  able  run?  of  elasticity  expectations  models are  elasticity  of  is  the to  discussion  industry  is  and  of  with respect  Rather,  Therefore,  d e p e n d on p r i c e  this  obtained  supply w i l l  expectations.  animals,  the  this  today  elasticity  the c o n v e x i t y  ensure a p o s i t i v e  as measured by  production  by  of  dependent  the  expectations  as m e a s u r e d  following  a l s o d e p e n d e n t on  to ending stock  importance  from economic t h e o r y :  are  is  upward s l o p i n g s u p p l y c u r v e ) .  elasticity  Given  but  the  industry,  a s measured by t h e  farmers'  demonstrate  supply  structure  supply with respect  The  the  not o n l y  tomorrow,  expectations.  (i.e.,  supply  supply,  J  L  of  is  . Ft. Zt '  f  J  elasticity  possibilities  sensitivity  3Zt * 9Pt  r9HPt . Zt, 9Zt Yt  in  of  be  1  E l a s t i c i t y of Expectation  interpreted  elasticity  production  J  can  technological  substitution  output  1  The t o t a l  direct  Cross E l a s t i c i t y o f Output  r9IlPt . Pt-. 9Pt Yt  =  J  Equation manner.  Direct E l a s t i c i t y of Supply  the a  negative  their beef  Jarvis  to  context  results change of  the  72 model  developed  consequences  for  in current  this  chapter,  they  output  given  change  a  focus  on  the  in  expected  (3.25)  and shown  price: 9Y*  3Z  This  P Z  t  t  tt  derivative  t o be n e g a t i v e holding  current  output  models  are  output  all  that  other  supply.  not  in  but  3g*  =  anwt  3Pt  3Zt  = 3IIz  e  t  3P  (i) whether is  The  sign  the  input  normal,  then  conversely, Therefore, demand f o r  3P  the  + 3IIz  3z  t  of  is  p  the  are  inputs  sign  will  determined.  are  .  is  Yver the  of  interest:  i)  in  a  current  * 3Pt'  3z  3P  t  and  azt  t  of  animals  a  unknown and d e p e n d s on  inferior  input.  of  is if  non-inferior  to  .  is  negative  due  t  ^  sign  it  is  inputs  an  If  the  input  positive  and  inferior  implies  input.  that  the  increase.  The s e c o n d term on t h e Variable  t  a n o r m a l or  assuming inputs  t  decrease  misinterpret  due t o a change  and i i ) a change i n e n d i n g p e r i o d s t o c k change in c u r r e n t p r i c e ; 3C  Jarvis  they  are  demand  anwt  3Pt  the  will  future  d e c i s i o n s depend.  statics  input  in expected  constant,  rather  output  comparative  price ;  increase  variables  incorrect  current  an  Consequently,  on w h i c h c u r r e n t  Two o t h e r change  signed in Equation  indicating  price,  variables  was  right  chosen in  Therefore,  hand s i d e  is  easy  t h e model a f t e r  the  optimal  to  handle.  output  input  level  levels is  73 independent  of  expected  future  prices  and  consequently,  3nwt g of  = 0.  z t  input  the  This comparative  demand, t h e  static  structure  requirements,  of  indicates  technology  independent  of  that  alone  in  terms  determines  changes  in  price  are  opposite  expectat ions. (ii)  The r e s u l t s  of  this  comparative  static  *  3Yt  to  the  results  presented to  Young's  indicates  d i s c u s s i o n of  negative  indicates animals  and  that  given  there  is  Zt  a change  d  Z t  ,  identical sign  of  technology  Equation  is  the  price  of  "^f^  t e r m on t h e  increases,  change  s  a  ^  s  o  ceteris  a  in current  of  with  not  only  Equation  producers.  negative.  This of  paribus. of is  change  animals positive  negative,  price  The s i g n of  or  zero,  is  Therefore,  depend on t h e (3.25),  in  price.  discussion presented e a r l i e r .  expectations  positive,  does  3Zt  function.  to  as  right  3npt  of  This derivative  can  but  be  *  sign  in end-of-period stock  the p r o f i t  a  the  which  iL^I 3Pt  is  in end-of-period stocks  represents  given  the  it  model.  first  (3.25),  a decrease  ||iL  expectations  the p r o f i t  in expected p r i c e .  Finally,  However,  3Zt  t h e change  from t h e c o n v e x i t y  .  anpt  =  therefore,  when c u r r e n t drc, 3Zt  ^  that 3Pt  is  in  theorem to  artzt From t h e  7  for  show c o n s i s t e n c y  Applying hand s i d e  achieved  structure  depends  on  the of  price  74 3.7  A  MULTI-OUTPUT,  COW-CALF It  is  now q u i t e  model  output,  multi-input  maintain  five  the  consist  producer  of  operation  be s o l d ; the  the  animal  animal  for  of  the  of  animal  of  in  can b  vector  of  (i.e,  time  of  available  A  b  for  periods.  The  problems:  i)  is  more p r o f i t a b l e  to  price  an u n c e r t a i n  case,  the  e  is  animals,  an and  shows  combining  the  the  (1980)  technology  transformation  an I - d i m e n s i o n a l  A  retain  price.  an N - d i m e n s i o n a l  F(.)  or  and Denny  supply during that  function  his  it  animals, of  v a l u e of  to  by a c o n c a v e  is  cow-calf  which c a t e g o r y )  where q i s  output  will  of  stock  described  of  supply  out  a known o u t p u t  multi-capital  transformation  possibilities  two  and E p s t e i n  end-of-period stock  dimensional vector aggregate  over  present  (1977)  beginning-of-period stock  of  heifers,  multi-input  Epstein  qi),  consists  output  at  q = (q1 , . . . ,  (3.2)  cows,  future  = 0,  in Section now  the  ,Y)  will  f a c e d w i t h two b a s i c  animal  be  a multi-  categories.  animals  p e r i o d at  single  section  bulls,  e x p e c t e d net  is  of  this  F(q,A ,/f  inputs  (i.e.,  out  the m u l t i - o u t p u t ,  sale  sale  farm  function of  five  multi-output,  the  the  d e t e r m i n i n g whether  Generalizing to  farmer  animals  type  and i i )  This  stock  producer the  producer.  of  the  to d e s c r i b e  and c o r r e s p o n d i n g l y ,  from the  determining  producer  extend  set  capital of  to  assumptions  t o m a x i m i z e the  multi-output  the  the  objective is  cattle  cow-calf  and c a l v e s )  The  sell  straightforward  the  of  categories  steers, also  of  all  that  MODEL OF A REPRESENTATIVE  PRODUCER  output  except  MULTI-INPUT  vector  vector  of  N-dimensionsl Y  is  period.  an  NThe  technological  vector  of  inputs  75 w i t h the vector  vector  of  s u p p l y as  beginning stock  of  of  cows and the  the  is  increasing  individual  residual. the  F(.)  vectors  of  components of  any  point  factor  prices  prices  is  are  in  the  vector  A .  the  The  select  it  the  known but  probability  q and A ; b  time,  uncertain.  subjective  of  distribution  and t o  of  the  d i s c o u n t e d sum of  anticipated  future  planning horizon,  subject  stocks,  animal  a strategy  the  accumulation  vector  to  of  the  output  individual  decreasing  of  of  current  next  in  the  output  and  is  period's  assumed  concerning  t o m a x i m i z e the  of  equations  vector  the  e  vector  producer  to determine  in  is  vectors  prices  animal  animals  end-of-period stock  components of  At  of  profits the  price  to  this  have  a  vector  of  expected  over  a  value  two-period  initial  vector  expectations,  and i d e n t i t i e s .  output  This  and  of the  strategy  c a n be summarized a s : (3.27)  max  subject  to A  and.the  following i )  i i ) .... ill)  known  identity  C  =  b  X- tV V t' t'V w  A  A  E F l  t  +  e  RHt_  ,  1  , e +A2Ca _j t  b e e , e H = H,.^ -RH,..! + * 3 C a _ t  t  p  is  c §  / e e (C _ + R H _ t  1  a current  in period is  (  restrictions:  e , e = B _^ +X 1 (Jt-1 ,  t  t  t  [ p  b B  _ b €3^.=  t  t-0" (lb  >> 0,  » v)  w known  b  b S =  . . iv)  where  1  E  E  e  1  ),  period vector  of  output  prices  assumed  t,  a current  in period  t  1  t,  period vector  of  input  prices  assumed  76 ^ steers,  is  i  percentage  and h e i f e r s §  bred  the  is  the  that  of  e  d e n o t e s end of  period,  A  is  of  of  vector  become b u l l s ,  replacement  heifers  in p e r i o d  t,  period,  animals  s t o c k s c o n s i s t i n g of  five  animals,  B  is  the  stock  of  bulls,  C  is  the  stock  of  cows,  S  is  the  stock of  steers,  H  is  the  s t o c k of  heifers,  Ca  is  the  stock  calves,  RH  is  the  stock of  The a n i m a l more  and  successfully calved  d e n o t e s b e g i n n i n g of  categories  that  2  cows  b  a  calves  respectively,'  percentage  i n p e r i o d t-1  of  of  replacement  accumulation  complicated  in  interrelationships  and  the  heifers.  constraints  multi-output  between  the  are  significantly  c a s e and r e f l e c t  different  the  categories  of  animals. Constraint period at  t  the  calves  is end  that  i)  shows t h a t  identically of are  the  equal  the to  previous  retained  number of the  bulls available  number of  period plus  as b u l l s  at  the  bulls  left  over  the p e r c e n t a g e  end of  the  in  of  previous  period. Constraint available cows  in p e r i o d t  left  number of previous  ii)  over heifers  period.  at  indicates is  that  identically  the  entering  end of the  the  the  equal  number  to  cows  number  of  previous period plus  the  b r e e d i n g h e r d at  the  of  the  end of  the  77 Constraint beginning steers of  of  at  the  calves  iii)  shows  period  t  end of  at  is  the  the  that  the  identically  previous  end  number of  of  steers  equal  to  period plus  the  previous  that  the  the  the  at  the  number  of  percentage  p e r i o d that  become  steers. Constraint  iv)  beginning  of  the of  heifers  calves minus  at  at  the  the  period t end of  end  replacement Finally,  indicates  of  the  heifers  constraint  v)  period t  and  replacement  heifers  In in  the  any  each  t,  category  on t h e  optimal  fixed  stock  of  of  current of  output  farmer  output  as  he e x p e c t s  discounted to  the  are  female,  herd.  number of  calves  percentage that  of  of  at  cows  successfully  t.  f i x e d or p r e d e t e r m i n e d .  He must  v i e w s the  of  the  inputs which  number  to combine  with  the  for  each  stock  and  he d e t e r m i n e s ,  end-of-period  residual.  are  for  present  the  optimal  in each category  price  to  number  percentage  breeding  the  the  animals  from  the  to  at  of  quantity  animal,  the  i n p e r i o d t-1  period  being  the  heifers  p e r i o d which  that  equal  bred  animals  period  animals  is  the  as  decide  category  shows  b e g i n n i n g of  period  enter  of  equal  plus  previous  that  b e g i n n i n g of  at  identically  p e r i o d t-1  the  calved  is  number  valued  End-of-period  by t h e  each animal  farmer  category  stocks at  next  the  period  or:  (3.28) z  where z  it J  it  =  [ 1  1  ( 1  +  r  )  = (z, it  * t *it-1 E  z  (  nt  )  is  ) ]  '  1  =  l  f  ••'  ' ' n  d e f i n e d as a v e c t o r  of  expected  prices. A  multi-output,  multi-input  dual  profit  function  can  be  78 used t o r e p r e s e n t ,  i n any p e r i o d t , t h e m a x i m i z i n g b e h a v i o r o f  the  producer.  representative  This  i s defined a s :  (3.29)  n(P ,W ,z ;Ap = max  [P'Y - W'q. + z» A*: (q ,A£,A* Y ) € F ] /  t  t' t' t  Y  q  The r e p r e s e n t a t i v e demand,  farm's  and end o f  applying Hotelling's  A  vector  period  of o u t p u t  inventory  Lemma t o E q u a t i o n  supply,  input  c a n be d e t e r m i n e d by (3.29).  These e q u a t i o n s a r e d e f i n e d a s : (3.30)  * Y  b  it  " "p  <j\  =  lt  =  A  where Y * t , profit  ( P  t  - w. n  ( t  t  , W  , z  t V  i=l,...,n,  s  V t'V t) W  i =1  A  ^ t ' W ^  q * t , a n d A*  maximizing  1,  i = l,...,n, are  quantities  the  representative  of output  supply,  and end o f p e r i o d s t o c k demand r e s p e c t i v e l y , the  vector  f i x e d stock It  of  prices  (p  of a n i m a l s ,  A  b  (3.5),  estimates described The postulate for  the  similar  i n Section system  of  Equation  Moreover,  Equation  (3.29) long  can again  (3.21)  of animal can  with respect to run  be  structural  determined  equations  in  (3.30)  c a n be  used  an e c o n o m e t r i c model by s p e c i f y i n g a f u n c t i o n a l  equation.  in  as  (3.5).  the vector  p r o d u c e r s , and s p e c i f y i n g  each  to  f o r each c a t e g o r y  technology  n ( . ) , determining  cattle for  of  stock.  of  t  a shadow p r i c e  appropriate  functions  , w , and ^ ) and t h e l e v e l s of t h e  be o b t a i n e d by d i f f e r e n t i a t i n g the  i n p u t demand,  .  s h o u l d be n o t e d t h a t  Section  f c  as  producer's  However,  the  of p r i c e  to form  expectations of  stochastic  before attempting  disturbances t o estimate  79 this  s y s t e m of  statistics  equations,  the  available  to  underlying transformation  3.8  are  describe  and  the  function w i l l  structure  In  an i n d u s t r y ,  d e s c r i b i n g the in  technology  determining  how  and among o u t p u t s change  variables.  Generally,  curvature  curves  substituted interest  of  rate  at  in p r o d u c t i o n ) .  are  supply.  the  the  Of  price  course,  relationships  changes  isoquants which  production  One  of  of  (i.e.,  fixed  ease  with  the  production  input  the  input  ratios  (q±/q^)  to changes  rate  of  measurement a  of t h e I  ±j = £  where F,  =  cofactor  of  9F  (F i / F j ) .  is  the  on  the  inputs  may  be  in  the  The n o r m a l i z a t i o n i s  invariant  of  n o r m a l i z e d change o f  t o changes 3  in the  the  marginal such  that  scale  of  is  the  (1974)  notion  of  l l> F  1  bordered hessian  2  of  output  inputs:  8 F / dq^q^  Diewert elasticity  , F  of  the H i c k s - A l l e n e l a s t i c i t y  with respect  < V k !•*«!>  = 1  measures  demand and  which  (a^j ) w h i c h m e a s u r e s  is  transformation  factors).  substitution  a., ij  structure  conditional  in  and t h a t  among  exogenous  the  other  substituted  = a., ji  is  the  i n p u t s or o u t p u t s may be  s u c h measurements a r e  substitution  in  and  Additionally,  elasticities  a s s u m p t i o n s of  measure  the  given  of  researchers  these measures determine  properties  (i.e.,  of  summary  be p r e s e n t e d .  PRODUCTION  inputs  a.. ij  other  CHARACTERIZING THE STRUCTURE OF  interested  and  elasticities  _ F and F  i n |F|.  extended  substitution  of  to  and the  g e n e r a l i z e d the multi-output,  multi-input  80 variable  profit  function  by  defining  the  following  elasticities: i) variable °ih  ( P  an e l a s t i c i t y  of  transformation  input q u a n t i t i e s t» t W  t»  , z  ; A  t  )  =  (  n  p  t  »  w  output  i and h d e f i n e d f o r  each p e r i o d  ' t  ,  z  t  between  ; A  t  *  )  3 2 n  (')/3P 3P ±  h  Ih -  and t:  l,...,n.  [3n(.)/3P ] • [3n(.)/3P l. h  ±  ii)  an e l a s t i c i t y  and k d e f i n e d f o r  of  s u b s t i t u t i o n between  each p e r i o d =  n  (  ,  '  )  9 2 n  i  an e l a s t i c i t y  and f i x e d Y  ij  ( p  factor  t' t' t w  z  ; A  t  )  j =  of  j  t:  (»)/  9 A  [3n(.)/3Aj] . iii)  fixed inputs  ^ ^  .  A  jk=l,...,n.  [3II(.)/3A£]  intensity  defined for  between  variable  each p e r i o d  n(.)a n(.)/3P 3A 2  t:  ,  b  1  quantity  ij » 1  n.  [3n(.)/3p ] • [ a n ( . ) / 3 A ] b  ±  These e l a s t i c i t i e s of  variable  factors changes  p r o v i d e m e a s u r e s of  outputs,  to changes in  inputs,  in p r i c e s  quantities  Hotelling's  of  Lemma and t h e are  measurement  and f u r t h e r m o r e  ih  = a  hi  '  V  Diewert of of  (1979)  rank a t  of  a  n  d  Y  ij  has a l s o  prices  factors.  of  the  following  fixed  inputs,  and  W i t h the h e l p of  symmetry c o n d i t i o n s , a l l to  the  results  three  scale are  of  obtain,  " J I Y  shown t h a t :  transformation  most e q u a l  responsiveness  outputs,  n o r m a l i z e d t o be i n v a r i a n t  • V  elasticities  shadow  variable  fixed  usual  elasticities  a  of  and  the  is  a)  the matrix  positive  to n-1: c o n s e q u e n t l y ,  a  [a  ih  ]  semidefinite  and  ^  and  >  0,  vi;  81  b)  the  matrix  negative  3jj £  addition  number  of  k  semidefinite  consequently, In  [$j ]  of  Q,  to  at  (Ph) ih  Of c o u r s e ,  =  9 Y  above  measures o f  end o f  of  output  supply  =• l , . . . , n .  '  elasticity  of  to  is n-1:  substitution,  (Yi)  properties: with  respect  t:  can be d e f i n e d f o r  p e r i o d s t o c k of a n i m a l s  a  c a n be d e f i n e d  the c u r v a t u r e  i  this  equal  elasticities  each p e r i o d  P  substitution  most  measures  defined for * h  of  vj •  the e l a s t i c i t y  £  rank  non-normalized p a r t i a l  i)  and  of  the  to p r o v i d e a l t e r n a t i v e  to p r i c e  elasticities  (A ) e  i n p u t demand  u s i n g the  (q)  appropriate  prices. ii)  the  k defined for n  inverse  price  each p e r i o d  jk "  ' ^  elasticity  of  fixed factor  j  and  i  with  t:  '  = l,...,n.  .b where Rj  is  iii) respect  the  shadow p r i c e  of  the  elasticity  of  to the  S^j  jth  •A  =  3A J b  iv)  the  with respect for  b  the  jth  fixed  factor.  variable  d e f i n e d for  quantity  each p e r i o d  t:  ij = l,...,n.  Y i  elasticity  of  fixed  to the p r i c e  of  the  each p e r i o d  factor  ith  j's  variable  shadow  quantity  price defined  t:  - i i . • I*.  . Finally,  fixed factor  the  it  can be shown t h a t  the  following relationships  hold  82 between Kohli  the  normalized  and n o n - n o r m a l i z e d e l a s t i c i t i e s  (see  1976): i h "-. ih  a  e  B  Y  V  jk "  ij  C  =  where S i =  i3  1  1  '  S  k  s  8  h  TESTING  hl  \ j P  =  fixed  input  that  stated  In  this  Lau  (1972)  if  of  revenue  revenue.  a  the  can  properties  be p r e s e n t e d w h i c h d e s c r i b e on  that  function  MULTI-INPUT  for  such  the  section, these  where  profit  parameters  as  of  the  structure  of  a number of  properties. of  the  the This  homogeneity,  of  proofs  function  be r e c o v e r e d .  and j o i n t n e s s  by t e s t i n g  function.  of  conditions,  separability,  c a n be d e t e r m i n e d  share  share  FUNCTION  transformation  homotheticity,  j's  i's  USING A MULTI-OUTPUT,  regularity  indicates  relies  quantity  FOR STRUCTURE  certain  underlying  profit  V  1  has been p r e v i o u s l y  satisfies  result  i '  S  variable  VARIABLE PROFIT It  1  J1 / Si,  is  and S j = R j A j / n i s  3.9  e  =  J  P iYi/n  =  technology the  dual  theorems This  will  section  theorems may  be  found. Before  stating  the  theorems,  several  definitions  must  be  established: Definition of  outputs,  fixed k2,  q is  factors,  k 3 , a n d k4  scalar  1):  A function  a vector is  of  F(Y,q,A)  inputs,  s a i d t o be a l m o s t  iff  F (A  2):  An a l m o s t  k  l  Y, A  k 2  q, A  k 3  and  where Y i s  vector  of  homogenous of  degrees  ki,  =A  k 4  is  vector  a  A)  A  a  F(Y,q,A)  for  any  * > 0.  Definition  homogenous f u n c t i o n  satisfies  a  83 modified Euler  Theorem:  kl£3F Y. + k2E3F q., + k3E3F A = k4F. i i q  3Y  3q  ±  Definition said  to  fixed)  be  if  1  3):  3A  ±  ±  A multi-output,  separable  there exist  in  multi-input  outputs  functions  and i n p u t s  f and q s u c h  technology  is  ( v a r i a b l e and  that:  f(Y) - g(g,A) = 0. Definition joint  in  4):  A function F(Y,q,A)  inputs  if  there  exist  is said  to  be  non-  individual  production  t h e r e a r e no e c o n o m i e s o f  jointness;  functions: Y  i  =  l  f  (  X  i l  X  with the p r o p e r t i e s : and  ii)  i n i)  V  V  l  j  '  t h e r e a r e no d i s e c o n o m i e s of  Assume both F ( . )  that  and  n  the r e g u l a r i t y  (.).  Then  jointness.  conditions are s a t i s f i e d  the  following  theorems  can  for be  stated. Theorem degree  1):  A  production  k i n A , k>0, i f f  homogenous o f d e g r e e  function  the v a r i a b l e  1 a n d 1/k i n  profit  prices  is  homogenous of  function and  is  fixed  almost, factors  respectively. Theorem separable H  are  2):  production  function  is  i n Y , q , and A o r F ( G ( Y ) , J ( q ) , H ( A ) )  homogenous  function  A  of  degree  one,  iff  homothetically  where G , J ,  the v a r i a b l e  and profit  is defined as: n* = n(G(P), J ( q ) , H(A)).  Theorem 3 ) : separable  A multi-output,  in D e f i n i t i o n  3)  iff  multi-input  the v a r i a b l e  technology  profit  function  is is  84  defined  as: n ( f ( P ) , g(g,A)),  which of  implies  q and t h a t  that the  Theorem 4 ) : iff  the  the  A production  is  of  independent  i n d e p e n d e n t of  non-joint the  p.  in  inputs  variable  profit  holds: 2  3  To  these form  functional  form t h a t  and  functional  n(.)  does not the  Appropriate property.  of  analysis.  must  be  impose  to  postulated the  the  properties  to  a be  of  the  must  be  t e s t s c a n be p e r f o r m e d  necessary  a  to  parameters  be c a r r i e d  i n c l u d e s a d i s c u s s i o n of data  (i.e.,  properties  on t h e  these  statistical  operational,  Such a p r o c e d u r e w i l l  which a l s o  transformations  empirically  restrictions  form c o r r e s p o n d i n g  Four,  empirical  V ij.  theorems for  then  determined. each  j ,  P  make  tested)  r  VJ  functional  Chapter  function  differentiation  9 n(P,g,A) = O i  test  supply equations are  i n p u t demand e q u a t i o n s a r e  following  function  output  out  the d a t a  undertake  to in and the  85 FOOTNOTES TO CHAPTER  1  Cow-calf  farmers  existing  stock  prefer  THREE  to reproduce  in order  to m a i n t a i n  female  animals  the g e n e t i c  from  base of  the  herd. 2  Very In  few a n i m a l s 1982  purpose 3  there  imported for  where  (Agriculture  The v a r i a b l e authors  are  Canada  profit  This  section  5  For  6  Separabilty  relies  alternative is  breeding.  imported for  this  defined  some  1982). is  restricted  entirely  also  profit  on D i e w e r t  a s s u m p t i o n s on f ( . ) consistent  m a k i n g - - see B l a c k o r b y ,  p u r p o s e s of  1830 a n i m a l s  function  as a g r o s s o r  4  only  the  Primont,  function. (1973)  see Lau  with  by  and  (1974).  (1974).  decentralized  and R u s s e l l  decision-  (1978)  Chapter  Three. 7  See  Blackorby,  alternative 8  Primont,  and  Russell  (1978)  for  an  definition.  T h e r e have been a number of a t t e m p t s separablity Christensen  in  cost  (1973),  and p r o f i t  Denny and  to t e s t  functions—  Fuss  (1977),  for  consistent  see B e r n d t and  and  Woodland  (1978). 9  A  number  of  describing  Primont,  10 F o l l o w i n g  a  restriction  periods,  have u s e d t h e  aggregation  Blackorby,  increase  authors  and R u s s e l l  change  in  stock  of  (Gorman  when  (1968)  and  variable  the  (1978)).  an  on h e r d e x p a n s i o n w i l l  its to  problems  term " f i c t i t i o u s "  animals,  exogeneous limit over  r e a c h a new e q u i l i b r i u m l e v e l .  the a  industry number of It  should  to time be  86  noted  however,  that  h e r d by s l a u g h t e r i n g 11 E q u a t i o n greater  the  animals.  (3.22)  indicates  value  on t h e  could obtain  i n d u s t r y c a n r a p i d l y decrease the  by s e l l i n g  that  animal  in  it,  the  probability  that  if  the  farmer  the h e r d t h a n farmer  places  a  the v a l u e  he  will  retain  the  birth  to a  animal. 12 Assume t h a t male  (or  consistent female  the  female)  animal  with t y p i c a l  animals.  is  a cow w i l l 0.5.  biological  This  give  assumption  is  r e p r o d u c t i o n of male  and  87 4.  4.1  VARIABLE SPECIFICATION AND FUNCTIONAL FORMS  INTRODUCTION The p u r p o s e of  this  chapter  is  to d i s c u s s  the  methodology  employed i n p o s t u l a t i n g an e c o n o m e t r i c model and the  data  first  used  stage  requires  in  generating  in estimating  specifying  p r e d i c t i n g next  the  some  the  econometric  s y s t e m of  expectation  process  exactly  expectations  of  the  price  expectation time  procedure  series  average  expectation  the  (4.3),  system  equations  of  discussed.  predict  on a Box and J e n k i n s  (1976)  integrated  to  moving  represent  in  (3.30),  cow-calf  f a r m s and a s s o c i a t e d  different  the q u a n t i t y  inputs  Finally, different  specification  and  in  iv)  Section versions  of  to  and  of  the  the  facilitate to  the  stocks the  estimate information produced  ii)  cattle  the  functional  the  econometric  model  equations  is by  prices;  associated cattle.  forms a r e and  the  quantity  input  and  b e g i n n i n g s t o c k s of  (4.4), of  of  As  econometric  outputs  prices;  cross-  reported.  following  different output  sets,  u s e d on farms and a s s o c i a t e d  end-of-period  expected p r i c e s ;  identified  data  Specifically,  i)  for  a  This  necessary  required:  the  p o s i t e d to  alternative  are  transformations are  iii)  (4.2),  in  producers.  hypothesized  two  and t i m e - s e r i e s ,  estimation  of  is  (3.30)  t o be u s e d  Section  an a u t o r e g r e s s i v e  is  in  The  process.  Section  sectional well,  model  In  cow-calf  based  method whereby  (ARIMA)  In  is  results.  process  prices.  "quasi-rational"  describe  equations  expectation  period's cattle  to  the is  specified stochastic examined.  88 Furthermore,  null  statistically  the  linear  variable  homogeneity  "almost  hypotheses  in  presented  profit  in p r i c e s ,  homothetic"  are  function  non-joint  outputs,  for  testing  for  symmetry,  production in  and " a l m o s t  outputs,  homogeneous"  in  outputs. Before examining appropriate generating  to the  summarize final  the  theoretical  the  specification  multi-output, Douglas  expectations the  form  of  a simple  is  imposes  was  well  chosen.  elasticity  of  as  well  profit  of  to  overall  In  other  words,  that  to  profit  than  case  output  case.  2  for  ratio  revenue  overall  condition but  of  is  is  complexity  of  procedure)  represent A  the  Cobb-  with  p e r i o d are  the  exactly  functional  amongst  inputs  multi-output  one f o r  all  an  is  not  prices,  the i,  ith  is  by t h e  always s a t i s f i e d  in  t o be s a t i s f i e d the d a t a  the  output  required.  from e a c h o u t p u t must  generated  of  it  and  Cobb-Douglas  in output of  form  production  However,  revenue  lag  1  on the  to one).  generated  Casual observation  in  combined  own-prices.  total  unlikely  followed  function.  next  convexity  profit  be  initial  properties  than  would  a polynomial d i s t r i b u t e d  the  satisfy  was  Cobb-Douglas  equal  be g r e a t e r  the  the  this  output  the  it  form t o  was  complementarity  that  the  of  an  profit  prices  annual  substitution  that  (as  This  curvature  (i.e.,  known,  restriction  clear  past  known t h a t  function  greater  of  restrictive set  The  variable  expectations  1965)  technology  results.  functional  r e p r e s e n t e d by t h e p r e d i c t i o n s  It  that  statistical  multi-input  (Almon  procedure  model n e c e s s i t a t e d  assumption that  model  formation,  firm. the  is  single  i n the  sample  It  be  multi-  used  in  89 this be  study  revealed  that  these  convexity  c o n d i t i o n s would  satisfied. To c i r c u m v e n t  aggregate  output  this  problem,  price  it  was d e c i d e d t o g e n e r a t e  index u s i n g a t r a n s l o g  but m a i n t a i n i n g a C o b b - D o u g l a s s t r u c t u r e The  translog  flexible on  functional  functions  revenue  second  for  order  in  the  prices.  the  as w e l l as  the  and  of  the  With  in  the  price  are  input  function 1974). local  very  the it  the  determined was  convex  t h e n employed profit  the These  translog  distributed  price  lag  price  of  the greater  Cobb-Douglas flexibility  both  a  This greater  flexibility  multi-input  (Christensen,  Jorgenson,  functional an  is  achieved  variable and  Lau  lag by  translog 1971  form can p r o v i d e a arbitrary  of  flexible  and a p o l y n o m i a l d i s t r i b u t e d  to  in  function.  Cobb-Douglas,  while maintaining  approximation  was  satisfactory.  multi-output,  This  checking  i n A p p e n d i x D.  success  prices  index  s i g n s of  index  aggregate  polynomial  reported  prices  output  a  were  the  was d e c i d e d t o a l l o w  expectation process. specifying  of  restrictions  after  i n d e x was  estimated  initial it  in  nature  estimated  the  specification,  order  and  checking  price  g r o u p of  T h i s aggregate  case  3  side.  the  require  the H e s s i a n m a t r i x ) ,  estimation  e x p e c t a t i o n model,  Diewert  convexity.  (i.e.,  restrictive  results,  profit  does not  an  form  input  member of  a n o r m a l i z e d Cobb-Douglas v a r i a b l e  of  structure  such,  aggregate  results  structure  a  estimated aggregate  This  Within  index  is  three-output  functional  on the  form  satisfy  the  roots  fact,  estimating  to  conditions  characteristic that  a n d , as  shares  was e s t i m a t e d  in  not  and  second-  function.  In  90 addition,  it  estimation  of  arbitrary  function  1975).  This  priori  has the  first  that  three-input, empirical  one f i x e d  model  Appendix  of  of  approximation are  not  an  (Hanoch  imposed  a  choice.  factor  case.  generated  performed  time-series  using  of  for  An  the  data  this  flexible  These  of  the  functional  process,  results,  choice,  base,  three-output,  examination  expectation  well.  elasticities  use  of  an  expectations  assumes  prices.  was  It  expectation  Almon a  process  (Nerlove,  et  of  al.1979).  (ARIMA) m o d e l . multi-output,  econometric  It  multi-input  t h e main e m p i r i c a l  model.  Econometric time-series  is  verified including  are  also  to  generate  naive process a  more  reported  in  accurately producers  and  results.  are  achieved  expectations  approach  price  of  generated  base and a r e  actual  consequently  expectations a time  combined  translog profit  specification  price  T h i s was  process,  variable  predicting  represent  by t h e p r e d i c t i o n s o f  results data  for  price  "rational"  assumed t h a t  expectation  provides  sectional,  model  "quasi-rational"  exactly This  more  cow-calf  Nerlove's  represented  that  would  more e f f i c i e n t  adopting  lag  rather  decided  expectations  provide  allow  D.  The  price  of  restrictions  combined w i t h an Almon l a g  estimates  Five.  point  to  derivatives  f u n c t i o n was e s t i m a t e d  results  the  are  of  parameters  order  a combined c r o s s - s e c t i o n a l ,  a translog profit  by  the  on e l a s t i c i t i e s  form,  number of  and s e c o n d  at  implies  Using  that  a sufficient  the  with  a  function, theoretical  using  reported  series  in  a crossChapter  91  data  In  addition  set  is  cyclical  also  of  the  cross-sectional in  beef  measurements  compared t o the  the  utilized  nature  elasticity  of  to  the  the  cross-sectional  profit  beef  time-series  Because  data  set  cycle  results  a  function  number of are  not  variables  available  Specifically,  this  total  profits,  crop production,  used  on  current input  cattle prices  for  equations  of  the  will  which  allow  can  during a single  labour,  of  because  the  translog variable  be  period  functional research, data  these  sample  procedure.  cross-sectional  PRICE In  include  include  data,  net  demand.  It  variable  is  equations  results  not  Instead,  are  maintaining results  absent  used.  are  inputs on  prices, services,  a To  output  output  is  supply  the  normalized complete  and that  data,  specified  for  a the  quadratic  the  empirical  the  time-series  "quasi-rational"  expectation  reported  in Chapter  with  supply  unfortunate  from  be  estimated a  and  on  farms.  inventory  be  of  crop  and m a t e r i a l s  could  basis.  information  prices,  cattle  form  for  the  information  quantities  does  time-series  will  These  the  on c o w - c a l f  function.  form  or  to estimate  time-series  total  functional profit  a  does not  capital,  be s p e c i f i e d  profit  on  It  cattle  end-of-period  required  expected c a t t l e  available  will  set  farms.  prices,  inventories  total  data  cow-calf  From the  4.2  this  a  cycle.  However,  and  estimation.  production,  oyer  data,  and  compared  to  the  Five.  EXPECTATIONS  specifying  the  variables  used  in  the  econometric  92 model,  it  w o u l d be p r e f e r a b l e  representation futures  of  prices  precluded  for  whereas  this  categories quoted  expected  for  their  available  in  rates.  requires  price  prices.  of  and  some  prices  c o m b i n a t i o n of periods  include  a  time  weighted of  al.  (1979)  moving a v e r a g e of  Muth's  time  series  a  the  time  the  basic  Nerlove  s u c h an  rational  of  advantage series  it  of  allows  to time  a fully series  prices  are  for  use  in  expected in  this  predicting  these  expectation  exactly  by  generated  of the  back  p  g o i n g back q p e r i o d s ,  as  prices  going  Interestingly,  many of  solving  formation  exogeneous  because  all  Nerlove,  autoregressive  approach to e m p i r i c a l  properties  refers  the  for  a  require  expectation  are  (steers)  their  intergrated  the  expectations model.  a p p r o a c h d o e s not  function  important  (1976).  prices  using  past  (ARIMA) model e x h i b i t s  model t o d e t e r m i n e as  of  problems  necessary  farmers'  model  random d i s t u r b a n c e s  (1961)  that  represented  averages  shows t h a t  is for  series  d e s c r i b e d by Box and J e n k i n s et  it  cow-calf be  futures  prediction  process  can  two  animal  implies  a  provide  predictions  b)  this  be assumed t h a t  cattle  predictions  and  does  futures  feeder  and  Consequently,  unobservable  future  a)  study  define  will  study:  on f a r m s ;  market-determined  However,  of  must  a  The market  category  to  It  this  funds  exchange  prices.  one  U.S. studies  define  animals.  in  animals  Canadian  research  beef  use  only  of  to  (i.e.,  properties Moreover,  the  complete  expected  parameters).  This  one t o a p p l y more research  rational  expectation  a  price is  an  easily  yet  maintain  expectation  approach.  f o r m a t i o n as  "quasi-  93  rational". For  this  ARIMA(p,q) model.  study,  function  The  the  procedure  f o r each  general  expected  specification  w i l l  be t o e s t i m a t e  price  of  variable  an ARIMA(p,q)  in  an the  model  can  b e w r i t t e n a s : (1 - <\>  - <|> $ - . . . - <f> 3 )A Y 2  l  where  B  is  2  P  p  the back  d  shift  = 6 (l  t  t  - 0 3 -0 3 X  -  2  2  q  q  )et'  operator,  .d  .  A Yt  is  the observed  ^t  is  a  <$  is  an  <l  a n d 0^ a r e  t  This  - 0 3  ..o  )  i  model  random  variable  disturbance  intercept  term,  d  times,  term,  the c o e f f i c i e n t s  = 6 + 0(3)  t  d  and  c a n be c o n v e n i e n t l y  A Y  differenced  t o be  rewritten  estimated. as:  e . t  <f>(8) Average five  annual  major  Edmonton,  auction  Regina,  Agriculture each  each  of  Saskatoon, An  animal  estimated  market  w i l l  equations  for the  other  In  and Winnipeg)  market  were  be  only  presented  market  1983,  Canada were  model  for  (Calgary,  provided  by  was e s t i m a t e d  for  location."  not s i g n i f i c a n t l y  Therefore,  market  1946 t o  western  ARIMA(p,q)  results  location.  in  in each  Calgary  Appendix  for the period  markets  Canada.  category The  prices,  the  results  here.  locations  different  The are  for  in the  estimated  reported  in  E. Figure  autocorrelation presented.  4 . 1 , a  graph  functions  An e x a m i n a t i o n  of  the autocorrelation  for of  the  the  steer  structure  and  price of  these  partial  series  is  functions  9* FIGURE 4.1 Plot  of A u t o c o r r e l a t i o n and P a r t i a l A u t o c o r r e l a t i o n F u n c t i o n , Steer P r i c e S e r i e s , C a l g a r y  PLOT OF PARTIAL AUTOCORRELATIONS  LAG 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  -1.0 -0.8 -0.6 -0.4 -0.2 CORR. + + • + + 0.859 -0.265 0.040 -O.116 0.237 0.058 -0.113 -0.030 -0.088 -0.017 O.067 -0.129 -0.069 -O.083 O. 104 -0.061 -0.088 -0.036 0.036 -0.025 -O.087 -0.018 -O.093 -0.067 0.022 O. 109 -0.012 -0.084 -0.117 0.068 0. 1 15 -0.033  •  0.0 0.2 0.4 0.6 0.8 * * * * I IXXXXXXX+XXXXXXXXXXXXX 44 +XXXXXXXI 4< 4IX 4+ XXXI 4IXXXXXX 44+ IX 4+ XXXI 4+ XI 44XXI 44I 4+ IXX 4+ XXXI 44XXI 4+ XXI 441XXX 44XXI 44XXI 44XI + 4IX 44XI 4. 4XXI 4+ I + 4XXI 44xx^ 4+ IX 4 4IXXX 4+ I 44. XXI 44XXXI 4 4 1 XX 4+ IXXX + + XI +  1.0 *  PLOT OF AUTOCORRELATIONS LAG 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  -1.0-0.8-0.6-0.4-0.2 CORR. + 4+ + + 0..859 0..669 0..510 0..360 0.,290 O.. 28 1 O..251 O..210 O. 147 0. 065 0. 017 -0. 026 -0. 078 -O.. 123 -0. . 146 -0. 167 -0. 192 -0. 209 -0. 214 -0. 22 1 -0. 239 -0. 247 -0. 264 294 -o. 306 -0. -0. 275 -0. 223 -0. 178 -0. 169 -0. 17 1 -0. 150 127  -o.  444^ 444-  + 444444-  • 444444-  + • 444. 4444> 44-  0.0 0.2 0.4 0.6 0.8 4. 4+ + 4I + IXXXXXXX+XXXXXXXXXXXXX IXXXXXXXXXXXX+XXXX IXXXXXXXXXXXXX 44IXXXXXXXXX 4IXXXXXXX 4- • IXXXXXXX 4IXXXXXX 4IXXXXX 4IXXXX 4IXX + I 4XI + XXI 4XXXI 4XXXXI 4XXXXI 4XXXXXI 4XXXXXI 4 XXXXXI 4XXXXXXI 4XXXXXXI 4. XXXXXXI 4XXXXXXXI XXXXXXXI + 4XXXXXXXXI XXXXXXXI 4XXXXXXI 4XXXXI 4XXXXI 4XXXXI + XXXXI 4XXXI 4-  1.0 +  95 suggests  that  correct  this  differences.  the  series  problem, A  5  is  reproduced in Figure  in Figure  specification in  the  of  first  p r o c e s s of  of  component  find  best  After  diagnostic  these  The A R I M A ( 2 , 1 , 0 )  A  where  P  i t  =  * l  A  A indicates ?  ±  is  $^ + $  the 2  P  i t - l  first  price  < 1  *2  A P  each  animal  indicate  the  first  data.  In  function  an  initial  standard  an  a variety  errors  autoregressive  of  autoregressive  a d d i t i o n , a moving  i n c l u d e d i n an a t t e m p t  were  completed,  This  is  the"  remained  model p r o v i d e d t h e  lt-2  +  to  not  most  (2,1,0). best  fit  for  unexpected given  the  £  can be w r i t t e n a s  follows:  i t '  differences, for  the  a necessary  The e s t i m a t e d c o e f f i c i e n t s for  the  markets.  series is  p r o b l e m has  that  The l a r g e  specification  +  series  6  series.  of  this  provide  specification  price  nature  that  to  eventually  the ARIMA(2,1,0)  animal  partial  autocorrelation  used  checks  ARIMA  Furthermore,  integrated  to  specification.  appropriate  each  can be  Subsequently,  was  first  transformed  assumed  partial  were f i t t e d  average  the  and  to  stationary.  and s e c o n d l a g s may  specifications  the  is  t h e ARIMA m o d e l .  (2,1,0).  an a t t e m p t  t r a n s f o r m e d by  appears  it  is  In  autocorrelation  It  the 4.2  is  representing  4.2.  series  plot  presented  the  Therefore,  differenced price The  series  of  functions  been c o r r e c t e d .  non-stationary.  the  graph  autocorrelation  is  category,  for  are  ith  animal  condition each  category,  for  stationarity.  ARIMA(2,1,0)  reported  and  in Table  model,  4.1.  All  FIGURE 4.2 Plot of Autocorrelation and Partial Autocorrelation Functions, F i r s t Differenced Steer Price Series, Calgary PLOT OF PARTIAL AUTOCORRELATIONS LAG 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  -1.0 -0.8 -0.G -0.4 -0.2 0.0 0.2 0.4 CORR. * + + + + + + + I 4 IXXXXXXX40.266 -0.417 XX+XXXXXXXI 4 4 XXI 4 -0.060 4 -0.252 XXXXXXI • + 0.043 IX + 4 0.022 IX + 4 XXI 4-0.080 4 0.095 IXX + 4 XXI + -0.070 4 0. 141 IXXXX + 4 -0.030 XI + 4 0.081 IXX + 4. -0.056 XI + 4 0.007 I 4 4 -0.027 XI • 4. -0.034 XI 4 4 -0.049 XI + 4 XXXI 4 -0.128 4 -0.022 XI + 4 -0.043 XI 4 4 -0.029 XI 4+ 0.059 IX 4-0.049 * XI 44 0.010 I + 4 XXXI + -0.116 4 XXXXXXI 4-0.222 4 0.024 IX + 4 0.031 JX • 4. -0.122 XXXI • 4 I 40.013  0.6 +  0.8 •  1.0 +  PLOT OF AUTOCORRELATIONS LAG  -I.O CORR. *  1 O.266 2 -O.317 3 -O.277 4 -O. 181 5 0. 031 6 0. 198 7 . O.053 8 -0. OOO 9 -0. 04 1 10 0. 006 11 O.04 1 12 0..032 13 -O..043 14 -0..057 15 -0 .036 16 O.,005 17 -0. 006 18 -0..060 19 -O..051 20 0 028 21 0..029 22 O .068 23 0 .008 24 -0..083 25 -0 , 124 26 -0 .202 27 -0 .029 28 0 .237 29 0 .079 30 -0 .049  -0.8 -0.6 -0.4 -0.2 O.O • • + • + I 4>  44-  • 4444. 4444. 4. 4444444 4 4  4 4 4 4  0.4 4-  4 IXXXXXXX4 4 4XXXXXXXXI  + 4-  0.2 +  XXXXXXXI XXXXXI IX 1XXXXX IX I XI I IX IX XI XI XI I I xxt XI IX IX IXX I XXI XXXI XXXXXI XI IXXXXXX IXX XI  4 4 4 4 4 4 4  4 4  4 4 4 . 4 4 4 4 4 4 4 4 4 4 4 4 4 4  0.6 4-  0.8 4-  1.0 •  TABLE  4.1  Estimated C o e f f i c i e n t s ARIMA(2,1,0) Model, C a l v e s , Cows, and H e i f e r s ; C a l g a r y Estimated Coef f i c i e n t s  Equat i o n  Steers  Calves  Cows  * **  Standard Error  $1  .4199  . 164*  $2  -.3962  .163*  $1  .5262  .153*  $2  -.5853  .160*  $1  . 3343  . 168**  -.3589  .166**  $1  .3022  .171**  $2  -.3017  $ Hei f e r s  Steers,  2  significant significant  at at  10 p e r c e n t level 5 percent level  . 169**.  98 estimated  coefficients  percent  or  condition estimated  the  at  Moreover,  $^ + $^ < l i s  estimated equations,  animal base  predictions For  that  category,  used  for  all  steers  in  for  the  cases  and  each a n i m a l . farmers  expected  the  a prediction  each y e a r ,  10  necessary in  each  reported  calves,  the  price  and  For  predicted  plus  the p r i c e  This expected defined  as  the  is  F.  expected it  period  expected  value  the  is  at  from t h e  price  for  is  price assumed  its  sale  discounted  expected  Price  ARIMA p r i c e  however,  next  generated  estimation.  in Appendix  cows and h e i f e r s , animal  is  to correspond with  econometric  are  v a l u e a female  newborn c a l f . period  the  satisfied  d i s c o u n t e d back one p e r i o d and d e f i n e d as for  either  equation.  each data  level.  stationarity  From t h e s e for  significant  percent  5  for  are  own  of  back each  its one  female  animal. These expected p r i c e main d a t a  base  econometric  series  to complete  the  will  data  be  combined  requirements  with  necessary  the for  estimation.  4.3 DATA The  main  data  base  used in e s t i m a t i n g  models was a s s e m b l e d from a v a r i e t y conducted  by S t a t i s t i c s  and N a t i o n a l for  Livestock  inventory  Generally, Cansim f i l e s  and  prices of  Canada  Survey  sources.  (NLS) ) 7  data  were t h e on  Canada  and  cow-calf  cattle  surveys  Survey  primary  farm i n p u t s were o b t a i n e d  Statistics  econometric Two  (Farm E x p e n d i t u r e  expenditure of  of  the  (FES)  sources farms.  from t h e output  main  prices  99 were o b t a i n e d Market  reported  in  the  Livestock  Review.  The FES three  is  prairie  Columbia.  It  livestock survey  a probability provinces  is  agriculture  on f a r m s ,  is  farms  a  Data are  participating variable  farm i n p u t  is  random  of  frame  farm.  From  generated  for  western  survey.  for  targeted they  each  census  specific  that  region  participation  in  of  This  implies  in  the  in  the  interviews  data,  total  inventories  This  selected  by p e r s o n a l these  on  t o be i n c l u d e d  are  the  British  Canada.  agricultural  fashion  whether  collected  information  in  in  r e g i o n of  expenditures,  use  farms a r e  regardless  sample.  Peace R i v e r  from a s p e c i f i c  in  conducted annually  provide  and l a n d  Some l a r g e  survey  to  d e f i n e d as an a r e a  selected  survey.  survey  and t h e  designed  receipts,  a s a m p l e of is  from market q u o t a t i o n s  the  random  from  an e s t i m a t e  each  for  agricultural  each  census  region. The a c c u r a c y Agriculture estimates percent  generated the  questionnaire  for  seven period  the  1978  to  bench  measured a g a i n s t taken are  8  An  and a map of  extracting a cow-calf  Statistics  1981.  within  marks.  b r e e d i n g cows  for  every  the  five  C e n s u s of  years.  The  approximately example the  soil  10  of  the  zones  in  in Appendix A.  of  or more b e e f  variables  is  1981 FES  from t h e F E S ,  definition,  is  by the FES  census  purposes  production  this  which  Canada a p p e a r s  For  thirty  t h e FES  survey  of  western  of  Canada  fourteen This  information  on  beef-cattle  farm was d e f i n e d in  inventory.  provided  soil  zone  resulted  in  to  According  data  on  locations a  have  total  to  fortyfor  the  cross-  100 sectional,  time-series  Table  provides  4.2  sample  summary  of  fifty-six  information  observations.  on  each  variable  collected. Attempts animal  t o "estimate  category  were  multicollinearity specify  three  sold off  farms;  3)  total  crop  The  FES  sold off data,  is  does  provides  or a r e  period t  supply  is  minus t h e Steer finishing steers  each  serious  therefore,  total  cattle  to  supply  demand;  and  combination  rates  variable  of  on  of  animals  cattle  inventory  in  different  c a n be g e n e r a t e d .  illustration  Specifically,  information  the  of  how t h i s  supply  of  Figure variable  animals  is  follows: Cows on  t+1.  of  cow  equal  farms  the cows  in  on f a r m s  p e r i o d and t h e r e f o r e  not  Calves  nine  either  period t  s o l d in  part are  of  cows and h e i f e r s  cow  sold  in  on farms  to  Consequently,  female  in period  t  t+1.  normally  sold  off  hundred pounds.  in p e r i o d t  r e p o r t e d as reported  period  the  either  and m a i n t a i n e d  t+1.  in period  S t e e r s are  are  become  in  number of  approximately  Supply:  and  in period t  inventory  to  Supply:  in p e r i o d t  Heifers  number of  reported  Calf  direct  using a  this  become cows  at  provide  a diagrammatic  in  become p a r t  1)  for  to  decided  groups:  and growth  for  Supply:  or  was  due  end-of-period inventory  not  maintained  inventory  equations  9  rates,  determined.  Female  It  output  However,  1 0  values  d e t e r m i n e d as  t  total  supply.  calving  categories, 4.3  2)  supply  unsuccessful  problems.  aggregate  farms.  output  will  in  for  Consequently,  be s o l d d u r i n g  inventory  on f a r m  farms  in  the  t+1.  period  t  will  101  TABLE Summary of  FES  Variable  4.2  Data:  Cross-Sectional  Mean  C a s h r e c e i p t s from Custom Work $ Miscellaneous  Minimum  Maximum  1 ,869,000  19,548  25,377,000  Farm E x p e n s e s $ 1 , 133,500  116,310  5,232,300  C a s h Wage, H i r e d L a b o u r §  6,155,200  C a s h Wage, F a m i l y  Labour $  1,650,800  25,571  6,180,800  Cash V a l u e , H i r e d Room and B o a r d $  Labour  413,360  30,686  2,372,100  3,864,700  49,032  15,202,000  3,570,700  222,840  15,158,000  12,817,000  267,290  73,786,000  1,491,900  74,612  5, 105,900  1,3831,000  470,260  63,170,000  700,480  31,288  1,702,900  1 ,802,500  53,395  4,628,800  Expenses $  1 , 147,900'  55,020  4,188,200  I n s u r a n c e Premiums $  3,379,500  68,834  10,846,000  Property  3,649,100  116,780  9,890,500  $  31 , 4 5 1 , 0 0 0  1,294,600  82,233,000  Grains  1 ,032,400  27,970  2,599,300  294,600  28,481  902,700  1 ,534,400  67,474  4,076,000  2, 121,900  66,505  7,906,600  1 ,309,800  27,204  3,758,900  783,390  38,084  1,856,400  1,484,900  59,141  3,995,100  Pesticide  Expenditure  $  Custom Work E x p e n s e s $ F e e d and S u p p l e m e n t s Expenses $ V e t e r i n a r y m e d i c i n e and Artificial Insemination Expenses $ Expenditure  on L o a n s $  Telephone Expenses $ Electricity Fuel  Capital  Expenses $  Taxes $ Cost Allowance  T o t a l A c r e s Seven A c r e s Tame Hay A c r e s Land Repairs Repair  Rental  t o Farm B u i l d i n g s to  Fences  $  $  Expenditure  Twine  and W i r e $  Expenditure  Hardware  $  341 , 1 10 2 4 , 5 1 3 , 0 0 0  102  Table Summary of  FES  4.2  Data:  Variable  (cont.) Cross-Sectional  Mean  Acres  of  Other  Acres  of  Summer  Acres  All  Acres  Improved P a s t u r e  Total  Other  898  87,378  508,120  6,693  1,637,000  1,864,000  71 ,841  3,927,800  203,090  26,874  809,560  1,928,300  119,470  4,792,600  7,546,700  339,300  26,578,000  22,922,000  1,480,200  69,540,000  2,331,600  171,020  6,675,600  Fallow  Crops  Machinery  Land $  Expenses  Seed E x p e n s e s  $  Maximum  25,177  Crops  R e n t a l Expenses  Minimum  $  Fertilizer  Expenses  $  9,938,500  458,540  46,615,000  Irrigation  Expenses  $  175,000  0  1,894,700  301,870  9,496  1,844,200  195,230,000  10,758,000  618,420,000  Other  Expenses $  Operating  Total Agriculture Receipts $  P o r t i o n of R e c e i p t s from 74,194,000 t h e S a l e of G r a i n s $  1 ,716,800  243,950,000  3,990,200  230,320  8,931,600  3,788,900  131 ,520  11,085,000  4,723,000  106,200  31,828,000  203,130  0  786,410  154,120  7,650  333,920  147,030  24,569  974,960  159,120  7,835  331,550  7,611  0  36,672  182,550  9,269  517,090  8,629  853  24,512  41,051  2,634  146,540  Total  Acres  Oats Fed Barley  All  Land  bu.  Fed  Wheat F e d  bu. bu.  Calves # Total  Cattle  and  Calves #  C a l v e s Born A l i v e L a s t S i x Months # Cows and H e i f e r s C a l v e Next Beef  Cows #  Bulls # Steers #  Six  Expected  Months  #  to  103  Cattle  Inventory  Cows  FIGURE  4.3  Supply  off  Farms  Inventory  t  Cows  t  Heifers  t+1  Heifers  t  Steers  t  Sters  Calves  t  Calves  Calves  Born  t  t+1  t+1  t+1 t+1  C a l v e s Born  t+1  104 either  be  sold  during  inventories  in  be  enter  s o l d or  supply  is  t+1.  equal  calves  steers,  and c a l v e s  in  each  cattle  in  number of  inventory  supply  enter  heifer  born d u r i n g p e r i o d t in t + 1 .  calves  born i n p e r i o d t  is  will  steer either  Consequently,  in period t  less  or  the  calf  plus  number of  the  heifers,  in t + 1 .  d e f i n e d as  the  sum of  animals  sold  category.  Annual average Canadian  cattle  auction  Saskatoon,  and  category.  These  average  price  number  of  weight  (in  revenue  prices  markets  Winnipeg) prices  for a l l  animals pounds)  animals  1 1  are were  cattle.  of  an  major  western  (Calgary,  Edmonton,  Regina,  available  for  used The  by  five  to  sale  cattle  the  by  animal  a  weighted  represented  m u l t i p l i e d by t h e  in  of  each  generate  weights  animal  (multiplied  multiplied  from  in each c a t e g o r y  o b t a i n e d from t h e  number of animal)  p e r i o d or  inventories  to the  of  Total  Calves  calf  number,  the  each  the  Total  d e t e r m i n e d by  average  weighted  average  category.  is  the  the  weight  of  an  price  of  all  the  end  of  to  the  average  cattle.  the  The t o t a l  number of  period is  taken d i r e c t l y  sum of  animals  in each  animals  in  from the FES  be p r e f e r a b l e gain  from  next p e r i o d . subtracting  expected p r i c e to generate  maintaining  of  it  revenue  and i s  equal  cattle  a variable the animal  was d e c i d e d t h a t next p e r i o d ,  r e p r e s e n t i n g the on t h e  T h i s expected gain v a r i a b l e the  at  category.  For econometric s p e c i f i c a t i o n , than u s i n g the  inventory  received  from t h e  rather  it  would  expected  f a r m and s e l l i n g was d e f i n e d by sale  of  animals  it  first from  105 the  v a l u e of  the  discounted  value  generated  using  v a l u e of  the  procedure, Finally, by  weight  of  A the  total  of  animals.  end-of-period stock  expected p r i c e s herd  was  total  the  from w h i c h  subtracted.  discounted expected gains period,  in each  i n d e x of  receipts an  the  crop output sale  is  crops,  crop price  index.  price  i n d e x was p r o v i d e d by A g r i c u l t u r e  FES  variables. to  reports  correspond  Cansim 1981.  All  was  by  this  generated. generated number of  the  average  by  dividing  as  reported  in  the  The a g g r e g a t e  crop  Canada and  to  expenditure data price  these  file  price  is  defined  from  on a p r o v i n c i a l  basis  set  to  twenty-four  therefore  expenditure  obtained  indexes are  for  i n d e x e s were  twenty-four  i n d e x e s were  data  reduced  1971.  Farm i n p u t  These p r i c e  was  Using  generated  of  by  The  animals  by t h e  multiplied  FES,  100 i n  the  category.  from t h e  aggregate  Next,  the  d i s c o u n t e d e x p e c t e d g a i n was  end of  quantity  to equal  of  d i s c o u n t e d e x p e c t e d g a i n per head  an a n i m a l  total  stock  the  beginning  dividing at  of  (ARIMA)  the  the  animals  beginning  required variables.  Statistics for  Canada's  each year  100 i n t h e  input  base  1978 year  to of  1971 . It groups:  was  decided  labour,  capital,  Labour expenses family  labour, as  to  aggregate and m a t e r i a l s  and  included expenditures  and room and b o a r d .  used  labour  this  wage was p a i d t o b o t h h i r e d and f a m i l y expenses  price  included  into  three  services. on  The h i r e d  was  Capital  the  expenditures  i n d e x and i t  hired labour  labour, wage  rate  was assumed  that  labour.  expenditures  on  repairs  to  106 buildings,  repairs  expenses,  taxes,  rental, given  and  stock  using  to  land.  a Cobb-Douglas aggregator in  unit  services.  f l o w s of Materials  feed  and  this  category,  and s e r v i c e s  insemination,  miscellaneous  expenses.  The m a t e r i a l s  generated  using  defined It  Finally, revenue and  price  of  for  included expenditures  on  medicines,  artificial  fuel,  irrigation,  and o t h e r  price  operating  index  was  function  an  also  for  the  sum of  total  in  real  in  all  to  than  specify separate  was d e f i n e d  categories  and  as is  FES.  estimate  (the  rather  This variable  animals  from t h e  specification,  variable  category.  beginning  of  profit  revenue  from  is  generated cattle  discounted expected gains)  e x p e n d i t u r e s on  defined  generated  and r e p r e s e n t s  3  aggregator  a tractable  f i x e d stock  obtained d i r e c t l y  total  is  from a  per  and s e r v i c e s  for  each animal  number of  sales,  services  annual  expenses,  Cobb-Douglas  was d e c i d e d ,  for  total  rental  electricity, farm  the  land  variables.  o n l y one o v e r a l l ones  a  the  machinery  expenses,  index  function'  veterinary  telephone,  hardware,  price  expenses  supplements,  loan  representing  The c a p i t a l  1 2  depreciation,  financial  variable  each v a r i a b l e  the  capital  c u s t o m work,  a flow of  fences,  variable  inputs.  taking  sales,  and  All  by  crop  subtracting  variables  t e r m s by d i v i d i n g by t h e consumer p r i c e  are index  (1971=100). The d e f i n i t i o n s are of  of  summarized i n T a b l e all  data  used  in  each e x p e n d i t u r e 4.3. the  In  and  price  a d d i t i o n , a complete  transformations  is  variable listing  reported  in  107  TABLE Definition  4.3  of V a r i a b l e s  (Translog) Definition  Var i a b l e P  C a t t l e Output P r i c e  P^  Expected C a t t l e  P  Crop Output P r i c e  3  P  Labour Input  P  C a p i t a l Input  P 6  A  b  Price  Index  Price  Weighted Average Expected Gain A l l C a t t l e  Index Rate  Index  Price  Weighted Average Index A l l C a t t l e  Index of t h e P r i c e of a l l C r o p s P r o d u c e d  Index  Price  Index  of  the H o u r l y  Index o f t h e R e n t a l of C a p i t a l  wage Price  M a t e r i a l s and S e r v i c e s I n p u t P r i c e Index  Index of t h e P r i c e of A l l M a t e r i a l s and S e r v i c e s  Beginning C a t t l e  T o t a l Number o f A n i m a l s B e g i n n i n g of Each P e r i o d  Si  C a t t l e Revenue  S  Expected C a t t l e  2  Index  Inventories  T o t a l Revenue from t h e S a l e of A l l C a t t l e D i v i d e d by T o t a l P r o f i t  Share  Revenue  Share  Share  T o t a l Expected Gain Revenue from t h e S a l e of C a t t l e Next P e r i o d D i v i d e d by T o t a l P r o f i t  S3  C r o p Revenue  T o t a l Revenue from t h e S a l e of A l l Crops D i v i d e d by T o t a l P r o f i t  S4  Labour E x p e n d i t u r e  S5  C a p i t a l E x p e n d i t u r e Share  E s t i m a t e d E x p e n d i t u r e of t h e Flow o f C a p i t a l S e r v i c e s D i v i d e d by T o t a l Profit  S6  M a t e r i a l s and S e r v i c e s E x p e n d i t u r e Share  T o t a l E x p e n d i t u r e on A l l M a t e r i a l s and S e r v i c e s D i v i d e d by T o t a l P r o f i t  Share  Total Expenditure for H i r e d and F a m i l y L a b o u r P l u s Room and B o a r d D i v i d e d by T o t a l P r o f i t  108 Appendix  B.  The obtain  NLS  provides  estimates  This farms  each  For  were  input  The  econometric equations:  or  equations 1)  total  t o the  variables'  in  the  each v a r i a b l e  is  procedures  case.  input  1982.  Each  to  for  series  4.4.  data, is  information  of  on  for  farm  cow-calf  base  specified  for  two  output  total  end-of-  supply;  and 2)  variables for  addition,  provided input  indexes  were  the the  is  that  generated  corresponding  output  price  basis  aggregate  groups  for  following  price  Canada o v e r 100 i n  price  defined  represent  western  output  addition,  reported  1956 t o  estimates  and p r i c e a complete  in Appendix  C.  indexes  in  the  changes,  the  period  FES  for  the  1956 t o  1971. of  cattle  C a n a d a , were o b t a i n e d d i r e c t l y the  In  period  supply  beginning-of-period stocks  of  inventories  were  on a t i m e - s e r i e s  index has a base of  western  time-series  data  outlined In  on  outlined.  three  for  to  limited  Both  case.  on a  the  provide  be  output  Canada the  for  data  this  can o n l y  determined  groups,  Definitions in Table  of  animals  cattle  c r o p output  procedures  price  Finally, year,  total  previously  These  three  Canada,  demand.  Agriculture corresponding  study,  inventory  cattle  FES  from w h i c h  number of  each p r o v i n c e  this  consequence  inventory  according  the  the  total  The NLS does not  expenditures  period  for  western  in  rates.  farms.  the  the p u r p o s e s of  Included  calving  reports  for  source  inventories.  category  collected  1982.  alternative  cattle  publication  in  basis.  of  an  variables listing  for  from t h e  each NLS.  are  summarized  of  the  time-  109 TABLE Definition  of V a r i a b l e s  Variable Pj^  Cattle  Output P r i c e  Expected C a t t l e  2  Index  Price  Index  P-j  Crop Output P r i c e  P4  Labour  P P  C a p i t a l I n p u t P r i c e Index M a t e r i a l s and S e r v i c e s I n p u t P r i c e Index  5 6  A  b  Input  Price  Beginning C a t t l e  Qc  Quantity  A  End-of-Period  e  (Time-Series  Data)  Definition  —e  P  4.4  of  Cattle  Index  Index  Inventories  Produced  Inventories  Weighted Average TimeS e r i e s P r i c e Index All Cattle W e i g h t e d A v e r a g e TimeS e r i e s Expected Gain All Cattle T i m e - S e r i e s Index of P r i c e of a l l C r o p s Produced  the  T i m e - S e r i e s Index H o u r l y Wage R a t e  the  of  Time S e r i e s Index of t h e R e n t a l p r i c e of C a p i t a l T i m e - S e r i e s Index of t h e P r i c e of a l l M a t e r i a l s and Services T o t a l Number o f A n i m a l s B e g i n n i n g of E a c h P e r i o d , Time-Series O u t p u t of a l l Time-Series  Cattle,  T o t a l Number of a l l A n i m a l a t t h e End of t h e P e r i o d , Time-Series  110 B e f o r e p r o c e e d i n g w i t h the the  model,  it  is  interesting  using a cross-sectional base  in  the  In are  (FES)  over  the  because  producers  size,  beginning stocks optimal  are  of  level  Consequently,  interpreted  under  In  the  breeding  of that  the  to)  of  of  data  level  in  of  of  a fully  of  cattle  would  expect  reducing  can be c o n s i d e r e d  to  the  herd  be  at  exogeneous  choice  should  adjusted  beginning stocks  time  be  beginning  (FES)  corresponding This  elasticities Five.  a of  be  stocks in  the  priori choice  will  be  the  Consequently,  cattle  under may  not  the have  variables.  (Silberberg  1978),  supply estimated  be g r e a t e r using  prediction  by  exogeneous  of  estimates  have  However,  restricted  herd.  of  Principle  will  cattle  interpreted  own e l a s t i c i t i e s  data  is  female  should  t o changes  of  period considered.  increase  the  beginning  that  cross-sectional  Chapter  the  Le C h a t e l i e r  conclude  1  One  restricted  elasticities  choice  completely  Given  (NLS). "  (NLS)  beginning stocks  the  data,  over  capability  assumption  equal  cattle  which h e r d s i z e can  elasticities  can  consequences  time-series  a s s u m p t i o n of  time-series  increased  r a t e at  adjusted  of  animals.  generally the  the  period.  not  given  variables.  the  data,  four year  that  of  versus  cross-sectional  declining  stock  to c o n s i d e r  specification  estimation.  the  some  econometric  on  than  (or  at  time-series the  challenged  one using least data  magnitude  of  empirically  in  111  4.4  STOCHASTIC SPECIFICATION AND ESTIMATION TECHNIQUES The  transcendental  postulated  for  function.  the  multi-output,  The r e s t r i c t e d  as a s e c o n d o r d e r the  - °  functional  multi-input  translog profit  logarithmic  three-output,  be w r i t t e n U  logarithmic  Taylor  three-input,  variable  function  series  one  form  fixed  profit  is  defined  expansion.  factor  is  case,  For it  can  as:  «  _ ° _ 6 6 l n I l ( P , A ) = a . + E a . l n P . + hZ Z ° 1=1 1=1 h=l Z 6 , l n P . l n A + B, l n A + i 1 k b  1  1  i  y^lrtAnP^  h  1  h  6  b  where  n  (P,A ) is  costs  of  b  restricted  variable  r e p r e s e n t i n g output and c r o p s , A  b  is  the  Hessian  restrictions (4.2)  6  of  prices  beginning stock  degree  on t h e  in  =  However,  l  one  function  satisfies  (Tl6)  Chapter  of  output  prices  problems of  assumes (at  that  least  and e x p e n d i t u r e  8lnP  ±  all  requires  the  share  = s. = l i ?  i  6 o Z 6 r t 1=1  generally  of  cattle  materials. of  the  i and h and  the  following  = 0.  preclude  direct  Equation  conditions share  equations  for  »  J  (4.1).  translog variable  revenue  q  n  the  in  locally)  o b t a i n e d by a p p l y i n g H o t e l l i n g ' s b  and  total vector  Symmetry  for  the p a r a m e t e r s  Three,  airJI(?,A )  capital,  Yhi,  h  estimation  if  minus  parameters:  Multicollinearity econometric  revenues  on f a r m s .  O  1  b  expected p r i c e  labour,  cattle  b  six-dimensional  6 . " It E Y,, = 0, h = 1....6, Z Z Y = n. h = i fi. 1=1 a. = l . 1=1 D  E  U.3)  a  cattle,  Yih  one  (total  is  of  of  requires  h o m o g e n e i t y of  P  prices  and i n p u t  matrix  profit  inputs),  , lnA lnA , kk  b  Lemma t o  equations each  (4.1):  input  profit (J[ )  for can  to each be  1 12 where  Pi  is  quantity are  of  the  the  ith  of  output  a f f i x e d with negative For  econometric  function w i l l true  profit  analysis, account  in p r o f i t  or  profit  is  share  error  by  normally  expenditure  function in  any d e v i a t i o n  the  econometric  procedure  estimation.  Finally,  Furthermore, with  on  the  by  for  e  )  zero  E ( e  lt js  )  e  =  0  0  l j '  a  V  fc  n  d  * ' s  equations revenue is  due  it  is  assumed t h a t  ei's  and  semidefinite equations  of  ft  of  errors  are each  means  is  (ei)  to  to  m a t r i x , ft .  share  the v e c t o r  correlated  =  must  errors  actual  a  positive  The  variance-  because  implies avoided  d r o p p i n g one s h a r e  ~ N(0,a*), lt Jt  to  econometric  the  terms  is  across equations  T h e s e c o n d i t i o n s can be w r i t t e n  E ( e  the  assumed  random  of  disturbance  The s i n g u l a r i t y  contemporaneously  is  of  maximizing l e v e l s  must be p o s i t i v e  be s i n g u l a r .  profit  T h e s e random d i s t u r b a n c e s  variance-covariance  constraint  the  shares  representation  disturbances  from p r o f i t  (4.3).  adding-up  is  behavior.  shares  in  qi  appended t o e a c h e q u a t i o n  stochastic  matrix  ±  input,  translog variable  function  terms  distributed  independent.  or  i n a p p r o x i m a t i o n as w e l l as  covariance  e  the  translog  appending a d d i t i v e  equation  and  exact  in o p t i m i z a t i o n .  semidefinite  will  the  assumed t h a t  expenditure  random e r r o r s  are  the  errors  it  modeled  estimation,  true  output  signs.  the  specifying  (4.3),  ith  input,  If  maximizing  In  or  function.  then  for  the  be c o n s i d e r e d an  approximate  in  price  that in  the it the  equation  in  the  assumed  to  be  but  as:  temporally  113 The c r o s s - s e c t i o n a l , utilized  time-series  in  the  econometric  necessitates  the  use  account  of  freedom,  yearly the  estimation  covariance  differences  covariance  dummy v a r i a b l e s share  of  and a r e  nature  in  of  the d a t a .  to  the  sample  Equation  estimators  estimators  attached  of  (4.3)  to  1 5  take  • To save d e g r e e s  t a k e the  form of  the c o n s t a n t  of  yearly  term i n  each  equation. The  share  inventories, rewritten  equations  crops,  labour,  for  cattle,  capital,  incorporating error  end-of-period  and m a t e r i a l s  t e r m s and y e a r l y  c a n now  dummy  be  variables  as: (4.4)  6  S  i ' i a  3  I /ih  +  l n P  h  +  6  i  l  n  A  I A i k  +  D  n=l  where value are  Dk  is  The  cross  Hessian matrix necessitate  the  of  regression  (SUR)  equation  is  use  of  a  >  1  6  Dk t a k e s  other  in  Zellner's to  which  equivalent are  t o be  (4.4).  parameters, is  imposed by t h e  the  variables  the  To  efficient  seemingly  unrelated  The m a t e r i a l s '  SUR e s t i m a t e s is  to  of  until  dropped  convergence  share  ensure  the  t o maximum l i k e l i h o o d  iterated  least  ensure  estimation  equation  below,  generalized  Zellner's  employed.  symmetric  discussed  multivariate  estimate  dropped  the c o e f f i c i e n t s  =  k (i.e.,  and a l l  restrictions  technique  invariant  asymptotically  to  the  o f ft .  1  defined.  and o t h e r  estimation  are  year  equation constraints  squares procedure  singularity  for  k and z e r o o t h e r w i s e )  as p r e v i o u s l y  i  e  k=l  a dummy v a r i a b l e  1 in year  +  non-  parameters and  estimates (Barten  are if  1969).  1 14 In the  order  variable  for there to exist  profit  Equation  symmetry,  homogeneity  the the  translog  must  function,  necessary  these  and  matrix  of  are  to  in  However,  for  do n o t h o l d  generally  c o n d i t i o n f o r the t r a n s l o g  (4.4) with respect  to p r i c e s  be s y m m e t r i c .  equations  should  the e s t i m a t e d  property  that  Y i h = yhi,  share  is  that  function  homogeneous of d e g r e e  implies  zero  following  the  satisfy  f o r a l l i and h .  o f h o m o g e n e i t y o f d e g r e e one i n  profit  the  (4.4).  hold  symmetry  that  imposes  monotonicity,  satisfy  implies  variable  of  set of d a t a .  sufficient  Hessian  the  equations  properties  an a r b i t r a r y  function  The p r o p e r t y  properties  These p r o p e r t i e s must a l s o  profit  the  the  between  transformation  o f d e g r e e one i n p r i c e s ,  variable  This  satisfy  s y s t e m of s h a r e  but may h o l d o v e r A  4.1  in p r i c e s .  estimated  relationship  f u n c t i o n and t h e u n d e r l y i n g  function,  and c o n v e x i t y  a dual  in  that  the share  prices.  restrictions  prices  for  equations  This  condition  the  estimated  on  parameters: 6  Z Y.. = 0 h=l 6 Z y = 0  h = 1,...6, and  6 Z  i = 1,...,6.  i  i =  1  6,  n  1=1  6  =0  1=1  In a d d i t i o n ,  t h e f o l l o w i n g a d d i n g up r e s t r i c t i o n s  on t h e dummy  variables:  3 Z 3 k=l 6 Z B  1=1  The properties  = 0  i = 1,...,6 and  =0  k = 1,2,3.  are  imposed  fcl  properties  of  monotonicity  which a r e e a s i l y  and  convexity  summarized as l i n e a r  a r e not  restrictions  115 on  the  share  properties  equations.  with the share  estimation.  To  must be p o s i t i v e A  necessary  supply  f o r revenues  positive  negative.  for convexity  profit  convexity  function  A  i s that  with  the p r e d i c t e d  shares  expenditures.  in p r i c e s own  and  the H e s s i a n to  i s t h a t own  derived  necessary  respect  these after  for  and  of  evaluated  and n e g a t i v e  for  are  are  be  monotonicity,  condition  elasticities  the c o n s i s t e n c y  equations w i l l  satisfy  elasticities  condition  Rather,  of  demand  sufficient  the  variable  is  positive  prices  semidefinite. This Hessian matrix in  terms o f  the  1  21  Y  + S  Y  1  2 1 S  Y  [H] = '  .  Y  where  61  +  S  6 1 S  Y  than  22  +S +  S  2  (  S  2-  1 }  Y  statistically  f o r these  restrictions  likelihood  ratio  restrictions unrestricted  S  the  imposed  null on  is written as:  1  6  26  + S + S  and  the  l S e  2 6 S  W W "  S  1  *  semidefinite. the hypotheses  in p r i c e s ,  will  test  [H]  6 2  on t h e s h a r e  The l i k e l i h o o d r a t i o under  +  properties.  test  (4.4)  •  62  zero  characterized  in  ... Y  l S z  maintaining  homogeneity of degree  function  2  shares.  •  Rather  A  1  [H] must be p o s i t i v e  linear  coefficients  and e x p e n d i t u r e  + S (S -l)  n  c a n be c o n v e n i e n t l y  estimated  p r e d i c t e d revenue Y  [H]  it  o f symmetry a n d  is preferable  Table  to  test  4 . 5 summarizes  the  e q u a t i o n s as n u l l  hypotheses.  be u s e d f o r h y p o t h e s i s  testing.  compares t h e v a l u e o f t h e l i k e l i h o o d hypothesis the  likelihood function  model) (La).  (Lo) to It  the  (i.e., value  is well  known  with of the that  1 16 -2(InLa-lnLo)  is  asymptotically  The n u l l  hypothesis  whether  the  critical  v a l u e of x  number of  is  v a l u e of  testing  homogeneity  of  satisfied, describe  for  degree  these  conditions  the  estimated  Of p a r t i c u l a r  underlying  transformation  homothetic"  outputs;  and i i i )  cattle  Three. are of  the  share  conditions  for  as  share  consistent will  the  with again  scale  also  of  returns  the  to  in  in  'outputs;  and  be imposed on  the  will  be  done  on  defined of  the c o w - c a l f  be  "almost  in  Section  the  Table (4.4)  each the  industry.  determined  whether  to  i)  homogeneous" between (3.9)  of  on t h e  4.5  in  crops Chapter  function parameters  summarizes  which are  profit  the  as:  transformation  properties.  of  used  described  restrictions  be u s e d t o t e s t  be  is  study  production  Equation  three  can  been  this  translog variable  are  m a x i m i z a t i o n have  transformation  ii)  joint  equations.  these  scale  the  underlying  the  sufficient  function A likelihood  to  be  ratio  property. revenue  be u s e d t o p r o v i d e a measure  (RTS)  than a  symmetry  testing  f u n c t i o n can  The e s t i m a t e d p a r a m e t e r s can  will  equations  interest  exhibiting  restrictions  less  on  f r e e d o m , where k i s  profit  imposing l i n e a r  estimated  linear  test  in  supply,  by  or  properties,  for  These c h a r a c t e r i s t i c s  tested  greater  statistical  properties  "almost  of  depending  hypotheses.  function.  and  is  zero in p r i c e s  the  certain  rejected  restrictions.  these maintained Once  not  -2(InLa-lnLo)  e s t i m a t e d model and f u r t h e r under  or  with k degrees  2  independent  After  rejected  d i s t r i b u t e d as C h i - s q u a r e d .  of  share  short  run r e t u r n s  Generally, under  equations  the  estimates  to of  maintained  117 TABLE Testing  for  4.5  Structure with Linear R e s t r i c t i o n s on t h e Share E q u a t i o n s  Property  Linear  Restrictions  Equations(4.4): Symmetry  Ho:  T  H o m o g e n e i t y o-f D e g r e e Zero i n P r i c e s  Ho:  E  Almost  Homotheticity  Output  Prices  Almost Homogeneity Output P r i c e s  i  "  h  Y  j  h  =  0  on  Null  v i  ' » h  =  Share Hypotheses  1  6  b  in  h=1  Y,u = 0  Vi = 1.....6  n  3 Ho:  E  Ho:  E Y i =1  Ho:  E Y-u = 0 i-4  h = i»,5,6  E 6. = 0 1-1 '  Vi = 1  =  ' = 1.2  Y  i =1  = 0  i h  h =  1,2,3  h -  1,2,3  in j  h  = 0  , h  Ho: Joint Production Technology in C r o p s and Beef  HO:  a  Ho:  a  i  3  3  h  =  0  0  h =  1,2  6  1 18 hypothesis (1982)  of  homogeneity  in  technology.  h a s d e r i v e d a f o r m u l a t o measure  non-homothetic restrictions measurement For measure  multi-output  to  i s taken a l o n g the expansion variable  of  scale  to  to  technologies.  the m u l t i - o u t p u t  following  returns  a r e imposed on t h e f o r m u l a  returns  However,  scale  in  Furthermore,  ensure  that  the  path.  translog profit  can  Weaver  be  function, a  estimated  u s i n g the  formula: 3 = .1 - 1/Z S , k=l  RTS  K  where Sk i s d e f i n e d o v e r returns  to scale  Finally,  revenue  f o r each s o i l  other  profit  of  estimated  the  expenditure respect  function,  to price b  Own e l a s t i c i t y  The  b  under If the  own  The  h  - Y /S i h  total  ±  +? /S l i  determined. formula  elasticities  the  translog  be  functions  will  the p r e d i c t e d of  net  revenue and  output  i  with  in price  s u p p l y c a n be w r i t t e n a s :  - 1  i  elasticity  own  For  s e t can  i = 1 . . . . 6 , h = 1 , . . . 6 , i ^ h.  ±  the assumption that  changes  of  be c a l c u l a t e d .  choice.  and  measure  of t h e t e c h n o l o g y  elasticity  of n e t o u t p u t  e (P,A ) = S ± i  these  A  Ph c a n be w r i t t e n a s :  e (P,A ) = S i h  of  parameters  shares.  only.  zone w i l l  characteristics  be d e s c r i b e d by e l a s t i c i t i e s variable  shares  i =1  of c a t t l e price  expectations  elasticity  of  6.  supply  is  generated  e x p e c t a t i o n s a r e not a d j u s t e d . are allowed, cattle  For the t r a n s l o g v a r i a b l e  c a n be w r i t t e n a s :  (eii)  an  supply profit  estimate (nii)  function,  of  c a n be this  1 19  Total  Direct  Cross  Elasticity  Elasticity  Elasticity  Elasticity  Expectations  of  n11 [  where  §  i  V  +  represents  price  of  price  of  cattle  form  -  2  0  Y ^ ]  percentage  it  was  for  the  necessary  that by  are to  variable a  of  change change  P* P l x  in the in  .  expected  the  elasticities  not  profit  (1974))  data  current  an  choice  on a  quadratic be  in  this  can  However, time-series  alternative  function  would  of  sample.  available  specify  normalized  Lau  the  time-series  variables  the  developed  estimates  using  some  decided  the  [s  +  cattle.  be g e n e r a t e d  basis,  i]  i  c a u s e d by a p e r c e n t a g e  Alternative  because  / g  functional  case.  functional appropriate  It  was  form  (as  for  this  purpose. The n o r m a l i z e d q u a d r a t i c group order  of  flexible  function  functional  a  member  forms and w i l l  provide  a p p r o x i m a t i o n t o an a r b i t r a r y  normalized  quadratic  three-input  one  fixed  profit factor  function.  function case  is  for  of a  The  the  c a n be w r i t t e n  the  second  variable  three-output, as:  (4.5)  + i$aooA  b 2  + E P!A i=l  b  ,  1  where II'  i s n / p " and P' i s 6 i i  previously maintains  defined. linear  P./P, 6  and  all  variables  The n o r m a l i z e d q u a d r a t i c  h o m o g e n e i t y of  the  profit  are  functional  function  in  as form  prices  120 but  symmetry  bij=bji,for variable  of  the  i  and  all  profit  Hessian matrix j .  In  function  conditions  (11^) t o  equations  can  requires  addition,  satisfies  obtained  restriction  the  least  the  6  be  if  at  ( n ) i n Chapter Three,  the  quadratic  locally  net  output  the  supply  by a p p l y i n g H o t e l l i n g ' s  Lemma  to  (4.5): U  -  6  M-(P,A )  )  -Y,.  b  where Y i  is  the  ith  net  output  Assuming a s t o c h a s t i c that  previously  function and, each  in a d d i t i o n , in  for  in  for  the  (4.6) similar  translog  appending a time  variable  industry,  the  to  way,  net  to  profit  trend variable  in a rudimentary  cow-calf  can now be r e w r i t t e n  (4.7)  the  ( 4 . 6 ) to a c c o u n t ,  t e c h n o l o g i c a l change equations  specification  discussed  equation  quantity.  for  output  as:  5  Y  where  i • ± b  t  is  +  i = 1  a  Vj  time  +  a o  /  V  +  +  £  trend variable  i  i  = 1  and  ei  ' ' 2  is  a random  error  term. Econometric in zero  the  estimation  translog  in p r i c e s  case  will  be  but  choice  is  the  ( 4 . 7 ) can p r o c e e d as  symmetry  same a t  of all  the  observations,  output  equations.  defined  as:  e e  q  ii  The  = fi F' /Y D  i i i  / x  i  own  price  i =l 2  1  degree  hypotheses.  quadratic  c a n e a s i l y " be d e r i v e d d i r e c t l y  described  and h o m o g e n e i t y of  imposed as m a i n t a i n e d  Because the H e s s i a n function  of  the  variable  profit  elasticities  of  estimated  net  from t h e elasticity  of  supply  is  121 The e l a s t i c i t y defined  of  net  Yi  with respect  to  price  is  Pj  as: 'ij  (A  b  )  is  Finally, estimate  of  V i , j i r< j .  ij j  The e l a s t i c i t y factor  output  of  net  d e f i n e d as  allowing  total  output  Yi  with respect  to  the  fixed  :  for  adjustments  elasticity  of  in  expectations,  s u p p l y can a g a i n  be  an  generated  as: Total Elasticity  Direct Elasticity 1  [6 1  11  Cross Elasticity  E l a s t i c i t y of Expectations x  J  P'/Y ] 11 r 1 J  +  t 8  12 2 7  / Y  l  [5 ] 21  X  ]  P j [ 3 F  where a l l  variables  This  completes  functional now t u r n  are  as p r e v i o u s l y the  t o a d i s c u s s i o n of  and d a t a  the  ^  ]  defined.  discussion  form s p e c i f i c a t i o n  1  ,  of  stochastic  transformation.  econometric  results.  We  and can  122 FOOTNOTES TO CHAPTER FOUR  1  The Almon l a g e x p e c t a t i o n model was c h o s e n f o r  two  first,  agricultural  this  economics Shumway,  model  for n.d.);  t h e model i s 2  3  Fuss  4  It  (1977)  The  one  price  a  addition  index  because  between  of  the  (Ospina  and  and e s t i m a t i o n  Cobb-Douglas  it  some  was  Statistics  Collection  and  Estimation  Unit,  a vector  was  of  to generate energy  observed that  number  order  of  an  inputs. for  prices  each varied  times:  however,  information. autoregressive  reduced the  cases  (1976).  expectations  added no new  of  of  variable  locations.  a  higher  and L i n  technique  price  market  signs  in  for  estimate  components e i t h e r  stationarity  output  similar  was d i f f e r e n c e d  Futhermore,  See  the  transformations  changed  7  specification  location  average  predictions  see Y o t o p o u l o s , L a u ,  input  The s e r i e s these  6  and s e c o n d ,  employs  systematically 5  in  price  was d e c i d e d t o  market  used  straightforward.  function  aggregate  commonly  generating  F o r an example of profit  is  reasons:  and moving  significance  of  or  the  estimated  coefficients.  the  necessary  condition  for  Number 3,  Data  violated. Canada,  Methodology  Estimating  Paper  Procedures  Agriculture  Statistics  of  the.  Livestock  Division,  Ottawa,  1 982. 8  Statistics  9  It  C a n a d a , M e t h o d o l o g y Paper  was n e c e s s a r y  to  include a t o t a l  b e c a u s e on e x a m i n a t i o n ,  the data  Number 3, crop  revealed  p.117.  supply that  the  variable cow-calf  123 farm as d e f i n e d g e n e r a t e d a p p r o x i m a t e l y total 10 The  revenue number  from t h e of  bulls  remained s t a b l e fact  and t h e  at  P  are  of  = rental = asset  land  price price  = r a t e of  t  r  Pi  14 I t  is is  2 P  of  was  analysis.  Livestock  Market  issues.  defined  as:  Review,  land, land prices  , set  equal  t o 3%  rate. aggregator  the p r i c e ;  x  magnitude  (xi  includes a l l Consequently, variations  of  sample  thirty  outside  it  land,  the aggregate  j j  sectional with  b u l l market,  this  1979),  of is  s h o u l d be n o t e d t h a t  the  the  Given  function  is  defined  as:  1  where P ( . )  x  percent.  has  = np™ ,  ±  i j/  of  Canadian herd  various  growth of  = interest  P(P )  P  is  of  13 The C o b b - D o u g l a s p r i c e  =  in  Canada, Ottawa, price  5  from t h e  reported  (Barichello  i  aggregate  t  P~  a  the  bulls  of  = (r - P )/(1 + r)P  t  where p  P  in  40 p e r c e n t  crops.  s p e c i a l i z e d nature  11 T h e s e p r i c e s  12 The r e n t a l  of  approximately  decided to e l i m i n a t e  Agriculture  sale  30 t o  is  the the  ith ith  these  input, input  quantity). factors  is  cattle  in  greater  cross-sectional moving  the  into  the  affect  the  cross-  cow-calf  farms  time-series western  potential data  may  First,  include only  cows whereas  farms w i t h b e e f  sample  and  elasticities.  defined to  there  index,  two a d d i t i o n a l  or more b e e f  i n the the  price  caused  data  Canada.  for by  output farms  cross-sectional  124 classification. using  this  data  those u s i n g the set,  it  for  the  is  the  variable  calculated  sample:  that  sectional  to  specify  been  using  a  are  1980).  Covariance  simply  because  they  each  on t h e  to  of  between  assumes  more  the  are  estimators  form the  magnitudes  ensure  estimation;  model  data  functional effect  than  certain.  f i x e d whereas  etal.  for  efficient  combined c r o s s - s e c t i o n a l ,  such parameters  are  not  difference  covariance  model assumes t h a t  the  proposed  covariance  parameters  Second,  a different  is  calculated  i n magnitude  form s p e c i f i c a t i o n  The p r i m a r y  the  be l a r g e r  function;  elasticities  1)  elasticities  sample.  profit  have  when  components. is  should  functional  estimation  output  time-series  15 Two t e c h n i q u e s  series  set  necessary  alternative of  Therefore,  are  expedient.  and the  2) two  timeerror  methods  that  the  error  components  stochastic used i n  this  cross-  (Judge, study  Table Regression  s  h  a  r  Cattle  Inventories  .86 (8,4)* -.241  (8.2) Crops  -.33  Labour  -.078 (4.6) .077 (4.9)  Capital  Materials  Coefficients-Translog  Profit  Function  Prices  e  Cattle  5.1  (5.1)  -.288  Inventories  -.241 (8.2) .289  (7.5) -.107  Crops  -.33 (5.1) -.107  (2.6)  Labour  -.078 (4.6) .014  (2.9)  Capital  Materials  .077 (4.9)  -.288 (6.1)  -.01  (2.1)  .054  -.036  .011  .015  -.039  .147  .014 (2.9)  .015 (1.4)  .02 (2.3)  -.007 (1.4)  .037 (2.2)  -.01 (2.1)  -.039 (4.0)  -.007 (1.4)  -.02 (3.3)  -.001 (.05)  .054  .147  .037  -.001  .051  * t - s t a t i s t i c s i n parentheses  .037 (5.2)  (3.4)  (1.4)"  (4.0)  Stock  (4.9)  (4.8)  (2.6)  .315  Dummy  (6.3)  Constant  .787 (6.3) 1.09  (8.2)  1981  Variables 1980  1979  .156 -.004 -.151 (6.9) (.42) (7.1) -.053  (3.5)  .02  (1.1)  -.585  -.048  (4.3)  (2.2)  -.002 (1.7)  -.095 (3.8)  -.019 -.002 (4.6) (1.1)  .02 (5.9)  .002 (1.5)  .055 (2.5)  (.90)  -.012  (3.8)  -.252  (2.4)  -.008  .033  (1.7) .056  .019 -.006 -.013 (5.1) (3.5) (4.0) -.055  0  .055  1 25 5.  5.1  PARAMETER  ESTIMATES AND SUMMARY  STATISTICS  INTRODUCTION In  this  chapter,  discussed  for  Four.  Section  In  equations profit  and  (5.2),  the  out  In  are  reported  (4.4)  estimated parameters multi-input  Statistical  of  elasticities  the  last  econometric  this  e q u a t i o n s which are  of  (5.3),  estimated  derived  normalized  to  industry of  constitute  quadratic of  the  is  choice the  time-series  using  from a  elasticities  compared t o e a r l i e r  results  translog  main  dissertation.  Section  results  Measurements  These  share  testing  and i n c l u d e s e s t i m a t e s scale.  and  Chapter  the  variable  the c o w - c a l f  to  of  of  of  f i n d i n g s of  variable  in Section  presented.  technical  are  structure  returns  empirical  the  the m u l t i - o u t p u t ,  function  carried  results  e a c h model s p e c i f i e d  for  determine  empirical  net  based  output  multi-output,  profit  function  choice  are  again  supply  multi-input  are  reported.  generated  and  results. j  5.2  EMPIRICAL  RESULTS  USING  A  TRANSLOG  VARIABLE  PROFIT  FUNCTION Estimates expenditure procedure Table These  of  the  share for  5.1.  equations  estimating  Seven  parameter  systems  estimates  for  of  the using  of  the degree  the m a t e r i a l s  five  revenue  Zellner's  equations are  were r e q u i r e d  represent  homogeneity  of  derived  iterations  coefficients  symmetry and  parameters  for  maintained zero  in  and (SUR)  given  in  convergence.' hypotheses prices.  and s e r v i c e s  of The  expenditure  1 27 equation  are  derived  a d d i n g up c o n s t r a i n t s . parentheses. All  output  statistically  also  level.  of  for  indicate  Moreover,  are  output  equations.  of  But  are  of  labour  in  and  the  given  in  beginning c a t t l e with  period is  the  the  for  inventory  the total  demand  statistically share  share  coefficients  t-statistics  5  10 p e r c e n t  in both  not  expenditure  price  coefficients,  significant  c r o p revenue  stock  at  coefficients  end of  total  at  a  supply  own i n p u t  remaining p r i c e  highly  and is  output  for  significant  asymptotic  This  significance  estimated  and c a p i t a l  level.  t-statistics  the  positive  own  coefficient the  are  5 percent  statistical  The  this  For  significant  the  s u p p l y and t o t a l  from z e r o  estimated  t-statistics  positive  c a t t l e are  different the  homogeneity,  coefficients  statistically  significance.  beginning stock cattle  at  The a s y m p t o t i c  percent  level  price  condition  coefficients  84  Asymptotic  significant  elasticities.  percent  symmetry,  1  own  necessary  using  equation.  equations, are  of  the  marginally  1.7  and  1.5  price  and  respect i v e l y . Generally, beginning  the  cattle  econometric  statistical stock  specification  significance  coefficients of  the  of  provide  variable  the  support  and f i x e d  for  the  inputs  as  def i n e d . It for  is  the  interesting  covariance  coefficients  are  level  input  1979.  for  all  But  they  t o examine t h e  estimators  statistically share are  in  estimated Table  significant  equations  statistically  for  the  coefficients 5.1.  at  the  years  insignificant,  These  10 p e r c e n t 1981  and  except  for  128 the c a p i t a l provide varied  strong between  between are  share  the  not  equation, evidence  the  and  efficient  maintain  the  parameter  Goodness-of-fit  account  crop, the  table  for  variation  1981.  and  This  in the  64.6,  shares  that  that  all  These of  is  the  share  equations  ensure Symmetry  homogeneity  in  tests  critical general  is  4.5  of  rejected  of  in  The at  provided in  equations of  adequate.  equal  to  the  inventory,  estimation,  the  to  Table  respectively.  the  to  estimation.  end-of-period  are  Given  these  R  2  In  addition,  null  hypothesis  zero.  The  only  to  test  conditions Hessian  tested  null  first  matrix  The half  Chi-squared s t a t i s t i c these  properties  exception  a 5 percent  level  in  estimated duality  and null  results of  validation  the  for  u s i n g the  Chapter F o u r . the  preliminary  necessary  the  in  of  provide  the  are  of  the  consistency  is  that  reported  values  equations.  it  prices  in Table are  data  necessary  estimated  from t e s t i n g  results  However,  satisfied.  defined  the  rejected.  statistical  to  is  are  equations  utilized  result  soundly  the model.  have  varied  4 4 . 9 , 6 1 . 6 , and 5 6 . 9 p e r c e n t  estimated c o e f f i c i e n t s  hypothesis  that  in the  the  for c a t t l e ,  and c a p i t a l  reports  it  specification  measurements c a n be c o n s i d e r e d q u i t e 5.2  results  coefficients  indicates  estimates,  indicates  c r o s s - s e c t i o n a l data  Table  These  1 9 7 9 , and a g a i n  summary s t a t i s t i c s  72.2,  labour,  1980.  intercept  (1978)  dummy v a r i a b l e  This  the  year  from a homogeneous sample and c o n s e q u e n t l y ,  generate  5.2.  the  that  base y e a r  base y e a r  drawn  for  Table  linear  hypotheses of 5.3  these for  and i n d i c a t e  the  estimated  is  that  of  significance.  are  h o m o g e n e i t y of  two the  share prices  129 TABLE G o o d n e s s of Share  Equation  R  5.2  Fit  Statistics SEE  :  Cattle  .7220  .0358  End-Of-Period Inventories  .6463  .061 5  Crops  .4493  .0672  Labour  .61 56  .0054  Capital  .5690  .0049  Ho:  All Coefficients E q u a l to Zero  x  2  198.01  d.f.  X (.01)  30  50.98  2  Dec i s i o n Reject  130 TABLE Testing Test  Ho:  . A*  d.f.  x  2  for  (-05)  5.3 Structure Decision  x  2  (.01)  Decision  Homogeneous o f Degree One i n Prices  12.46  5  11.07  Reject  15.09  Accept  Symmetry  15.26  10  18.31  Accept  23.21  Accept  "Almost Homothet i c "  31.82  3  7.82  Reject  11.35  Reject  "Almost Homogeneous'  35.70  4  9.49  Reject  13.28  Reject  Non-Joint Production  31.02  4  9.49  Reject  13.28  Reject  *  X = - 2 ( l n L a - InLo)  131 Since  the  properties  of  rejected  at  statistically  u n r e s t r i c t e d model, properties  in  it  the  is  symmetry and h o m o g e n e i t y a r e the  not  10  percent  unreasonable  estimation  in order  level  to  in  impose  to perform  not the these  additional  tests. Checking r e g u l a r i t y shares all  are  positive  observations  profit  function  Convexity checked the  of  indicates  the  matrix  is  convex  reports  if  the  all  shares  variables)  and e s t i m a t e s  is  results  not c o n v e x  prices also  are  reported  that  are  of  the  that  the  It  2  is  prices  in  prices. are  The  eigenvalues.  (using  exogeneous  Unfortunatly,  variable  worth  profit  function  n o t i n g however,  the  3x3  for  Hessian  these  Table  matrix the  of  Hessian  non-negative.  Hessian  full  is  the H e s s i a n m a t r i x  the means of  and  t h e means of  non-convex, point.  are  illustrate  positive  of  the  The e i g e n v a l u e s  at  is  sample  Hessian matrix results  output  prices  to  at  variable  that of  the  input  sub-matrices  are  exogeneous v a r i a b l e s  the  in Table '5.4.  Hessian matrix each  indicate  convex.  Given  at  determined  in p r i c e s .  3x3 H e s s i a n of  of  translog  for  function  eigenvalues  elements  negative  property.  profit  respect  are  revenue  monotonicity  eigenvalues  with  predicted  these  that the  variable  function  predicted  shares  satisfies  this  the  and e x p e n d i t u r e  by c o m p u t i n g t h e  profit  5.4  which  conditions,  In  Table  reported that  at  but one v a l u e  non-convex H e s s i a n m a t r i x .  this  the  property 5.5  for  the  each  s h o u l d be eigenvalues  negative;  However,  it  for  observation.  e a c h sample p o i n t is  checked  five  again is  the  These  eigenvalues  indicating  interesting  to  a  note  1 TABLE Hessian  Cattle Cattle  .615  Inven.  5.4  Coefficients  and  Eigenvalues  Hessian c o e f f i c i e n t s Inven. Crops Labour C a p i t a l  Materials  -.013  -.261  -.095  .068  -.330  -.013  .04  -.022  -.007  -.021  .002  Crops  -.261  -.022  .181  .009  -.042  .131  Labour  -.095  -.007  .009  .062  -.006  .041  .068  -.021  -.042  -.006  .002  .001  .002  .131  .041  .001  .16  Capital Materials  -.33  Eigenvalues  Hessian Output Input  Matrix Price  Price  :  .9228  Sub-Matrix Sub-Matrix  .0932  .0569  .0363  :  .737  .076  .022  :  .162  .060  .0008  -.0439  -.0069  Eigenvalues 0.92746 0.92659 0.88902 0.88348 0.90472 0.92363 0.91942 0.90425 0.91351 0.89467 0.91187 0.92406 0.91199 0.93385 0.91502 0.93252 0.88055 0.88311 0.90214 0.89024 0.89305 0.91269 0.90104 0.88165  0.90167 0.90456 0.89725 0.90214 0.94763 0.98123 0.92820 0.92364 0.95250 0.95157 0.96264 0.93718 0.95429 0.93047 0.95249 0.97379 0.95767 0.98458 0.96825 0.99325 0.93761 0.93860 0.97837 0.96089 0.98904 0.95162 0.99734 0.94313 0.98830 0.95834 0.93973 0.94574  for  -0.08158 0.09111 -0.06818 0.07085 -0.08110 -0.07411 -0.07741 -0.07169 -0.07677 -0.06949 -0.08022 -0.07805 -0.07336 -0.07944 -0.07719 0.10822 0.07087 0.07378 -0.07358 0.06892 -0.07254 -0.07046 -0.07300 0.06997 -0.07536 -0.07520 -0.06991 -0.07429 0.10956 0.17964 0.08791 0.08288 -0.07229 0.10290 0.07903 0.09400 -0.07258 0.08425 -0.07543 0.11181 0.09423 0.11562 0.1051 1 0.16478 0.07718 0.09178 0.09870 0. 11081 0.09913 0.11010 0.09857 0.07667 0.10929 0.07945 0.0691 1 0.07320  TABLE 5.5 , • H e s s i a n M a t r i x at each O b s e r v a t i o n 0.05807 0.03151 -0.05993 0.05898 0.06693 0.04109 -0.06380 0.04558 0.05937 0.02968 0.061 1 4 0.04038 0.06032 0.03462 0.06324 0.03729 0.05916 0.03153 0.06387 0.03791 0.06010 0.03134 0.05682 0.03563 0.05734 0.03411 0.05283 0.02903 0.06467 0.04570 0.06044 - 0 . 0 5 7 6 5 -0.06607 0.04672 -0.06131 0.04828 0.06249 0.03636 -0.06876 0.04446 0.06473 0.03879 0.06365 0.04391 0.06258 0.03689 -0.06582 0.04589 0.06419 0.03856 0.06004 0.03964 0.06343 0.04348 0.06166 0.04158 -0.06680 0.04847 -0.05663 0.04408 -0.05879 0.04592 -0.05722 0.04372 0.07137 0.04176 -0.06138 0.04421 -0.07356 0.04135 -0.06031 0.04507 0.07031 0.04060 -0.05891 0.04436 0.07383 0.04341 -0.07297 0.03945 -0.06689 0.03902 -0.07034 0.03683 -0.06893 0.05123 -0.06278 0.04801 -0.06007 0.05093 -0.05609 - 0 . 0 6 6 8 3 .0.05304 0.04772 -0.06043 0.05228 -0.07140 0.04639 -0.05788 0.05420 -0.07213 0.04458 -0.06034 0.04978 -0.07047 0.04764 -0.07010 0.04357 -0.06474 0.04352 -0.06608 0.04370  0.01281 0.01832 0.01797 0.01915 0.01409 0.01375 0.01417 0.01323 0.01285 0.01581 0.01437 0.01288 0.01135 0.00871 0.02020 0.02838 0.02427 0.02415 0.01706 0.02114 0.01907 0.01760 0.01734 0.02331 0.01890 0.01758 0.01971 0.01875 0.01502 0.01071 0.01553 0.01504 0.01108 0.01016 0.01076 0.01202 0.01008 0.01358 0.01278 0.01026 0.00944 0.00758 0.01238 0.00932 0.01323 0.01469 0.01011 0.01057 0.01067 0.01241 0.00936 0.01124 0.01119 0.00971 0.00995 0.00940  0.00014 0.00016 0.00014 0.00016 0.00015 0.00015 0.00015 0.00014 0.00014 0.00015 0.00014 0.00015 0.00015 0.00014 0.00016 0.00017 0.00015 0.00016 0.00015 0.00016 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.0001 5 0.00016 0.00015 0.00015 0.00016 0.00016 0.00016 0.00015 0.00016 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00016 0.00015 0.00015 0.00014 0.00015  134 that  for  larger  each  then  whereas  observation  the  the  other  point  absence  of  the  FFF  are  shown t h a t  do  is  does  not  not  sum,  close  it  share  equations  are  significant  with  duality  of  properties  and m o n o t o n i c i t y . profit  function  conclude that well  the  and t h a t  behavior  of  are  reported  percent  of  the  the  in outputs  level  of  testing  the  true  result  of  the  does  revenue  and  statistically  will  indicates  satisfies  linear  in  represent  the  prices,  the  Consequently,  equations  to  required  be assumed t h a t  share  that  the  homogeneity  in p r i c e s .  coefficients  equations,  4.5 of  in  that  true  one  can  have  performed  the p r o f i t  maximizing  producers.  share  in Table  homothetic"  convex  estimated  characteristics  it  adequately  cow-calf  expenditure  symmetry,  estimated  they  Using the  defined  is  an  e q u a t i o n s p r o v i d i n g a good f i t  function  Finally,  indicate  generally  statistical  profit  Wales  estimates.  expenditure  estimated variable  true  indicate  this  coefficients  Furthermore,  the  a good a p p r o x i m a t i o n t o  estimated  the d a t a .  zero.  prices.  may  the  share  to  may not  Wales c o n c l u d e s t h a t  the  magnitude,  that  in  a non-convex r e s u l t rather  significantly in  prove  p r e c l u d e o b t a i n i n g good e l a s t i c i t y In  is  one  non-convex  provide  Neverless,  to  relatively  optimizing behavior,  function. not  function  eigenvalue  and c l o s e  estimates  underlying p r o f i t has  values  remaining values  These  (1977)  one  one  underlying  Four.  bottom  half  rejected  significance.  can  the  revenue  test  for  transformation  Chapter  is  of  at  certain  function  These s t a t i s t i c a l of  Table  both the  Subsequently,  and  5.3. 5  tests  "Almost-  and it  as  must  the  10  follow  135 that  "almost-homogeneous" in outputs  is  due  the  to  the  (1980),  w i t h the  Kunimoto  These  returns returns of  a  5.6, for are  f i n d i n g s of  to  scale  e a c h of  of  the  observation.  a given  for  significantly  provide  is  estimates,  last  possibilities from  that  rejected  at  scale  structural  the  of  are  the  cow-calf by  constant  definition  1981  revenue  an  estimate In  to  Table  provided  These  estimates  shares  for  decreasing  inputs  of  are  What t h i s  past  returns  to  although  (Ray test  c r o p s and  non-joint both  in  indicate  requires  statistical  production hypothesis indicate  scale  agricultural  between  the  zone l o c a t i o n s .  unaware  to  (Lopez  returns  means  be  each  is  that  increased  in  proportion.  these  returns  that  c a n be d e t e r m i n e d .  clearly  m e a s u r e s of  decreasing  studies  Chapter F o u r ,  predicted  similar  w i t h U.S.  of  zone l o c a t i o n s .  greater  consistent  Results  the  in outputs  author  However,  The  soil  The r e s u l t s soil  to  are  agriculture.  following  (4.4)  returns  using  increase  The  the  economic  characterized  measure  fourteen  all  not  within  results  contention  However,  in Section  generated  scale  the are  returns-to-scale estimates  other  This  nested  These  on C a n a d i a n  support  scale.  rejected.  almost-homogeneous i s  technologies  to  also  hypothesis.  (1983))  tests  production  a  that  almost-homothetic  consistent  to  fact  is  also  and  studies  in  agriculture.  small  in magnitude,  which  also  1982 and Weaver assesses cattle  reported  report  production  cow-calf of in  the  farms. non-joint  Table  5.3  c r o p s and c a t t l e 10  are  1983).  joint  on  testing  the  which  scale  studies  p r o d u c t i o n of 5  Canadian  percent  can  levels  and be of  TABLE Returns Soil  Zone  Returns  to to  1  .065  2  .094  3  .093  4  . 1 02  5  .071  6  .072  7  .071  8  .079  9  .072  10  .088  1 1  .071  1 2  .065  1 3  .072  1 4  .058  5.6 Scale Scale  137 significance. benefit  to  farms.  This  jointly  A  crop  the  o p t i o n of  the  form of The  producing cow-calf  is  again  joint  test  characteristic  this crops  does not  and  because reflect  as do t h e  to  is  the  results  a  cattle  or  significant on  cow-calf the  through  aware  for  this  the  farmer  cattle  published  possibilities  and  rejects  His  result  of  in  Lopez  Canadian (1981)  does  joint  production  must be  interpreted  aggregated  a specifically  technological Canada  and  in  results  data  and  defined  farm  study.  is  joint  structure  d e f i n e d by  transformation  scale  of  b a s e d on h i g h l y  technology  in western  non-homogeneous returns  is  in a working paper,  cattle.  it  Summarizing, production  and  directly  production  However,  carefully  crops  not  agriculture.  between  there  beef.  for  for  that  p r o d u c t i o n system a l l o w s  marketing grain  author  testing  indicates  function production  a  of  cow-calf  non-homothetic,  subject  to  between  decreasing crops  and  cattle. The s t a t i s t i c a l which  is  necessary  equal  interest  responsiveness These p a r t i a l the  are of  tests  to c h a r a c t e r i z e measures cow-calf  elasticities  exogeneous v a r i a b l e s )  standard errors  for  estimates  generated  profit short  are  f u n c t i o n and run  p r e s e n t e d above p r o v i d e  of are  of  choice given  using  consequently  elasticities.  input  farmers  each e s t i m a t e  cow-calf  to  production.  substitution changes  (computed a t in Table  are  in  the  fitted  should  information  5.7.  in  and  prices.  t h e means of Approximate  parentheses.  be  Of  translog  3  These variable  interpreted  as  138 TABLE Elasticities Cattle  Invent.  of  Crop  5.7  Choice Labour  (Translog) Capital  A Cattle  _ .03 1 .43 ( . 2 3 7 ) * (. 067)  I nvent.  -.025 (.055)  .075 (. 072)  Crops  -1 .63 ( .402)  Labour Capital Materials  B .602 ( .149)  .021 ( .019)  . 1 58 ( .036)  - .042  —  ( .078)  .014 ( .009)  _ .04  - .139  (. 261 )  1. 1 3 ( .408)  .054 ( .063)  2.48 (.42)  .28 ( .12)  .215 (.25)  -3.24 (.74)  1 .01 (. 223)  2 .02 ( .466)  3.34 ( .47)  - .015 -1 .32 ( .109)  ( .233)  c *standard error  in  Materials  parentheses  ( .008)  .003 ( .02)  .265 ( .061 )  .820 ( .144)  —  _ . 1 54  . 1 54 (.13)  ( .216)  .293 ( .248)  —  - .414  _  ( .168)  .769 ( .021 )  .116 ( .288)  .011 ( .122) D  -1 .024 ( .416) .05 ( .575)  _  -1 .61 ( .523)  139 B e f o r e p r o c e e d i n g w i t h a d i s c u s s i o n of that a  the  theoretical  number  of  a  elasticities.  slopes,  non-positive  describing  convenient and D) In price  as  c r o p supply are  an  and c r o p s level  elastic  that  A,  altered  for  given.  must  have  substitute inventory  that  Table  all  a  it  is  5.7,  sub-matrices  one  indicating  expected  cattle of  (A,  B,  cattle  inelastic  of  farmers'  than  are  and  cattle at  the  5  indicating  This  implies  significantly  prices.  response  to  that  is  The own positive  level  of  changes  85 in  end-of-period  substantially  these output  one  however,  implies  not  for  a confidence  in expected c a t t l e  magnitude  cow-calf  are  supply  in current  cross  inventory,  significant  and c r o p s  (with  This  s u p p l y and  own p r i c e s .  inventories  prices.  to changes the  an  in  changes  (.075),  of  of  and g r e a t e r  cattle  end-of-period  percent)  that  have  or  end-of-period  to changes  to  than  argue  four  statistically  positive  response  but  From  into  in  own e l a s t i c i t i e s  are  of  of  response  must  functions  indicates  Own e l a s t i c i t i e s  (1.13)  and a r e  elasticity  inventories  these  a negative  5.6  cattle,  quantities  in  less  is  Table  table  the  response  output  of  defined.  sub-matrix  percent  signs  demand f u n c t i o n s  elasticities  the  elasticities  (1.43)  provided  confirmed.  the  to d i v i d e  input  the  recall  Three  s u p p l y and e n d - o f - p e r i o d  of  are  about  supply  there  cattle  An e x a m i n a t i o n  In  C,  and  between  expectations  output  table,  in Chapter  predictions  derived  slopes,  relationship  priori  priori  Specifically,  non-negative  demand.  model d e v e l o p e d  this  altered  in  prices.  own e l a s t i c i t i e s , response  to  one  can  changes  in  1 40 expected  cattle  significant  price  output  cattle  cycle).  changes  in current  output  are  the  cattle  existence In that  Rather, cattle  cycle).  In  that  they  are  percent  shift  small  increase  decrease  in c a t t l e  respectively.  only  is  and  between In  Table  effects  subsitutes  5.8,  to  cattle over  support  Using  the  in  increase  and c r o p the  of  scope  for  a summary of  the  in  of  -.042%  cattle  prices  but a  -0.03% the  major a  in a and  one small  -.139%  standard  are  and  errors  statistically  level.  c h a n g i n g the farms  cross  in a decrease  results  cross price  on c o w - c a l f  substitute  Finally,  outputs  5 percent  a  (-.025%)  prices  supply  definition,  a  in  (-1.63%).  price  example,  output  inventories  cross  For  results  cattle  from t h e s e  presented.  indicate  recall  quantities  this  categories.  and  two  positive  t h e m a g n i t u d e of  at  c r o p s and c a t t l e  are  between  elasticities  crop  cattle  significant  no the  fluctuations  results  and  in expected c a t t l e  One can c o n c l u d e there  in  substitution p o s s i b i l i t i e s ,  production  However,  that  changes  these  in crop p r i c e s  reduction  percent  is  responds p r i m a r i l y  with p r i c e  A one p e r c e n t  away from c r o p  significant  counter  (i.e.,  words,  output  inventories  respectively.  implies  to  elasticities  cross price  increase  end-of-period  a  attempt  substitutes  r e l a t i o n s h i p amongst a l l  causes  there  imply c o m p l e m e n t a r i t y .  estimated  -.602%  (i.e.,  cycle.  cross price  elasticities  one  price  other  minor  supply  correlated  a cattle  negative  i n an  output  determining output  imply  the  relatively  adjustment  positively  of  is  elasticities output  composition  in western  price  and  that  Canada.  own  price  TABLE  5.8  Summary o f C r o s s P r i c e a n d Own Price Elasticity  Cattle  Cattle  Elastic  Inventories  Crop  Substitute  Substitute Substitute  Inventories  Substitute  Inelastic  Crop  Substitute  Substitute  Elastic  142 Estimates elasticities price  input  a  5  cross  a r e shown  price  negative  percent  level  prices,  On  other  inputs  is  in input  labour  hand,  but  an i n e l a s t i c  estimate  not  not  In  sensitive  coefficients more  stable  less  than  are  absolute  that  farmers  utilized  words,  relative  to  in  elastic response  decrease  for  the  capital  absolute  input.  value  However,  this  different inputs  from  used  The m a g n i t u d e o f  employment of employment  value  substantially.  of c a p i t a l  i n own p r i c e .  that  in  significantly  the q u a n t i t y  to changes indicates  one  demand f o r t h i s  statistically  other  and m a t e r i a l s  own d e r i v e d demand e l a s t i c i t y  indicating  zero.  own  implies  inputs  5.7.  demand  i n d i c a t i n g an  cow-calf  and m a t e r i a l  negative  is  This  input  The  than one i n  of s i g n i f i c a n c e ,  t o an i n c r e a s e of  price  for labour  and g r e a t e r  inputs.  quantity  own  in sub-matrix D in Table  d e r i v e d demand f o r b o t h  the  and  demand e l a s t i c i t i e s  significally at  of  capital  of l a b o u r  is  these  inputs  is  and m a t e r i a l  inputs. The s i g n s of t h e c r o s s p r i c e defines  i n p u t s as s u b s t i t u t e s  side,  a  negative  complementarity  substitutibility. capital (with  increases a  standard  A  one  error  increase  i n the p r i c e  capital  demanded  by  of  of  labour  at  Conversely,  t h e 85 p e r c e n t  r e l a t i o n s h i p between l a b o u r  implies  i n the p r i c e  demanded  increases  input implies  elasticity  increase labour  .13).  the  elasticity  cross price  of  On  the  by  of  .154%  a one p e r c e n t quantity  .293% ( w i t h a s t a n d a r d e r r o r  T h e s e two m e a s u r e s d e f i n e , a substitute  price  percent  the q u a n t i t y  in sub-matrix D  or complements.  cross  and a p o s i t i v e  elasticities  of  confidence  and c a p i t a l .  of  .248). level, For  a  143 given  set  of  substitution mutatis  relative  effect  between  mutandis,  that  from l a b o u r and towards On t h e materials  the  estimate  evidence  materials  of  respectively. materials the  Table cow-calf  5.9  both  small  labour  is  the p r i c e  standard errors  materials  and  labour  employed  significant  -.414%  at  complementarity  summarizes t h e  between  fact  that  the  -.011%  labour  5 percent  between  a  reduces  and  t h e c o m p l e m e n t a r i t y between  statistically  capital.  or c a p i t a l  by  for  between  complementarity  p r o v i d e d by t h e of  and  The m a g n i t u d e of  materials of  of  and level  capital  and  significant. relationships  between  inputs  for  farms.  Turning  now  values  of  input  prices,  the  to  results  at  i n an  of  sub-matrix output  the  at  in a reduction  and c a t t l e 5 percent  the  increase  15  percent  which  with  increase in  the  s u p p l y of  level)  B,  supply  c o n s i d e r a one p e r c e n t  inventories  significant  examine  elasticities  This  significant  results  of  i n the p r i c e  respectively.  inputs  in  estimated not  increase  demanded  degree  statistically  is  s u b s t i t u t i n g away  capitalization.  between  the  Again,  is  materials  period  of  increase  quantity  whereas  than  the  implies,  implies a stronger complementarity  and t h e o t h e r  one p e r c e n t  of  capital  farms a r e  combined w i t h the  and l a b o u r  Further  labour.  greater  strength  and  h a n d , a one p e r c e n t  elasticities  materials  the  cow-calf  by - 1 . 0 2 4 % and - . 0 5 1 %  labour  the  labour  r e d u c e s the q u a n t i t y  capital these  other  prices,  level)  respect  i n the p r i c e  level  -.014%  and - . 0 2 1 %  provides  of  of  end-of-  (statistically (statistically  respectively,  i n c r o p p r o d u c t i o n of  to  .054%  but  it  (although  TABLE  Labour  5.9  Summary  Classification  Labour  Capital  Elastic  Capital  Substitute  Materials  Complement  of  Farm  Inputs  Materials  Substitute  Complement  Inelastic  Complement  Complement  Elastic  145 this  result  implies  that  of-period On price  not  significantly  different  from z e r o ) .  c a t t l e p r o d u c t i o n , and t o a l e s s e r  inventories, the  of  crops  is  other  capital  are  hand,  results  (-.04%)  intensive  a one p e r c e n t  in a large  s u p p l i e d (-.265%)  inventories  labour  increase  supply  all  statistically  end-  i n the  in  and a m i n o r d e c r e a s e now c a t t l e  extent,  operations.  decrease  but  This  flow  quantity  in end-of-period  increases  by  are  percent  and i m p l y t h a t c r o p p r o d u c t i o n and a g a i n ,  lesser  extent,  intensive  by  the  but  by  of  from  production  is  changes  in  of  the  that  of  5  to a  capital  of  materials  the  cost  of  increasing total  estimate  This  is  result  (by  would  cattle  Furthermore,  cattlemen's inputs  in  significantly  would i m p l y t h a t  intermediate  cattle  decrease  inventories not  intensive.  argument of  large  (End-of-period  this  crop supply  this  groups)  that  significantly  p r o d u c t i o n and s u b s e q u e n t l y ,  the  cattle.  an  output  example,  the  interest  rate  of  the  are  i n the p r i c e  significantly  material  price  Generally, price  in a  but  also  supports  the  significantly  zero.)  result  supply  inventories,  increase  -.769%.  .003%  different  affects  of  results  supply  increase  period  a one p e r c e n t  effect  .820%,  cattle  of  at  operations.  Finally, has  end  significant  .158%.  These e s t i m a t e s level  of  policies  that  i n p u t have t h e which  uses  distort  effect  the  of  input  downwards  the  relative  i n c r e a s i n g the  s u p p l y of  more  intensively.  Canadian government's p o l i c y  of  s u b s i d i z i n g the  on f a r m l o a n s would t e n d t o d e c r e a s e  farm c a p i t a l  resulting  i n an  increase  For  the  price  i n t h e p r o d u c t i o n of  1 46 crops  and a d e c r e a s e  production input  of  cattle.  intensities The  final  is  of  > 1 ),  This  labour  and c a p i t a l  in a decrease  end-of-period  (0  of  standard  classification  inferior in  of  tests  normal  inputs  in  1.01%  material  as ( ei j  expected  increase  .18% and  statistical  in  the  prices  effects  cattle,  labour  tests This  of  on t h e  however,  the  the  < 0) . inventory  quantity  respectively  inputs  demanded that  in  production  the  all  of but  indicate  errors of  capital  to the  labour  by  three of  with  be  is  a  of  is  In  the  inferior  supports  reversed as  this  in  the  superior  Additionally,  estimate  to  have  classified  t o be an  now d e f i n e d  normal  respect  inputs.  variable  inferior.  labour  summarized i n T a b l e  cattle  is  crops  c a n be  appears  each  as  and  demand f o r  classification  for  classification  cattle  and m a t e r i a l s  on  calculated  elasticities  of  i n an  c r o p s where c a p i t a l  materials  production  or  increase  demanded by  larger  conveniently  <_ 1 ),  the q u a n t i t y  classification.  The  £ ei j  result  Statistical  demand  of  superior  inputs:  large  estimates  inputs  as  and  provides  be u s e d t o c l a s s i f y  of  production  5.10.  will  production  input.  to  inventories.  Increases  superior  according  prices.  be d e f i n e d a s  considerably  (C),  the  to output  will  in  outputs  in  demand w i t h r e s p e c t  However,  can  of  a one p e r c e n t  prices.  inputs  Classification  magnitude)  summarized i n T a b l e  normal  Consider  -.015%.  in  input  elasticities  ( e ij  smaller  sub-matrix  elasticities These  (although  results  input. output  the  in  the  These  input  supply  are  5.11.  labour  consistent  as a s u p e r i o r with  the  input  major  in  the  emphasis  TABLE  5.10  C l a s s i f i c a t i o n of Outputs W i t h R e s p e c t t o I n p u t Use Labour  Cattle Inventories Crops  Capi t a l  Intensive  Intensive Less  Intensive  Materials  Less  Intensive  Intensive  1 48  TABLE  5.11  C l a s s i f i c a t i o n of I n p u t s W i t h R e s p e c t t o O u t p u t Use Cattle  Inventor ies  Crop  Labour  Superior  Normal  Normal  Capital  Inferior  Normal  Super i o r  Ma t e r i a 1  Superior  Normal  Infer ior  1 49 still  placed  western  on  in  the  classification  classification the  is  consistent  designed  or c r o p s w i l l  to  have q u i t e  away from l a b o u r  migration  off  which  will  farms and i n c r e a s i n g  prices,  on t h e  other  labour's  capital's  superior  hand,  of  labour  capitalization.  farm  prices  in  crops,  different  crop  cattle  migration  increase  substitution  prices  of  either  effects  on  rural  will  give  rise  to  encourage  increased  capitalization.  Increased  will  result  in  increased  employment. It  would  presented  in  be h e l p f u l  this  However,  research  reports  which  t o compare  section  agriculture.  such d i s a g g r e g a t e d farm  of  with  w i t h a net  Increasing  farm  p r o d u c t i o n of  production  combined  development.  cattle  in the  farm and an e m p h a s i s on i n c r e a s i n g  Policies cattle  cowboy  Canada whereas  inferior  off  the  with  the  other  author  estimates  outputs  the  and  of  elasticity studies  is  inputs  on  unaware  elasticities  estimates  of of  combined  Canadian any  past  choice  with  for  specific  data. Completing  multi-output, requires  a  this  effect  of  reporting  multi-input calculation  s u p p l y as d e f i n e d that  the  cattle  price  changing expectations For elasticity  of  of  cattle  the (4.4)  measure  variable total of  cattle the  supply  is  profit  account  reproduced  not the  the  cattle Recall  only  of  the  effect  of  supply.  estimating here:  of  Four.  on c a t t l e for  for  function  elasticity  but a l s o  prices  formula  results  Chapter  takes  fluctuations, of  convenience,  empirical  translog  in Section  elasticity  of  the  total  150 Total Elasticity  n  D  r  e  c  Cross Elasticity  t  [ -e1„ 1]  "  u  i  Elasticity  t « i  +  V  +  i  §  -  1  1  [ £  +  [  g  12  E l a s t i c i t y of Expectations *  ]  -  2  V  i  g  ^ l  1  '  ]  •  [3 Pj P21  The  direct  elasticity  5.6).  supply  [e^ ]  variables,  total  t o be 1.43 and -.03 r e s p e c t i v e l y  elasticity  expectations. average  Section  for  —e — 1 3P /3P  measure  —  elasticity  P  estimate  of  taking  a  weighted  d e r i v a t i v e s of each ARIMA model estimated  (4.2) of Chapter  series  an  (Table  of the e l a s t i c i t y of  by f i r s t  Four.  T h i s d e f i n e s an estimate  • which i s then transformed  2  price  is a  T h i s i s determined  of the f i r s t  in  cross  e  Thus, a l l that i s r e q u i r e d to generate  this  and  C ] 2 3 are c a l c u l a t e d , a t the means of the  e l a s t i c i t y of supply exogenous  of  using the mean  of  each  —g  and  1  P  2  of e x p e c t a t i o n s .  to provide a p o i n t estimate of the T h i s value i s c a l c u l a t e d  to  be  .4186. Given that the c r o s s e l a s t i c i t y that  the  elasticity  of  of supply  expectations  i s positive,  i n d i c a t e s that accounting f o r adjustments cattle  prices  always decrease this  effect  caused  elasticity  in  i s not  strong  supply  of  cattle  enough to  zero  this  expectations  by changes i n c u r r e n t c a t t l e p r i c e  the e l a s t i c i t y  e l a s t i c i t y of c a t t l e  i s negative and  supply.  of will  However,  to  reduce  the  total  or  less.  The  total  i s c a l c u l a t e d to be 1.41.  T h e r e f o r e , the r e s u l t s of the e s t i m a t i o n do not support a perverse  short  run  supply  response.  clearly  i n d i c a t e s a p o s i t i v e short  cattle  in  western  Canada.  run  Rather, supply  the evidence function for  Some s p e c u l a t i v e reasons  for this  151 result  will  be o f f e r e d a f t e r  the  time-series  based  results  have been e x a m i n e d .  5.3  EMPIRICAL RESULTS USING TIME-SERIES DATA Before  discussing  normalized quadratic t o emphasize the series  the  variable  reasons  results profit  for  of  first  resulting  two  is  cyclical  years.  The  1956 was a p p r o x i m a t e l y to  13 m i l l i o n head by Given  series  that  series cattle second  the  sample w i l l price  adjusted  total  first  d a t a used in  characteristic  under  of  cattle  number of  of  allow  the  are  cattle  over  number  is the  on farms  in  increased  generated using  for  of  econometric  c h o i c e can  that  to changes  can t h e n be compared t o  may  However,  greater  i s more i m p o r t a n t .  the c o n s t r a i n t  assumption of  production The s e c o n d  characteristic  increasing cattle  fully  the  industry.  increased s i g n i f i c a n t l y  certainly  condition  the  time-  capture  in the cow-calf  the c r o s s - s e c t i o n a l r e s u l t s .  the  values  important  additional  fluctuations.  predictions  sample, e l a s t i c i t i e s  not  a  1982."  data  words,  is  fully  11 m i l l i o n h e a d : t h i s  price  procedures,  undetected in  have  not  nature  well defined price  inventories  thirty  may  characteristics  the  in  cattle  last  it  using  parameters.  influence  that  function,  estimating these  The c r o s s - s e c t i o n a l r e s u l t s  The  generated  not the  go time-  variability  estimation. Using a  be  time  The  time-series  calculated  inventories.  in  in  other  inventories  have  i n exogenous p a r a m e t e r s ,  these  elasticities  given  beginning  Or  under  generated  an o p t i m a l b e g i n n i n g i n v e n t o r y  (i.e.,  cross-  1 52 sectional  results).  Initial supply  estimates  equations,  of  the parameters  total  cattle  inventory  demand, w e r e , d e r i v e d  However,  the  P  variables =  1  differenced intercept  presented  equation.  To c o r r e c t  used in the  estimation  the  model  t e r m can be  indicates  interpreted  the  the  estimation.  in Table  5.12.  These  time  of  homogeneity of  zero in p r i c e s .  in  The consistent  signs  of  the  with a p r i o r i  statistically  significant  the  level  10 p e r c e n t  in  is both  coefficients equation. price  of  the  the  first-  estimated (Kmenta  variable  can  be  parameters  are  required  for  were  Hessian  Asymptotic  estimated  positive:  inventory  coefficient  using  5  the  estimated  at  the the  under  the  matrix  and  t-statistics  of  Contrary  coefficients  not to  are  level  However,  only  and t h e  the  crop the  is  end-  positive but a  price  5 percent  input  significant  a necessary  price  significant  The at  own  are  coefficient  statistically  translog case,  not  price  significant  statistically the  is,  significance.  statistically equations.  cattle  is  coefficients  That  5 percent  coefficient  level  are  price  expectations.  are  at  problem,  parentheses.  coefficients  of-period  trend  are  maintained hypotheses  given  that  estimated  equations  degree  this  Using  iterations  symmetry  first-order  as a t r e n d v a r i a b l e  The  Three  technique.  were t r a n s f o r m e d  re-estimated.  Consequently,  convergence.  are  SUR  each  in  transformation  in  using Z e l l n e r ' s  output  end-of-period  indicated  1971, p . 2 9 0 ) . droped  two net  test  and  6  the  s u p p l y and t o t a l  Durbin-Watson  autocorrelation all  of  price  in  either  own  output  sufficient  153 TABLE  5.12  Regression C o e f f i c i e n t s , Quadratic P r o f i t Function  Coefficients  Cattle  Cattle  9989.8 (3.4)*  Price'  Expected Crop  Gain'  Price'  Labour  Inventory -14677.0 (2.6)  14677.0 (-2.6)  18339.0 (1.6)  -2983.5 (-5.1)  4912.9 (4.3)  Price'  Capital  Equation  0495.21 (-.14)  Price'  3014. 1 (.42)  3542.2 ( .26)  -7174.7 (-.26)  4.4 (9.4)  3. 1 (3.4)  Constant  -304.93 (-1.7)  361.76 (1.02)  R  .8384  Beginning  Stock  2  .6941  d.w.  1 .4  SEE  696.92  *t-statistic  in  1370.6  parentheses :  Ho:  1 .5  a l l coefficients equal to zero  z?~  136.38  d.f. 11  x (•°5) 2  19.68  Dec i s i on Reject  154 condition  for  generating  Finally, stock  of  the  level  The  term  variable  for  is  level.  been b i a s e d a g a i n s t  reported  technical in other  1982).  beginning  significant  cattle  95 p e r c e n t  at  the  at  equation  confidence  equation only  that  level,  intercept  80  percent  the  in  is  the  technical  p r o d u c t i o n but  a bias  limitations therefore favor  change  bias studies  in  prohibit  this of  these  favor  change of  has  end-of-  of  result  the  advancements  that  farmers  animals. increases  to  been a c h i e v e d  enable  farmers  crop  in  aggregate  able  data  equation  and  The t e c h n i c a l  indicates  that  maintain  larger  result  to  However,  is  bias  technical  by  cattle technical  to e f f i c i e n t l y  this  been  Vlasterin  been  primarily  Moreso, the  have  be t e s t e d .  end-of-period inventories  T h i s has  and  crop production.  c o u l d not  inventories.  p r o d u c t i o n has  Laurence,  studies  estimating  enabled  numbers o f  cattle  (McKay,  favor  has  observed  against  Additionally,  demonstrate  this  the  indicates  cattle  the  inventories.  The  in  the  positive  This  for  elasticities.  equations.  for at  significantly  supply  statistically  the e n d - o f - p e r i o d i n v e n t o r y  confidence  period  are  term  negative  output  coefficients  in both output  intercept  significantly whereas  estimated  cattle  5 percent  positive  feed  large  consistent  with  herd over  the  p e r i o d of  study. Summary measures  reported  in  .8384 and  .6941  period  Table for  inventory  of  g o o d n e s s of  5.12. total demand  fit  estimates  The e q u a t i o n s have R cattle  supply  respectively.  and  2  are  measures  total  These  also  end  of of  statistics  1 55 indicate output  that  the  estimated  quantities  well.  transformed v a r i a b l e s )  equations  The D u r b i n - W a t s o n implies  serious  problem.  Finally,  the  hypothesis  that  to  null  z e r o shows an e a s y Because  many of profit to  only  satisfied.  of  whether  to  coefficients  the  determine  the  That  these  output  for  (i.e.,  results,  it  represent  the  it  of  statistic are  a for  equal  estimated,  is  variable  not  duality  possible are  equations  consistency  of  their  fully  can  be  estimated  properties.  the is,  monotonicity  both  obtaining  is  predict  equations a  assumed  the  the d u a l i t y  positive the  semidefinite  are  that  at  satisfy  positive  coefficients  satisfy  profit  requirement  both equations  own p r i c e  equations probably  therefore  the  not  quadratic  estimated  Furthermore,  condition  Hessian matrix From  properties two  observation.  necessary  normalized  w i t h the d e s i r e d  response.  is  e q u a t i o n s c a n be  Consequently,  the  satisfy  output  output  the  Both e q u a t i o n s each  autocorrelation  estimated c o e f f i c i e n t s  unknown.  However,  evaluated  all  (for  in  rejection.  the p a r a m e t e r s  determine  that  variation  statistic  a Chi-squared test  two net  function are  e x p l a i n the  positive). estimated  properties  maximizing behavior  of  net and  cow-calf  producers. Using Four,  the  formulas presented  estimates  of  given  in  Table  means  of  the  elasticities, table  into  the  partial  5.13.  These  exogenous it  will  sub-matrices  in Section  of  Chapter  elasticities  of  estimates  computed at  variables.  be c o n v e n i e n t (here A,  (4.4)  B,  In  are  choice  describing  are  these  t o once a g a i n d i v i d e  and C ) .  the  the  TABLE Elasticities  5.13  of C h o i c e  (Quadratic)  Prices  Cattle Cattle Invent.  .19 -.099  Invent. -.083 .037  Crop -.269 16  Labour .031  Cap. .043  .067 - . 0 3  Materials .295 -.10  Beginning Stock 1 .8 47  157 In  sub-matrix A,  as c r o s s p r i c e period are  own e l a s t i c i t i e s  elasticities  inventories  consistent  are  for  both  elasticity  estimates  cattle  response to p r i c e  total  displayed.  with a p r i o r i  however,  less  response  (although  inelastic  than  the  (.19)  model.  The a l t e r n a t i v e  in Table  5.14.  restriction  for  results  of  both c a t t l e  reduced.  These  It  is  is  supply  positive: (.037) inelastic  inventories  estimate  model.  However,  significantly  estimates  that  under  herd  size  (i.e.,  levels),  the  provide  principle  own period  empirical  discussed  in  is  with the  cross-sectional  s u p p l y and end of  results  lower  translog  are  compared  the  general  constrained  elasticity  of  inventories  is  evidence  to  Section  support  (4.3)  of  7  worth  noting that  estimated e l a s t i c i t i e s cow-calf  are  is  increasing  Le C h a t e l i e r  translog  the  indicate  supply- f o r  Four.  of  inventory  i n magnitude)  own-elasticity  to optimal herd  Chapter  and  end-of-period  using  adjustment  the  well  s u p p l y and end-of-  and  supply response  obtained  What t h e s e  as  t h a n one i n d i c a t i n g an  smaller  cattle  one  supply  Own e l a s t i c i t i e s  o b t a i n e d u s i n g the c r o s s - s e c t i o n a l the  cattle  expectations  supply  are  of  variations.  •The i n e l a s t i c consistent  the  farmers  expected c a t t l e  support  respond  prices  t h e m a g n i t u d e of  than  results  time-series  presented e a r l i e r  relatively to  the  less  changes  to  in  that  changes  in  current  cattle  given  i n sub-  prices. The matrix  estimated A  of  Table  cross 5.13  price are  elasticities consistent  with  a  priori  158  TABLE  5.14  Summary o f Own E l a s t i c i t y Translog (Cross-Sectional)  Cattle Inventory  1 .43 .075  of  Supply Quadratic (Time-Series)  .19 .037  159 expectations  and  c r o p s and c a t t l e end-of-period inventory  supply  between  a substitute  (-.269),  inventory  and c a t t l e  elasticity which  indicate  between  (-.083),  supply  This  demonstrate variables  is  However,  translog  model. scope  influence  to  the  the  these in  and  end-of-period cross  price  is  .16  these  generated  changes  output  supply  between  that  However,  for  between  inventories  relationship  opposite  considerable to  between  c r o p s and e n d - o f - p e r i o d  result  cross-sectional  cattle  and  (-.099).  suggests a complementary  inputs.  relationship  in  the  results  the  two  again  exogeneous  c o m p o s i t i o n on  cow-calf  farms. These e m p i r i c a l when  inventories  of  crop prices  results  an  in the  increase  the  other  an  increase  cattle  hand,  respect  in a reduction  cattle crop  to  input  the  prices.  The  and s e r v i c e s  equation  using  one p e r c e n t  supply  obtained  increases  percent services  by the  in  are  increase  total  but  an o p t i m a l  in a r e d u c t i o n  in  causes  inventory.  of  output  On level,  in  both  supply  with  estimates  derived  from t h e  and h o m o g e n i t y  translog  price  increase  supply  at  elasticity  -.031%  the  an  periods  inventories.  price  end-of-period  increase will  for  the  during  in  are  results  variable  in  held  elasticity  symmetry  increase  cattle  results  the  in c a t t l e  animals  prices  that  increasing,  inventories  B defines  materials  but  are  s u p p l y and e n d - o f - p e r i o d  Sub-matrix  total  indicate  animals  number of  if  in  findings  of  variable  estimated  is  will  consistent profit .067%.  of  or  materials  s u p p l y by  with  function)  by  cattle  A  decrease  inventories capital  the  restrictions.  labour  (which  for  A one and  .043% and .295%  160 respectively and - . 1 0 %  but d e c r e a s e e n d - o f - p e r i o d i n v e n t o r i e s  are  sub-matrix  with respect  positive,  1;8%  of  these  for  indicating  results  Following elasticity  again  cattle  of  and f o r  cattle  to  to  output  5.15  cattle  the  supply  preferences production.  outlined, for  the  the  in  The m a g n i t u d e  farmers'  reports  t h e means of  cattle  .47%.  future  estimates  increase  both  by  cow-calf  indicate in  decrease.  that  is  no  That  evidence  the  total  the  time-  value  exogenous  of  this  variables,  of  positively  that  sloped  total  expected  prices.  to  earlier  and  run  elasticity  non-optimal  levels  inventories  approach  of an  of  cattle optimal  supply  However,  cattle  in  supply  it is  inventories level,  the  will  response However,  tendency short  These r e s u l t s  therefore,  cattle  throughout.  this  decrease  less.  supply  farmers  supply  that  allowed  output  cow-calf  indicate  enough  short  prices  and c a t t l e  s u p p l y t o z e r o or  presented  e x p e c t a t i o n s are  is,  and  to  strong  strongly  the  prices  evidence  if  cattle  end-of-period inventories  elasticities  that  increase  previously  Table  changes  sufficiently  quite  of  Both  s u p p l y can be c a l c u l a t e d  changing c a t t l e  there  elasticity  a one p e r c e n t  inventory  indicate  e s t i m a t e d at  always  alter  the  each o b s e r v a t i o n .  adjust  will  in  procedures  These e s t i m a t e s to  that  p r o d u c t i o n over  estimates.  elasticity,  shows  animals w i l l  and a n i m a l s h e l d  current  series  C  to beginning i n v e n t o r i e s .  b e g i n n i n g number of by  -.03%  respectively.  Finally, supply  by  is run  support  one can c o n c l u d e functions is  worth  noting  inelastic but  as  are  for cattle  elasticity  of  161 TABLE Total  Elasticity  5.15 of  Cattle Total  Means of 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982  Exogeneous V a r i a b l e s  Supply  Elasticity .16 .095 .073 .102 .121 .083 .104 .084 .103 .080 .067 .071 .078 .071 .105 .134 .101 .102 .128 .071 .037 .036 .046 .103 .151 .082 .057 .058  of  Supply  162 cattle 5.1  supply  increases  provides a visual  the  effect  cattle  of  function  series  results.  results  whereas  price  the  which  the  in t h i s as  total  reported  in past  of  in  open economy w i t h c a t t l e  the  terms  of  aware  of  uncertainty  relatively expected prices  external  in c a t t l e  current  of  cattle  of  this  price  and c a t t l e  it  is  supply  of  is  short  run  appropriate  to  but  this  supply,  Canadian  Second,  Three  behaviour.  in  the  is  a  U.S. cause  f a r m e r may or may  cattle  the c o w - c a l f  in current  perverse  market  eitherway,  future  of  Canada  determined  The c o w - c a l f  may be t h a t  marketings  5.16  estimates  industry.  influence  the  predicting  changes.  these  no e v i d e n c e  prices  factors  more t o c h a n g e s  Table  research.  to  prices.  these  of  of  estimates  North American c a t t l e  Factors  consequences  in  (from B to A  presentation,  w h i c h may  small  be  time-  results.  to changes  the Canadian cow-calf  in  not  the  elasticity  chapter,  First,  fluctuations  s l o p e of  cross-sectional  functions  the  why t h e r e  c a n be i d e n t i f i e d  market.  the  elasticity  s t u d y and o t h e r  run b e h a v i o u r  factors  of  time-series  supply  empirical  the  some e x p l a n a t i o n  short  the  decreases  Before concluding t h i s offer  only)  c r o s s - s e c t i o n a l and  to adjust the  on t h e  Figure  cases.  p r o v i d e s a summary of  elasticities  both the  s l o p e of  complete  generated  illustration  expectations  expectations  and from D t o C)  To  (for  C and D r e p r e s e n t  price  in both  for  becomes e l a s t i c .  C u r v e s A and B r e p r e s e n t  increases  supply  fact,  accounting  changing p r i c e  supply  Allowing  and i n  cattle defining  as a c a t t l e c y c l e  this  increases  prices. farmer  prices  The  responds than  fluctuations tends  to  to in  imply  163 FIGURE  5.1  Supply F u n c t i o n s , Cross-Sectional versus Time-Series Cattle  Price  Cattle A B C D  -  Cross-sectional Cross-sectional Time-series Time-series  Price expectation No a d j u s t m e n t Price expectation No a d j u s t m e n t  Supply  adjustment adjustment  1 64 TABLE 5.16 Summary o f C a t t l e Elasticity  Supply  with r e s p e c t to the P r i c e Feeder C a t t l e  Elasticities of:  Non F e e d e r C a t t l e  A l l Cattle  T h i s Study All Cattle (Canada) Translog (cross-sectional)  -  -  1.41  -  -  .16  -  -  -.45  -.98  .30  1.42  -1.24  Quadratic (time-series) Other Studies Ospina & Shumway ( U . S ) Langemier & Thompson ( U . S . ) feeder  cattle  non f e e d e r c a t t l e a l l cattle George & King (U.S.) all cattle  -  -  -.42  Tryfos  -  -  -.009  (Canada)  -1.06  Yver ( A r g e n t i n a ) a l l cattle (short all  run)  -1.61  cattle  (long  run)  1.15  165 some  regularity  It  not  is  to p r i c e  to  surprising c h a n g e s as  fluctuations. current  then if  This  indicates  on c o w - c a l f  farms.  output  expected  variations. that  they  This  composition  will in  allow  for  a  case.  do not  respond cyclical  preference Third,  output  cow-calf  response  the  defined  imply  scope  not  farmers  production.  considerable  is  clearly  would  future  This  cow-calf were  factor  p r o d u c t i o n over  evidence  their  these  empirical substitution  farmers  to changes  for  to  alter  in p r i c e s  and  findings  and  prices.  To c o n c l u d e conclusions  is  this  dissertation,  presented  in Chapter  a summary of Six.  166 FOOTNOTES TO CHAPTER  1  Asymptotic parameter  2  t-ratios estimates  Using rather impose  point  to  of  defined  their  as  on  t h e model  imposes c o n v e x i t y expansion)  and i s  the  asymptotic  complicated non-linear  convexity  procedure  are  FIVE  at  standard  of  only  1978).  one  one  can  However,  this  (i.e.,  the  point  costly  the  errors.  transformations  (Lau  rather  ratio  computationally  to  perform. 3  I  would l i k e  deriving 4  the  to  1975.  5  Each  Ken W h i t e for  the  for  23-203,  variable  Canada, L i v e s t o c k  Ottawa,  is  various  transformed  his  assistance  elasticity  numbers r e a c h e d a h i g h of  Statistics  Statistics  Dr.  standard errors  Canadian c a t t l e in  thank  in  estimates.  15.6 m i l l i o n  and A n i m a l  head  Products  issues.  according to  the  following  formula: x  6  t  "  K-i  V  The v a r i a b l e s for  (5,  indicated 7  •  In  were t r a n s f o r m e d u s i n g a l t e r n a t i v e  however, that  first-order  addition,  restrictions because  the on  only  restriction  except  Le  the  two  c a n not  for 0  = 1 the Durbin-Watson  autocorrelation Chatelier  cross-price  output  test  remained.  Principle  implies  elasticities.  However,  equations  be t e s t e d ,  estimates  are  see D i e w e r t  estimated (1974).  this  167 6.  SUMMARY AND CONCLUSIONS  The p u r p o s e of of  the  this  dissertation  chapter  and t o  is  report  to p r e s e n t  a brief  the p r i n c i p a l  summary  findings  and  conclusions. The c o w - c a l f reproducing decisions  animals  facing  feed to heavier in  the  The  farmer  is  and  the  weights  to  selling  farmer  sell  the  interesting supply  in  over  the  of  the  producer  heavier calves. that In  For  there the  positive  to  the  the will  due t o  find  The aim of  it  animal  a  breeding  rise  implies  in  Given  an  the  to  retain For  becomes  to  animals this of  all  elasticities  of  beef  in  this  heavier  to  slaughter  to  obtain  indicates animals. will  be  weights.  to develop a t h e o r e t i c a l that  the  fattening  the  farm  in  animals  steers,  either  run,  of  future,  short  cow-calf  an  increase  i n h e r d s i z e and a v e r a g e  was  to  the e l a s t i c i t y  the  supply  increase  of  animals.  gradually  into  b r e e d i n g the  be a d e c r e a s e  model  and  period.  it  and i n  study  now,  animal  in the  l o n g e r and f a t t e n i n g  and c o w s ,  the  the  give  may have been s o l d .  aggregate  this  can  profitable  or  the  keep i t  basic  an a n i m a l  p r o d u c i n g new  whereby  negative  (heifers)  run,  The  of  and e x p e c t e d e c o n o m i c c o n d i t i o n s .  expected to p e r s i s t  heifers  long  maximizing  retain  p u r p o s e of  is  otherwise  weights In  run  will  keeping  weights.  or  a long adjustment  beef  herd that  implies  selling,  production decisions  short  positive  cattle  sell  or  activity  progeny. to  economic c h a r a c t e r i s t i c  the  price  the  primary  whether  an a n i m a l  h e r d depends on p r e v a i l i n g These b a s i c  are  before  breeding herd for  decision  engaged i n t h e  explains  profit this  168 behavior run  in  the  supply  short  response  run and t o e m p i r i c a l l y  and  investment  estimate  behavior  short  of  cattle  producers. In  developing  the  theoretical  model,  was assumed t o have a p r e d e t e r m i n e d beginning current beef  of  beef  prices The  vector  each  and f a c t o r were  prices  given  initial  inputs  and,  output  prices,  about  stock  of  animals  output  s u p p l y d u r i n g the  period.  valued  at  expected output  price  supply  is  valued  dual output  predetermined  of  at  the  output  output  stocks variable  supply,  an e c o n o m e t r i c Using was  response  of  run  the  in  next  time,  period's  at  animals  to  an  prices,  farmer  end of  next this  with a  economic  and h i s  determines  the  exthe  p e r i o d and stocks  p e r i o d and c u r r e n t  the are  output  period.  c a n be c h a r a c t e r i z e d  where p r o f i t s prices,  animals.  By  are  using a  a function  input  prices,  of and  applying  Hotelling's  optimal  quantities  demand, and e n d - o f - p e r i o d  inventories  profit  input  of  End-of-period  output  of  the  the  price  function  stock  function,  These e q u a t i o n s  the  can be u s e d  to  postulate  model.  the  analysis  at  any p o i n t but  input  period,  behavior  expected  c a n be d e t e r m i n e d .  short  next  retained  profit  prices,  Lemma t o  price  s i m p l e dynamic  variable  farmer  animals  responding  pectations  This  at  were known  combines the  variable  environment  Moreover,  of  cow-calf  uncertain.  farmer  of  period.  stock  the  theoretical  carried cow-calf  elasticity  out  to  farmers. of  model,  a  determine In  cattle  this  comparative short  model,  supply  the  depends  run  static supply  s i g n of on  the  three  169 factors: the  i)  the  substitution  production price One  technological possibilities  tomorrow;  expectations can  supply  The input,  in  specifying next  of on  moving  cattle  series  average  expected  by  main d a t a  base  econometric To  these  beginning  farmers' price.  run  negative  prediction  elasticity of  in  s y s t e m of  estimated the  output,  equations  required  t o be u s e d i n  predicting  "quasi-rational" exactly  expectation  the p r i c e  expectations  procedure  an a u t o r e g r e s s i v e  the  is  producers.  to  was  model.  based  integrated  represent  ARIMA model was e s t i m a t e d  to complete  the  full  information  was  produced  prices;  of  the  and  The  for  requirements  each  predictions  m o d e l s were c o m b i n e d w i t h data  the  necessary  the for  estimation.  outputs  farms and  the  hypothesized  An  variable  estimate  following  stocks  process  of  not a  expectations  method whereby  process.  generated  of  This expectation  was  is  ii)  today  in c u r r e n t  industry sign  A  industry;  a short  inventory  prices.  model  price  that  estimating  expectation  producers.  expectation  output  in  was p o s i t e d t o p r e d i c t  time  ferent  stage  some  cow-calf a  the  end-of-period  period's  process  result  the  sensitivity  to changes  the cow-calf rather  of  production  the  depend on p r i c e  first and  iii)  from t h i s  from e c o n o m i c t h e o r y : unknown and w i l l  between  with respect  conclude  elasticity  and  structure  ii)  associated cattle stocks  the  variable required:  by  cow-calf  quantity  input  of  prices;  profit i)  the q u a n t i t y  farms different ii)  function,  the  and  cattle.  Two  surveys  dif-  associated  inputs  u s e d on  end-of-period  and a s s o c i a t e d e x p e c t e d p r i c e s ; of  of  the  and i v )  the  conducted  by  170 Statistics  Canada  inventory a  (FES  and e x p e n d i t u r e  cross-sectional  series  and NLS)  data  data  data  sample.  Because  of  the  time-series  measurements  over  the  cycle. the  Generally,  main  prices  were o b t a i n e d Market  It  (total  cattle  demand,  and  variables fixed The  of  supply  obtain  to  elasticities  set  The FES  is  Statistics  NLS  is  nature  allowed  inputs  for  a  time-  of  beef  elasticity  be  compared  to  single  p e r i o d of  the  were  obtained  Canada and c a t t l e  quotations  for  a  reported  three  sold off  crop  tractable  aggregate farms,  supply),  from output  in  the  capital,  share  revenue  equations  employed  be g e n e r a t e d  Hotelling's  each  s y s t e m of  were u s e d t o  Alternative  form  variable  for  was profit  Lemma  for  estimates u s i n g the  test the of  for  and  Zellner's  SUR  cow-calf the  The  structure  and t o  data  estimated calculate  industry.  elasticities  time-series  was  each output  input.  equations.  and  cattle.  (combined w i t h t h e c r o s s - s e c t i o n a l  this  choice  for  of  functional  equations  input  and s e r v i c e s ) ,  multi-input  the  inventory  aggregate  beginning stock  logarithmic  variables  end-of-period  and m a t e r i a l s the  econometric  output  three  estimation,  of  farms. the  a  econometric  estimate  coefficients  farm  the m u l t i - o u t p u t ,  share  was  for  cyclical  during  representing  for For  sources  which c o u l d  from market  transcendental  technique  then  of  specify  total  expenditure  sample)  to  factor  function.  cycle  decided,  (labour,  postulated  the  primary  Review.  was  specification,  used to  prices  whereas  data  results  Cansim f i l e s  Livestock  one  beef  cross-sectional  on c o w - c a l f  series  production,  the  were the  data  of  choice  sample.  could  However,  171 a number of function  variables were  Specifically, total  not  this  profits,  prices,  prices  for  total  set  farms.  It  functional  variable  profit  profit  functional For  the  equations  were g e n e r a l l y  profit  properties  of  monotonicity.  Unfortunately, negative  at  profit  on  inputs current  prices,  input  and s e r v i c e s ,  net  cattle  output  and  supply  supply  absent  from  be  specified  Instead,  is  output  was  unfortunate  and that  the d a t a , for  a  the  a normalized quadratic  the  revenue  a  testing  of  the  to  indicated that the  However,  i s convex estimated  one it  in p r i c e s . share  is  share  was  the  data.  estimated duality  prices,  the a s s o c i a t e d  because  the  the  in  the  with  required  the H e s s i a n m a t r i x  each o b s e r v a t i o n . function  fit  homogeneity  failed  case,  and e x p e n d i t u r e  good  by c a l c u l a t i n g  convexity  function  significant  satisfied  linear  Convexity  profit  statistically  function  symmetry,  can c o n c l u d e t h a t  crop  It  providing  each o b s e r v a t i o n  of  i n f o r m a t i o n on  data,  c o u l d . not  of  statistical  variable  information  demand.  variable  coefficients  Furthermore,  basis.  used.  translog  equations  profit  farms.  total  variable  estimated  share  full  the q u a n t i t i e s  and m a t e r i a l s  for  function.  form was  include  prices,  time-series  form  the  time-series  include  on c o w - c a l f  end-of-period inventory  translog  true  did  specified  the  a  not  cattle  available  because  at  did  capital,  cattle  were  on  p r o d u c t i o n , or  expected  of  From the equations  data  labour,  inventories  estimate  available  crop  u s e d on c o w - c a l f cattle  required to  and  determined  eigenvalues.  eigenvalue  was  assumed t h a t  the  Consequently,  one  equations  have p e r f o r m e d  1 72 w e l l and t h a t behavior  of  they  adequately  cow-calf  represent  equations  of  underlying  the  that  the  western  transformation and j o i n t  determined  function  subject  to  expenditure  characteristics was  determined  production  to decreasing returns  functions functions  inventory  the  all  a  having having  in  of  of  priori  imply  output the  results  s u p p o r t the  In  addition,  for  cattle  These  slopes,  cattle  with  derived  slopes,  and  supply  that  there  to counter are  existence  and c r o p s  i n own p r i c e s  a and  is  scope  cycle.  correlated  In  other  output  for  inelastic  no s i g n i f i c a n t  with  words,  output Rather price these  cycle.  elasticities  r e l a t i o n s h i p amongst a l l  own  prices.  a cattle  cross-price  the  i n d i c a t e d an  positively  of  indicated  whereas  the c a t t l e  cattle cycle.  significant  were  expectations  between  in expected c a t t l e  i n an a t t e m p t  over  industry choice.  non-negative  end-of-period inventories  in c a t t l e  of  non-positive  supply  elasticity  results  scale  demand.  response to changes  response to changes  to  cattle. cow-calf  predicted  an e l a s t i c  indicates  It  and  of c o w - c a l f  c r o p s and  calculating  Own e l a s t i c i t i e s  substitute  function.  structure  relationship  fluctuations  certain  elasticities  end-of-period  changes  for  by  demand  adjustment  test  of  supply  These  revenue  i s d e f i n e d by a n o n - h o m o t h e t i c , non-homogeneous  conformed  substitute  the  characteristics  elasticities  input  of  transformation  p r o d u c t i o n between  Other  output  were u s e d t o  technological  Canada  maximizing  producers.  The e s t i m a t e d c o e f f i c i e n t s share  the p r o f i t  defined  categories.  changing  the  a This  output  173 composition western  between  c r o p s and  own  elasticities  of  materials  i m p l i e d an e l a s t i c  the  elasticity  own  inelastic  demand  employment the  of  of  for  employment of  defined of  these  effect labour  capital In  as  is  labour  and  it  farm p r i c e s  different  effects  will  give  encourage  To variable  in  more s t a b l e  complete profit  the  and  Moreover, this  capital  for  a  given  s u b s t i t u t i n g away  are  substitution  the  u s e d more  intensively  or  from  production intensively  than other  i n p u t s were  inferior.  concluded  that  crops, inputs.  classified From  this  p o l i c i e s designed  either  cattle  rural  development.  to  in  i n t h e p r o d u c t i o n of  each o u t p u t ,  Increased increased  labour  farms a r e  normal,  rise  relative  inputs.  suggested that  u s e d more  on  the  of  or c r o p s w i l l  to  have  quite  Increasing  crop  s u b s t i t u t i o n away from l a b o u r  which  increased migration off  capitalization. result  is  an  that  strength  Conversely,  of  indicated  implies  between  and m a t e r i a l s  was  whereas  capitalization.  results  superior,  increase  will  the  p r o d u c t i o n of  classification,  will  in  This  substitutes.  greater  inputs. input  the  being  prices  as  both labour  than c a p i t a l the  farms  inputs  capital  and m a t e r i a l s  cow-calf  elasticity  cattle,  input.  for  both  demand f o r  elasticity  prices,  and t o w a r d s  input  labour  implied that  Other of  cow-calf  demand  i n p u t s on farms  inputs  relative  input  demand f o r  this  capital  The c r o s s p r i c e  set  on  Canada.  The  to  cattle  cattle  farms  prices,  and  on t h e  increasing other  hand,  farm employment. empirical  function,  the  results total  for  the  elasticity  translog of  cattle  174  supply  was c a l c u l a t e d .  not  only  the  effect  supply.  of  the e f f e c t  of  It  cattle  will  prices  fluctuations,  cattle,  cattle  price  However,  this  the  elasticity  of  The e l a s t i c i t i e s profit  prices  magnitude The (as  u s i n g the  cattle  calculated  decrease  the  it  to  always  indicate  in  current  of  cattle reduce  quadratic  time-series  generally  consistent However,  data  similar)  with  elasticities  a  both c a t t l e  inelastic  and  on t h e  to  crops  supply in  elasticities. side  between  considerable  priori  smaller  output  relationship  c o m p o s i t i o n between  the  for  elasticity,  will  in  defined  crops  scope e x i s t s and  cattle  and for on  farms.  Finally,  allowed  were  implied that  output  cattle  results.  were  substitute  which a g a i n  changing the cow-calf  a  on  also  less.  normalized  the  (although  were p o s i t i v e .  price  but  s t r o n g enough t o  the c o r r e s p o n d i n g c r o s s - s e c t i o n a l  cross  expected)  elasticity  supply to z e r o or  measures  account  adjustments  cattle  estimates  than  for  was not  Own s u p p l y e l a s t i c i t i e s  inventory  the  f u n c t i o n combined w i t h  and  prices  effect  compare w i t h t h e c r o s s - s e c t i o n a l  and  cattle  takes  c a u s e d by c h a n g e s  estimated  alternative  expectations  of  accounting  always decrease  supply.  provided  of  was d e t e r m i n e d t h a t of  variable  measure  changing expectations  expectations  total  This e l a s t i c i t y  that  total  time-series  was a g a i n  adjust  short  was  cattle  estimates.  in c a t t l e  However,  tendency  run  of  determined that  to changes  decrease. this  elasticity  there  In if  of  was  calculating  this  expectations  are  prices, is  significantly  elasticities  supply  cattle  no  output  supply  evidence  to  s t r o n g enough t o supply to  z e r o or  175 less. short the  Therefore, run  supply  cow-calf  short  run  positively It some  industry,  cattle  production  of  determination: alternative  2)  and  3)  negative  p o s s i b i l i t y  indicates  western  that  in the  Canada  empirical.  the  results.  There  can  is  model  a  three  areas  increasing  our cattle  information  for  policy  implications  of  using  in  modelling  empirical for  of  the  cow-  consequences predicting  cow-calf  of  cattle  technology  for  separability—  the  Farm  the  data  for  this  Gorman  function-and  offering  of  side  provide  by  structure  processes  testing  are  for  processes the  input  and  profit the  dissertation  additional  specifying  variable  a  technological  discrete  precision  examination;  empirical  in  potential  specifically,  modelling  on  evidence  research.  expectation  Survey  aggregation  future  the  Expenditure  the  although  theoretical  complete  some  1)  price  greater  to  the  continuous  prices;  a  function  provide  industry—  using  with  for  and  that  throughout.  offer  understanding  are  empirical  appropriate  may  conclude  supply  sloped  is  may  e l a s t i c i t i e s  suggestions  which  calf  one  Polar this  presumably  necessary Form w i l l  provide  to  represent  impose more  exact  accurate  176 BIBLIOGRAPHY A g r i c u l t u r e Canada, "Food and Agriculture Regional L i v e s t o c k , " O t t a w a , Q u e e n ' s P r i n t e r , 1983. 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E/I1, Economic C o u n c i l of C a n a d a , 1981. M c F a d d e n , D. " C o s t Revenue and Profit Fuctions", Production Economics: A Dual A p p r o a c h t o T h e o r y and A p p l i c a t i o n s , V o l . 1 , (eds) F u s s , M. and D. M c F a d d e n , Amsterdam, NorthH o l l a n d , 1978. McKay, L., D. Lawrence, and C. Vlastium, "Production F l e x i b i l i t y and T e c h n i c a l Change in Australia's Wheat/ Sheep Zone", Review of Marketing and Agricultural E c o n o m i c s , 5 0 , 1982, 9-26. Mundlak, V . , " S p e c i f i c a t i o n Production Functions", 1963, 4 3 3 - 4 4 3 .  and Estimation of Multiproduct Journal of Farm E c o n o m i c s , 4 5 ,  Mood,  A . M . , Introduction to the Theory of Y o r k , M c G r a w - H i l l Book C o . I n c . , 1950.  Muth,  J.F., "Rational Expectations and t h e T h e o r y of M o v e m e n t s " , E c o n o m e t r i c a , 2 9 , 1961, 3 1 5 - 3 3 5 .  M y e r s , L . H . and J . H a v l i c e k , S h o r t - T e r m Hog S u p p l y " , 1967, 1395-1400. Nelson,  G.  and T . H . S p r e e n .  Statistics,  New Price  Jr., "Some T h e o r e t i c a l A s p e c t s of J o u r n a l of Farm Economics, 49, "Monthly  Steer  and H e i f e r  Supply",  182 American 117-125.  Journal  of  N e l s o n , G . R . , A p p l i e d Time H o l d e n - D a y , 1973. Nerlove, M. , "Lags 1972, 2 2 1 - 2 5 1 .  Agricultural Series  i n Economic  N e r l o v e , M . , D.M. G r e t h e r , E c o n o m i c Time S e r i e s ,  Economics,  Analysis,  1978,  Francisco,  Econometrica,  40,  and J.L. Carvalho, Analysis New Y o r k , A c a d e m i c P r e s s , 1979.  of  Nickell, S.R., The Investment Cambridge U n i v e r s i t y P r e s s ,  Behavior",  San  60,  Decisions 1978.  N o r e s , G . , " Q u a r t e r l y S t r u c t u r e of Economy", Ph.D. d i s s e r t a t i o n ,  of  Firms,  Oxford,  the A r g e n t i n e Beef Cattle Purdue U n i v e r s i t y , 1972.  Ospina, E. and C . R . Shumway, " M o d e l i n g S h o r t - R u n R e s p o n s e " , S t a f f Paper S e r i e s , D i r 78 SP-3, A g r i c u l t u r a l E x p e r i m e n t S t a t i o n , 1978.  Beef The  Supply Texas  Ospina, E. and C.R. Shumway, "Disaggregated Econometric Analysis of U.S. Slaughter Beef Supply", Technical Monograph 9, The T e x a s A g r i c u l t u r a l E x p e r i m e n t Station, n.d. P r a i r i e Farm P o l i c y Guide P r o d u c e r , 1981.  1981-82,  Saskatoon,  The  Western  in  Canada",  Pugh,  G . E . , "Some O b s e r v a t i o n s on the C a t t l e C y c l e C a n a d i a n Farm E c o n o m i c s , 13, 1978, 2 3 - 2 9 .  Ray,  S.C., "A Translog Cost Function Analysis of U.S. A g r i c u l t u r e , 1939-77", American J o u r n a l of Agricultural E c o n o m i c s , 6 4 , 1982, 4 9 0 - 4 9 8 .  Reutlinger, S., " S h o r t Run Beef S u p p l y Farm E c o n o m i c s , 4 8 , 1966, 9 0 9 - 1 9 . Samuelson, P.A., "Prices of Factors E q u i l i b r i u m " , Review or Economic 20.  Response",  and Goods S t u d i e s , 21,  Shephard, R.W., Cost and Production P r i n c e t o n U n i v e r s i t y P r e s s , 1953.  Functions,  Journal  of  in General 1953-54, 1Princeton,  Shumway, C.R., "Supply, Demand, and Technology in a Multiproduct Industry: Texas Field Crops", American J o u r n a l of A g r i c u l t u r a l E c o n o m i c s , 6 5 , 1983, 7 4 8 - 7 6 0 . S i d h u , S . S . and C A . B a a n a n t e , " E s t i m a t i n g Farm-Level Demand and Wheat Supply i n the I n d i a n P u n j a b U s i n g a T r a n s l o g Profit Function", American Journal of Agricultural E c o n o m i c s , 6 3 , 1981, 2 3 7 - 2 4 6 .  183 Silberberg, E., The Structure of E c o n o m i c s : A n a l y s i s , New Y o r k , M c G r a w - H i l l , 1978.  A  Mathematical  S t a t i s t i c s C a n a d a , " D a t a C o l l e c t i o n and E s t i m a t i n g Procedures of the L i v e s t o c k E s t i m a t i n g U n i t " , M e t h o d o l o g y Paper N o . 3, A g r i c u l t u r e S t a t i s t i c s D i v i s i o n , 1982. T r y f o s , P., "Canadian American J o u r n a l 107-113.  Supply F u n c t i o n s of Agricultural  Varian, H., Microeconomic A n a l y s i s , C o . , 1978. Wales, T.J., "On the F o r m s " , J o u r n a l of  Flexibility Econometrics,  of L i v e s t o c k Economics,  New Y o r k , of 5,  W.W.  and 56,  Meat", 1974,  Norton  and  Flexible Functional 1977, 183-193.  W e a v e r , R . D . , " S p e c i f i c a t i o n and E s t i m a t i o n of C o n s i s t e n t S e t s of Choice Functions", i n New D i r e c t i o n s i n E c o n o m e t r i c Modeling and Forecast ing in U.S. Agriculture, (ed) R a u s s e r , G . C . , Amsterdam, N o r t h - H o l l a n d , 1982. Weaver, R.D., "Multiple Input, Multiple Output P r o d u c t i o n Choices and Technology in the U.S. Wheat Region", A m e r i c a n J o u r n a l of A g r i c u l t u r a l E c o n o m i c s , 6 5 , 1983, 4556. White, K.J., "A General Computer Program for Econometric M e t h o d s - S H A Z A M " , E c o n o m e t r i c a , 4 6 , 1978, 2 3 9 - 2 4 0 . Woodland, A . D . , " S u b s t i t u t i o n of Structures, Equipment and Labor in Canadian Production", I n t e r n a t i o n a l Economic R e v i e w , 16, 1975, 171-187. Woodland, A.D., "Modelling the Production Sector of an Economy: A Selective Survey and A n a l y s i s " , D i s c u s s i o n Paper No. 2 1 , Department of Economics, University of B r i t i s h C o l u m b i a , 1976. Woodland, A.D., "Estimation of a Variable Planning Price Functions for Canadian 1947-70", Canadian J o u r n a l of E c o n o m i c s , 377. W o o d l a n d , A . D . , "On T e s t i n g Weak Separability", E c o n o m e t r i c s , 8, 1978, 3 8 3 - 3 9 8 .  Profit and of Manufacturing, 10, 1977, 355Journal  of  Yotopoulos, P.A., L.J. Lau, and W.L. Lim, "Microeconomic Output Supply and Factor Demand Functions in the Agriculture of the P r o v i n c e of T a i w a n " , A m e r i c a n J o u r n a l of A g r i c u l t u r a l E c o n o m i c s , 5 8 , 1976, 3 3 3 - 3 4 0 . Yver,  R.E., "The I n v e s t m e n t B e h a v i o r and t h e Supply Response of t h e C a t t l e I n d u s t r y i n A r g e n t i n e " , P h . D . d i s s e r t a t i o n , U n i v e r s i t y of C h i c a g o , 1974.  MM  APPENDIX  A.  Farm Expenditure Survey Questionnaire, 1981  SECTION A .  OPERATING ARRANGEMENTS  |  Section R "]7To  1. Al July 1,1981, w u this firm being operated it: (i) tn individual of family holding (excluding partnerships and corporations)?  (Co to Ovation 3)  (b) a partnership? (I) with a written agreement  (Co to Qutttlon i) (Co to Out a bit 21  (ii) with no written agreement (a verbal partnership)  (Co to Qutttlon 3)  (c) a corporation or company?  (Co to Qutttlon 31  (d) a community pasture or cooperative grazing association?  (Co to Qutttlon 3)  (e) a llutterile colony?  (Co to Qutttlon 31  (0 other? Please specify  If a partnership, record name(s) and address(es) of partner(s). If one or more of the partners operate another farm entirely separate from this farm, DO NOT INCLUDE this other farm when completing thli questionnaire for the partnership farm.  What are the names and addresses of the partners? Name  Address  Name  Address  Name  Address  (Co to Qutttlon 31  (Go to Qutttlon 3)  (Go to Qutttlon 3)  3. Is the operator a hired manager?  Yes |  No 11}  J  I What U the name and address of the OWNER? Name  4-SI04-4I4.I  Address  ID  (Go to Section B)  185  SECTION B.  AREA A N D LOCATION O F FARM LAND O W N E D , RENTED OR M A N A G E D  Section R  120  This section deals with all the land you OPERATE at the present time including cropland, woodland, waste land, pasture land and summerfallow. • Include land you MANAGE FOR OTHERS and land you RENT FROM OTHERS as wetl as land you OWN. • Exclude land you RENT TO OTHERS. I. Is the headquarters of the holding situated within the boundaries of the segment?  Yes  12?'  No  121 (X) one box  •  2. Wfll the land area figures in this questionnaire be reported in acres? . . OR I2S  hectares?  Total land operated at July 1,1981 3. Of the total land area you operated July 1, 1981, how much did you: (a) Rent or lease from others? (b) Own and operate? • Exclude land rented to others .  Land operated inside segment it July 1,1981  0)  126  (2) 123  NoneD 125  NoneD 122  NoneD 127  NoneD 124  129  130  NoneD  NoneD  4. Total land operated July 1,1981 (Sum 3a and 3b)  5. Of the total land reported above, what is the area of woodland? • Include woodlots,cut-over land, etc  Total Land Operated at July 1,1980 6. At July 1, 1980 how much land did you operate? Include land rented or leased FROM others. Exclude land rented or leased TO others EDIT:  131 NoneD  i  Are the figures in Column (I) greater than or equal to the corresponding figures in Column (2)7 Yes D (Go to Section C)  No D — - Make corrections with respondent. Continue  186  SECTION C.  Section R  LAND USE  J20o[  JTj  This section deals with land use for this year and last year. 1. Did you grow any wheat, oats, barley, rye, flaxseed, rapeseed or mustard seed last year OR are you growing any of these crops this year? Yes  No  201  (Go to Part B)  PART A: THE SEVEN GRAINS Total Land Operated at July 1,1980  to the nearest acre (hectare)  Total Land Operated it July 1,1981  to the nearest acre (hectare)  Seeded 1981 (this yea/) (2) 252  Seeded 1980 (last year)  0)  2. Wheat:  202  (a) Durum  NoneD  (b) Utility  NoneD  (c) Spring (red or white) .  NoneD  (d) Winter  NoneD  NoneD 2S3  203 NoneD  254  204 NoneD  255 Remaining for harvest in 1981  20S lluvetfed 1980 NoneD  256  206  3. Oats  NoneD  4. Barley . . .  NoneD  NoneD 257  207  5. Rye (a) Fall (b) Spring . . , 6. Flaxseed  NoneD  NoneD  259  209 NoneD  NoneD 260  210  NoneD  NoneD  "in"  7. Rapeseed (canola) 8. Mustard seed . . .  NoneD  9. Total seven grains (Sum 2 to 8)  NoneD  4-1IM-4I4.I  258 Remaliiinf for hsmstln 1981  208 lluveited 1980  NoneD  COMMENTS:  NoneD  261 NoneD 262  212  NoneD 263  213  NoneD  187  SECTION C.  i  LAND USE (concluded)  Transfer the totals reported in question 9, Box 213 and Box 263 to their respective boxes in question 10 below.  Total Land Operated at July 1,1980  to the nearest acre (hectare)  to the nearest acre (hectare)  Seeded 1980 Oast year) (1)  Seeded 1981 (this yew) (2)  PART B. - OTHER LAND USE  10. Total seven grains (from Boxes 213 and 263)  NoneD  11. Cqm (a) for grain  NoneD  NoneD (b) for fodder and ensilage 12. Other crops (Include mixed grains, sunflower seed, vegNoneD etables, pulses, etc.) 13. Tame hay (area cut or to be cut for hay, ensilage or seed). NoneD • Exclude wfld hay 14. Summerfallow  Total Land Operated at July 1,1981  NoneD  NoneD 214 215 216 217 218  NoneD NoneD None D NoneD NoneD  220 15. Improved land for pasture or grazing (improved by seeding, draining, irrigating, fertilizing, or brush or weed None D control) 16. Other improved land (barnyards, lanes, home gardens, NoneD improved idle land, etc.) 17. Woodland NoneD • Include woodlots, cut-over land, etc 18.Other unimproved land (unimproved hayland, native pasture, sloughs, marshes, etc.) Exclude woodland  NoneD  19. Total aO land (Sum 10 to 18).  NoneD  26S 266 267 268 270  NoneD 223 224  NoneD NoneD  22S  273 274 275  NoneD 222  EDIT: 1. Does the figure in Box 272 equal the figure in Box 127 (Page 3)7 Yes • No D — * • Make corrections with respondent. Continue. 2. Does the figure in Box 274 equal the figure in Box 129 (Page 3)7 Yes O No O—»*• Make corrections with respondent. Continue. 3. Does the figure in Box 222 equal the figure in Box 272? Yes D (Go to Section D) No D—»» Ask respondent for reason and write It bdow?  1104-414.1  264  272 NoneD  188  SECTION D.  GRAINS FED (NON-COMMERCIAL)  Section R  5  280  1. Did you feed any oats,barley or feed wheat to livestock during the 11-month period August 1,1980 to July 1,1981? • Include whole, chopped, rolled and crushed grain both with and without commercial supplements added. • Exclude - brand name commercially prepared feeds. — grains grown together  I  Report SEPARATELY all grains mixed together AFTER harvest  Yes  2. How will your grains fed Figures be reported?  No  2  8  1  J  (Go to Section Ej  Bushels  •  Tons of 2,000 lbs.  282  2  Metric tonnes . . .  282  3  3. For the last eleven months, that is, between August 1,1980 and July 1,1981, please estimate the total amount of the following grains fed to livestock:  Amount fed between August 1,1980 and July 1,1981 on total land operated 283  (a) Oats fed  NoneD 284  (b) Barley Ted  NoneD 285  (c) Wheat fed (feed, utility or other).  NoneD  COMMENTS:  4-1104-414.1  189  SECTION E.  CATTLE A N D CALVES  Section R  400  9  I. Since January 1,1981, hive you had, or do you have,cattle or calves on the land you operate? • Include - all animals on this holding, regardless of ownership. • Include - all animals OWNED BY YOU but pastured on a community pasture or public land. • Exclude - animals OWNED BY YOU but kept on a farm, ranch or feedlot operated by someone else.  No 401  Yes  2  (Co to Section Ft  Total Number it July 1.1981  PART A. INVENTORY AT JULY 1,1981  403 NoneD 404 NoneD 40S NoneD 406 NoneD 407 NoneD 402 NoneD 408 NoneD 409 NoneD 410  2. BuDs, I year and over 3. Cows (all cows and heifers which have calved at least once)  f (i)maalnly for DAIRY purposes. ( ( b ) mainly ma for BEEF purposes. (a) raised for DAIRY herd replacement  4. Heifers, 1 year and over (which have never calved)  (b) raised for BEEF herd replacement.. . (c) raised for SLAUGHTER  5. Steers, 1 year and over . 6. Calves, under 1 year old  NoneD  7. Total cattle and calves (Sum 2 to 6) 8. Does this figure (Enter Box 410) . account for all of the cattle and calves on the land operated, plus all those kept on community pasture and on public land?  f YesD9. Did you milk any cows YESTERDAY?  •(Co to Question 9) -Make corrections, then to to Question 9.  No D -  Yes  9  No 431  (Go to Part B)  Total Number 419  (a) How many cows were milked YESTERDAY? Litres (1 day's production) (b) How much milk did these cows produce YESTERDAY? (1 pound • 0.44 litre, 1 kilogram • 1 litre approx., 1 gallon • 4.S litres) JI04-4I4.I  420  ^  190  SECTION E.  CATTLE A N D CALVES (concluded)  PART B. CHANGE IN CATTLE AND CALF INVENTORIES FROM JUNE 3,1981 CENSUS TO JULY 1.1981. 10. Since the June 3,1981 Census of Agriculture, please report the number of:  Total Number 428  (a) Births, purchases, and transfers to the land you operate (between June 3, 1981 and NoneD July 1.1981) 429 (b) Deaths, sales, slaughterings and transfers from the land you operate (between June 3,1981 NoneD and July 1,1981)  PART C. CALVINGS AND DEATHS All questions below refer to 6 month periods Total Number 421 11. How many calves were born alive since January 1,1981, that is, during the past 6 months, on the NoneD land you operate? 424 12. How many cows and heifers are expected to calve before January 1,1982, that Is, during the next NoneD 6 months? 426 13. How many cattle (I year and over) have died, or have been destroyed, as a result of accident, inNoneD jury or disease since January 1,1981? 427 14. How many calves (under I year) have died, or have been destroyed, as a result of accident, injury NoneD or disease since January 1,1981?  COMMENTS:  4-1104.414.1  191  SECTION F.  PIGS (concluded)  PART B. CHANGE IN PIG INVENTORY FROM JUNE 3,1981 CENSUS TO JULY 1,1981  7. Since the June 3,1981 Census of Agriculture, please report the number of: a) Births, purchases and transfers to the land you operate (between June 3, 1981 and July 1.1981) b) Deaths, sales, slaughterings and transfers from the land you operate (between June 3,1981 and July 1,1981)  Total Number 640 NoneD 641 NoneD  PARTC. FARROWINGS, BIRTHS AND DEATHS  All questions below refer to 3 month periods  Total Number  ZSi— 8. How many sows and gilts farrowed during April, May and June 1981 on the land you operate?  NoneD 635  9. How many pigs were bom alive during April, May and June 1981 on the land you operate?  NoneD 636  10. How many pigs have died, or have been destroyed, as a result of accident, Injury or disease BEFORE weaning during April, May and June 1981?  NoneD 637  11. How many pigs have died, or have been destroyed, as a result of accident, injury or disease AFTER weaning during April, May and June 1981?  12. How many sows and gilts are expected to farrow during July, August and September 1981?  NoneD 638 NoneD 639  13. How many sows and gilts are expected to farrow during October, November and December 1981? *  4-JI04-4I4.I  NoneD  SECTION F.  Section R  PIGS  600  I. Since April 1,1981, have you had, or do you have, pigs on the land you operate? • Include all pigs on this holding regardless of ownership. • Exclude pigs owned by you but kept on a farm operated by someone else. No 601  Yes  (Go to Section G)  Total Number at July 1,1981 605  PART A. INVENTORY AT JULY 1,1981 2. Boars 6 months and over for breeding . .  None • 606  3. Sows for breeding and bred gilts  NoneD 607 None • 608  (i) Under 45 pounds (20 kg)  4. All other pigs  (ii) 45 to 130 pounds (20 to 60 kg).  NoneD 610  . (Ui) over 130 pounds (60 kg)  NoneD  5. Total pigs (Sum 2 to 4)  6. Does this figure (Enter Box 610)  COMMENTS:  U04-4I4.1  None O 609  account for all of the pigs on the land operated?. Yes •  «»  (Go to Part B)  No  »*•  Make corrections, then go to Part B  CD  9  SECTION G .  I. • • •  OTHER LIVESTOCK O R POULTRY  Section R [300  lu  At July 1.1981, do you have SHEEP and LAMBS, POULTRY or OTHER LIVESTOCK on the land you operate? Include all livestock and poultry on this holding regardless of ownership. Include all livestock OWNED BY YOU but pastured on a community pasture or public land. Exclude livestock and poultry OWNED BY YOU but kept on a farm operated by someone else.  Yes  No  301  (Go to Section Hf  Total Number at July 1.1981  PART A. SHEEP AND LAMBS  304  2. Sheep and Lambs  NoneD Total Number at July 1,1981  PART B. POULTRY  503  3. HENS and PULLETS, 20 weeks of age and over, kept for laying  NoneD  4. OTHER POULTRY (for example, broilers, turkeys, ducks, etc.) PLEASE SPECIFY  Total Number at July 1.1981  OFFICE USE ONLY  504 None O PART C. OTHER LIVESTOCK 5. Please list any OTHER LIVESTOCK (for example hones, goats, rabbits, etc.) • Exclude family pets.  PLEASE SPECIFY  Total Number at July 1.1981  OFFICE USE ONLY  SOS NoneD  SECTION H .  FARM BUSINESS EXPENSES (HI T O H17)  I  Enterfigurereported In Box 131, question 6, page 3  None  It the amount reported above greater than zero? Yes • (Below)  ^ No • (Co to Section K)  The following sections deal with firm operating expenses that you had during the calendar year 1980. In cases where records are not kept on a calendar year basis, expenses should be reported for the most current fiscal year end. Calendar Year refers to the period January I to December 31. Fiscal Year re fen to any twelve month period which a business uses as its income tax year (for example, April I to March 31.)  SECTION HI. RENTAL A N D LEASING EXPENSES FOR AGRICULTURAL LAND OR BUILDINGS  Section R  700  I. Did you have any cash rent, share rent or leasing expenses in 1980 for agricultural land or buildings rented or leased from others? • include - taxes paid by you on property rented from others. - community pasture or other grazing fees. Yes  N  o  701  2  (Go to Section H2)  Total expense in 1980 S 2. In 1980, what was the amount of your:  702  (a) Cash rent or leasing expenses?  NoneD 703  .00  (b) Share rent or rent-ln-klnd (estimated dollar value)?  NoneD 704  .00  3. Total rental and leasing expenses (Sum 2a and 2b).. . EDIT: 1. Is box 126, page 3 equal to zero? If yes, please specify reason for rent or leasing expenses 4-SI04-414.1  .00  S E C T I O N H2. O P E R A T I N G E X P E N S E S F O R M O T O R VEHICLES A N D FARM MACHINERY  Section R  1. Did you have any operating expenses for motor vehicles and farm machinery during 1980? • Indude farm business share of car.  Yes  No  7  n  l  I  2  | (Go to Section H3)  Total Farm Business Expense in 1980 S 2. During 1980,  what were your farm expenses for:  720  (a) Fuel,oil and lubricants: report amount paid before any rebates are received NoneD from claims made to the federal or provincial governments 721  .00  (b) Repairs, maintenance, license, registration and insurance costs, (include NoneD parts, labour, tires, batteries, antifreeze, etc.) 722  .00  3. Total expense (Sum  COMMENTS:  4-3104-414.1  2a and 2b)  .00  710  9  196  S E C T I O N H3.  SEED  Section R  1. Did you have any expenses during 1980 for the purchase of seed and seedlings? Yes  N  o  |73l|  | 2 | (Go to Section H4)  If seed treatment or cleaning costs were included in the purchase price, report total expense.  Total expense in 1980 S 2. During 1980, what were your expenses for:  732  (a) Wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed?  NoneD 733  .00  (b) Other seed? Please specify  None D 734  .00  .00  3. Total seed expenses (Sum 2a and 2b)  735 NoneD  4. What portion of the total cost for all seed was for seed bought from elevators, seed houses and seed dealers? • Exclude seed bought from other farmers  COMMENTS:  4-1I04-4I4.I  022  OR  .001  A  197  S E C T I O N H4.  FERTILIZER  Section R  740[jT  1. Did you htve iny expemei during 1980 Tor the purchase of fertilizer? Yes  No 1 1 741  | 2~)  (Go to Section HS)  2. Fertilizer expenses.  3. What portion of the total expense figure for fertilizer was used or will be used in the production of wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed?  S E C T I O N H5.  C H E M I C A L S (PESTICIDES)  Section R |7So[  | 9 |  1. Did you have any expenses during 1980 for chemicals to control all types of weeds, plants, Insects, rodents, etc.?  Yes  No 751  £]  (Go to Section H6)  If custom chemical application costs were included in the purchase price, report total expense.  Total expense in 1980 S 752 2. Chemical expenses (Include herbicides, Insecticides, fungicides and other pesticides)  .00  1  .00  1  753 None • 3. What portion of the total expense figure for chemicals was used or will be used in the production of wheat, oats, barley, rye, flaxseed, rapeseed and mustard seed? 4-1104-414.1  — OR 024  198  SECTION H6.  FEED A N D  SUPPLEMENTS  Section R  770  1. In 1980, did you have any expanses Tor Teed and supplements? • Include cost of hay and straw used for feed.  Y«[p  No  771  (Go to Section H7)  Total expense in 1980 S  2. In 1980, what were your total expenses for feed and supplements purchased from other farmers and from commercial channels?  772  .(XT  773 NoneD  1 m  .00  OR  3. What portion of the total cost of feed was for feed purchased through commercial channels? • Exclude feed bought from other farmers  SECTION H7. 1. In 1980,  did you  1  %  V E T E R I N A R Y A N D A.I.  j 9 |  Section R |?8o|  have any expenses for veterinary services, medicines or A.I. fees? Yes  E l  No  (Go to Section H8)  Total expense in 1980 S 782  i  .00  2. Total expenses for veterinary services, medicines and A.I. fees?  SECTION H8.  BUILDING A N D  F E N C E REPAIRS  Section R |790|  \  j_9  I. Did you have any expenses during 1980 for repairs and maintenance of farm buildings and fences? • Include farm business share of expenses for repairs to the farm or any off-farm dwelling. • Exclude capital expenditures, that Is, new construction, renovations and additions. Yes  No  791  (Go to Section H9)  Total expense in 1980 $ 2. What were your total expenses in 1980 for:  792  (a) Repairs and maintenance to farm buildings?  None D 793  (b) Fencing?  NoneD 794  3. Total expenses for repairs to farm buildings and fencing (Sum 4-1104-414.1  2a and 2b)  .00 °~ .00 .00  199  SECTION H9.  CONTAINERS, TWINE AND  WIRE  800; ! T  Section R  I. In 1980, did you have any expenset for small containers, baler twine, binder twine and baling wire?  Yes  No  (Go to Section H10)  801  Total expense in 1980 $ A  802  .00*  2. Total expenses for small containers, baler twine, binder twine and baling wire  S E C T I O N H10. S M A L L T O O L S A N D HARDWARE  MISCELLANEOUS  Section R  8lbl  T T  1. In 1980, did you have expenses for small tools and miscellaneous hardware? • Include hand sprayers, dusters, fire extinguishers, grease guns, shovels, carpentry and other like tools, and all other equipment costing leu than $200 per item. • Exclude materials accounted for in Section H8 (BUILDING AND FENCE REPAIRS)  Ye,[p  No  l l .1 J 8M  2  (  ColoSectionlill  l  Total expense in 1980 $  1  812  2. Total expenses for small tools and miscellaneous hardware required for the farm business  SECTION HU.  INTEREST O N F A R M L O A N S , CREDIT A N D MORTGAGES  |  Section R  |820J  ]~9~|  . In 1980, did you have any farm business loans or mortgages?  Ye,[p  No  821  ! 2 | (Go to Section HI 2)  Total expense in 1980 S 822 .00'  2. What were your total interest expenses for these loans? 824  (  „„  NoneD 3. What portion of your Interest expenses was for the purchase of real estate, farm vehicles, machinery, livestock, poultry, loans for building construction or renovation, o; land improvement? -3IM-4H.I  026  OR  .00  %  200  S E C T I O N H12.  ELECTRICITY, T E L E P H O N E H E A T I N G FUEL  AND  Section R Jjiloj  | »"]  t. Did you have my electricity, telephone or heating fuel expenses during 1980? • Include farm business share of house expenses. • Exclude installation costs. Yes  9  No  (Go to Section HI3)  831  Fsrm business share of expenses in 1980 832  2. What was the farm business share for: (a) Telephone expenses?  NoneD 833  00  (b) Electricity expenses?  NoneD 834  .00  NoneD 83S  .00  (c) Fuel expenses for heating, irrigation and grain drying? • Include natural gas, propane, heating oil, coal, wood • Exclude fuel expenses for motor vehicles and farm machinery already reported  3. Total telephone, electricity and hearing fuel expenses (Sum  S E C T I O N H13.  INSURANCE  .00  2a to 2c)  PREMIUMS  [Section R  J860  1. Did you have any property or crop insurance expenses during 1980? • Exclude - insurance on property rented to others. — insurance on motor vehicles and machinery reported earlier. - personal life insurance premiums. — unemployment insurance and liability insurance paid on behalf of employees. - Western Grain Stabilization Act (WGS A) levies.  Y..J] 2. During 1980,  No  |86T  2j  (Go to Section H14)  what were your total expenses for:  (a) Crop and hait insurance? • Include insurance from government and nongovernment agencies (b) Farm business insurance? Include - fire, wind and other property insurance on alt farm buildings, machinery and equipment — farm business share of insurance on the farm or on off-farm dwellings and contents - insurance on livestock and grain in storage  3. Total insurance premiums (Sum 4-S104-4I4.I  2a and 2b)  Total expense in 1980 S 863 NoneD 866  .00  NoneD 86S  .00  .00  201  S E C T I O N H14. W A G E S , SERVICES A N D FOR HIRED L A B O U R  SUPPLIES  Section R  1. Did you have any expenses for hired farm labour during 1980? • Exclude - paid labour for housework, custom work and contract work. - utilities, fuel and other items already claimed.  Yes  No  (Go to Section HIS/  851  Total expense In 1980 S T  2. What were your total cash wages for hired farm labour in 1980? • Include any contributions for Unemployment Insurance, Canada Pension Plan, Workmen's  852 Com-  None •  .00  S 853 3. Of the above cash wage expense, how much w u for your spouse  None •  .00 854  4. What is the estimated cash value of housing or lodging, food, fuel, transportation, utilities, etc. provided to hired farm labour during 1980?  None • 855  .00  .00  COMMENTS:  -JI04-4M.I  202  S E C T I O N H15. C U S T O M W O R K A N D M A C H I N E HIRE!  sect.o„R  M \*  The following section concentrates on operating expenses which are of a recurring nature such as stone picking, teed treatment and custom spreading of fertilizers. • Exclude - expenses where the benefits will be spread over many years, for example, dugouts, barns, clearing land, grain bins, etc. - seed, fertilizer and chemical materials, as well as custom work included in SECTIONS H3, H4 and H5.  Total expense in 1980 S . Did you have any expenses in 1980 for. (a) Tilling, seeding, swathing, combining and grain drying .  NoneQ  .00  (b) Seed treatment and cleaning  None D  .00  (c) Custom spreading of chemical fertilizer, spraying and dusting  None D  .00  (d) Grain, livestock and feed trucking  NoneD  .00  (e) Baling, chopping and feedlot cleaning  NoneD  .00  (0 Renting or leasing of any machinery or equipment for farm purposes .  None D  .00  (g) Other, please specify  NoneD 762  .00  2. Total custom work and machine hire expenses (Sum  .00  la to lg) ,  Did the farm operator report any custom work and machine hire expenses for 19807  Yes  •  No  Go to Section HI6  4-1104-414.1  I*  203  S E C T I O N H16. M I S C E L L A N E O U S F A R M BUSINESS EXPENSES  Section R  840  9  1. In 1980, did you have any expenses Tor accounting and consulting services, bank services, legal services, memberships (farm organizations, unions, etc.), promotion, firm magazines, bulletins and technical journals? • Exclude interest charges on bank loans.  Yes  No  841  2  (Go to Section HI 7)  Total expense in 1980 S 842  t  .00 \  2. Total miscellaneous farm business expenses  S E C T I O N H17.  f&^T  OTHER FARM OPERATING EXPENSES A N D DEPRECIATION  870  Total expense in 1980 $ 1. During 1980, what were your expenses for:  871  (a) Livestock and poultry purchases? . . . .  NoneD 872  .00  Cb) Property taxes?  NoneD 873  .00  (c) Depreciation or capital cost allowances?  NoneD 874  .00  (d) Irrigation levies and taxes?  NoneD 875  .00  (e) Other? Please specify  NoneD  .ooj  COMMENTS:  4-JI04-4M.I  204  S E C T I O N I. R E C E I P T S F R O M C U S T O M W O R K A N D MACHINE RENTAL  >!°L_i ?J  Section R  1. In 1980, did you have any cash receipts from custom work or from rental or leasing of your farm machinery to others? • Include custom feeding of cattle. • Exclude custom work done on an exchange basis, that is, where no money changes hands.  Yes  7  No  l l I1 9ll  2  /Go to Section J)  s  !  912 .00 ^  2. Total receipts from custom work and machine rental  S E C T I O N J. T O T A L A G R I C U L T U R A L RECEIPTS  | Section R  J900| | 9~j  1. What were your total agricultural receipts in 1980? • Include -  sales of all agricultural products. Box 703: landlord's share of products sold. Box 912: custom work and machine hire receipts. stabilization and deficiency payments. CWB payments received in 1980. cash advances for stored grain, patronage dividends and crop insurance ,  2. What portion of the above total was for the sale of wheat, oats, barley, rye, flaxseed, rape seed and mustard seed? • Include Canadian Wheat Board payments received ln 1980 CC/~T|OkJ OCV-IIWIN  K l \ .  SASKATCHEWAN AND BRITISH COLUMBIA ONLY: FEDERAL/PROVINCIAL AGREEMENT TO SHARE INFORMATION  To avoid duplication of inquiries and lo reduce the costs of data collection, this survey is conducted under a joint agreement to collect and share information, as provided by Section 11 of the Statistics Act, with the Saskatchewan Department of Agriculture and the British Columbia Ministry of Agriculture. Are you willing to share this information with the agency/agencies in your province? (please check)  Yes (O.K.  to share Information)  No (not O.K.  4-1104 -414.1  to share information) . . .  l??.2L_L?-4  MJJi  to o  B.  Year 1981  1980  1979  1978  Cross-sectional Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 1 4 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Data  Prices: Cows 46.59 46.59 46.59 48. 52 45.84 48. 52 48.58 48.52 48.58 46.59 45.84 48. 10 48. 10 48.10 51 .27 51 .27 51 .27 51 .77 49.34 51 .77 52.06 51 .77 52.06 51 . 27 49.34 52.05 52.05 52.05 55.80 55.80 55.80 58.27 54.62 58.27 56.39 58. 27 56.39 55.80 54.62 56.88 56.88 56.88 38.73 38.73 38.73 40.27 38. 19 40.27 40.06 40.27 40.06 38.73 38. 19 39.93 39.93 39.93  By S o i l cwt. Steers 74.66 74.66 74.66 76.58 75.82 76.58 75.81 76.58 75.81 74.66 75.82 73.98 73.98 73.98 79. 10 79. 10 79. 10 82.01 78.55 82.01 79. 18 82.01 79. 18 79. 10 78.55 78.60 78.60 78.60 91 .08 91 .08 91 .08 92.46 93.42 92.46 90.91 92.46 90.91 91 .08 93.42 87.28 87.28 87.28 65.35 65.35 65.35 66.53 64.24 66.53 63.38 66.53 63.38 65.35 64.24 60.48 60.48 60.48  Zone  Steer Calves 75.13 7 5.13 75. 13 75.64 72.92 75.64 74.56 75.64 74.56 75. 13 72.92 73.88 73.88 73.88 91 .90 91 .90 91 .90 94.01 93.66 94.01 92.26 94.01 92.26 91 .90 93.66 88.53 88.53 88.53 108.65 108.65 108.65 108.07 107.84 108.07 108.88 108.07 108.88 108.65 107.84 104.36 104.36 104.36 75.07 75.07 75.07 82.06 84.89 82.06 79.31 82.06 79.31 75.07 84.89 74.05 74.05 74.05  He i£ers 68.39 68.39 68.39 ' 72.36 69.91 72.36 70.30 72.36 70.30 68.39 69.91 67.55 67.55 67.55 72.93 72.93 72.93 75.86 71 .48 75.86 73.08 75.86 73.08 72.93 71 .48 71.14 71.14 71.14 88. 17 88. 17 88. 17 88.99 87.98 88.99 85.90 88.99 85.90 88. 17 87.98 81 .26 81 .26 81 .26 56.86 56.86 56.86 58.86 56.96 58.86 57. 17 58.86 57. 17 56.86 56.96 53.72 53.72 53.72  Hei f e r Calves 65.80 65.80 65.80 66.53 60.05 66.53 63.46 66.53 63.46 65.80 60.05 65. 16 65. 16 65. 16 80. 14 80. 14 80. 14 84 .64 79.26 84.64 81 .23 84.64 8 1 . 23 80. 1 4 79.26 79.40 79.40 79.40 94.29 94.29 94.29 96.75 91.44 96.75 99.57 96.75 99.57 94.29 91 .44 92.80 92.80 92.80 65.30 65.30 65.30 72.35 75.38 72.35 70.48 72.35 70.48 65.30 75.38 64.68 64.68 64.68  B.  C r o s s - s e c t i o n a l Data By S o i l  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Zone  P r i c e s : Indexes Building Fenc ing Repairs 253.50 223.00 250.20 286.40 253.50 223.00 253.50 223.00 254. 10 247.60 253.50 223.00 254. 10 247.60 253.50 223.00 254.10 247.60 253.50 223.00 254.10 247.60 243.70 276.70 243.70 276.70 243.70 276.70 236.60 217.00 210.50 266.80 236.60 217.00 236.60 '217.00 238.20 226.00 236.60 217.00 238.20 226.00 236.60 217.00 238.20 226.00 236.60 217.00 238.20 226.00 228.30 246.90 228.30 246.90 228.30 246.90 231 .00 199.40 204.70 252.50 231.00 199.40 231.00 199.40 226.00 207.90 231.00 199.40 226.00 207.90 231.00 199.40 226.00 207.90 231.00 199.40 226.00 207.90 213.80 221.60 213.80 221.60 213.80 221.60 205.30 180.10 183.00 230.60 205.30 180. 10 205.30 180.10 197.40 191.20 205.30 180.10 197.40 191.20 205.30 180.10 197.40 191.20 205.30 180.10 197.40 191.20 188.60 199.60 188.60 199.60 188.60 199.60  (continued) Machinery Operat ion 257.20 289.40 257.20 257.20 271 .20 257.20 271 .20 257.20 271.20 257.20 271 .20 273.90 273.90 273.90 213.80 232.70 213.80 213.80 222.30 213.80 222.30 21 3.80 222.30 213.80 222.30 223.30 223.30 223.30 182.60 200.20 182.60 182.60 193.30 182.60 193.30 182.60 193.30 182.60 193.30 193.00 193.00 193.00 170.60 181.80 170.60 170.60 181.60 170.60 181.60 170.60 181 .60 170.60 181.60 179.70 179.70 179.70  Seed 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 345.00 300. 10 300.10 300. 10 300. 10 300.10 300.10 300.10 300.10 300. 10 300.10 300. 10 300.10 300.10 300.10 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 223.00 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20 215.20  B.  Cross-sectional  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Data By S o i l  Zone  P r i c e s : Indexes Fertilizer Pesticide 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 366.60 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 317.70 266.00 266.00 266.00 266.00 266.00 266.00 266.00 266.00 266.00 266.00 266.00 266.00 • 266.00 266.00 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90 229.90  359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 359.90 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 327.40 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 281.60 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50 253.50  (continued) Twine 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 398.00 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 403.80 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 283.70 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40 217.40  Feed + Supplements 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 349.90 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 270.50 233.10 233.10 233. 10 233. 10 233. 10 233. 10 233.10 233. 10 233. 10 233. 10 233. 10 233. 10 233. 10 233.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10 216.10  B.  C r o s s - s e c t i o n a l Data By S o i l  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Zone  P r i c e s : Indexes Grain Oats Peed 359.90 314.50 356.10 331.20 359.90 314.50 359.90 314.50 495.50 469.80 359.90 314.50 495.50 469.80 359.90 314.50 495.50 469.80 359.90 314.50 495.50 469.80 427.90 426.30 427.90 426.30 427.90 426.30 263.80 225.90 273.10 , 243.30 263.80 225.90 263.80 225.90 358.40 328.80 263.80 225.90 358.40 328.80 263.80 225.90 358.40 328.80 263.80 225.90 358.40 328.80 324.00 322.40 324.00 322.40 324.00 322.40 221.00 209.60 234.80 214.50 221.00 209.60 221.00 209.60 278.30 254.50 221.00 209.60 278.30 254.50 221.00 209.60 278.30 254.50 221.00 209.60 278.30 254.50 248.90 247.20 248.90 247.20 248.90 247.20 202.70 190. 10 214.60 195.80 202.70 190.10 202.70 190. 10 265.60 256.90 202.70 190.10 265.60 256.90 202.70 190.10 265.60 256.90 202.70 190. 10 265.60 256.90 226.90 240.20 226.90 240.20 226.90 240.20  (continued) Barley  Wheat  387.20 362.00 387.20 387.20 574.50 387.20 574.50 387.20 574.50 387.20 574.50 424.50 424.50 424.50 282.90 272.20 282.90 282.90 435.30 282.90 435.30 282.90 435.30 282.90 435.30 322.40 322.40 322.40 202.50 194.10 202.50 202.50 311.90 202.50 311.90 202.50 311.90 202.50 31 1.90 226.60 226.60 226.60 201.90 194.20 201.90 201.90 290.50 201.90 290.50 201.90 290.50 201.90 290.50 209.80 209.80 209.80  408.70 367.80 408.70 408.70 483.20 408.70 483.20 408.70 483.20 408.70 483.20 439.50 439.50 439.50 305.90 286. 10 305.90 305.90 350.60 305.90 350.60 305.90 350.60 305.90 350.60 332.50 332.50 332.50 250.50 244.60 250.50 250.50 290.60 250.50 290.60 250.50 290.60 250.50 290.60 269.60 269.60 269.60 221.20 225.30 221.20 221.20 262.40 221.20 262.40 221 .20 262.40 221.20 262.40 223.00 223.00 223.00  B.  Cross-sectional  Year 1981  1980  1979  1978  Data By S o i l  Zone  P r i c e s : Indexes Soil Artificial Small Zone Inseminat i o n T o o l s 1 187.40 232.40 2 187.40 204.10 3 187.40 232.40 4 187.40 232.40 5 187.40 225.50 6 187.40 232.40 7 187.40 225.50 8 187.40 232.40 9 187.40 225.50 10 187.40 232.40 1 1 187.40 225.50 12 187.40 213.90 13 187.40 213.90 14 187.40 2 13.90 1 220.10 219.20 2 220. 1 0 176.90 3 220. 10 219.20 4 220.10 219.20 5 220. 1 0 206.50 6 220. 10 219.20 7 220. 10 206.50 8 220. 10 219.20 9 220. 10 206.50 10 220.10 219.20 1 1 220.10 206.50 12 220. 1 0 195.60 13 220.10 195.60 14 220. 10 195.60 1 212.00 194.60 2 212.00 160.90 3 212.00 194.60 4 212.00 194.60 5 212.00 186.00 6 212.00 194.60 7 212.00 186.00 8 212.00 194.60 9 212.00 186.00 10 212.00 194.60 1 1 212.00 186.00 12 212.00 181.30 13 212.00 181 .30 14 212.00 181.30 1 210.20 170.90 2 210.20 151.50 3 210.20 170.90 4 210.20 170.90 5 210.20 160.60 6 210.20 170.90 7 210.20 160.60 8 210.20 170.90 9 210.20 160.60 10 210.20 170.90 1 1 210.20 160.60 12 210.20 155.90 13 210.20 155.90 14 210.20 155.90  (continued)  Electric ity 211.50 242.90 211.50 211.50 188.80 211.50 188.80 211.50 188.80 211.50 188.80 267.90 267.90 267.90 175.00 204.30 175.00 175.00 188.80 175.00 188.80 175.00 188.80 175.00 188.80 267.90 267.90 267.90 180.00 186.70 180.00 180.00 188.80  180.00 188.80 180.00 188.80 180.00 188.80 267.90 267.90 267.90 175.90 186.70 175.90 175.90 175.80 175.90 175.80 175.90 175.80 175.90 175.80 232.80 232.80 232.80  Telephor 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 147.90 141 .70 141 .70 141 .70 141 .70 141 .70 141.70 141.70 141 .70 141.70 141.70 141.70 141 .70 141.70 141.70 141.20 141 .20 141.20 141.20 141.20 141.20 141 .20 141.20 141.20 141.20 141.20 141 .20 141.20 141 .20 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30 135.30  B.  Cross-sectional  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Data By S o i l  Zone  P r i c e s : Indexes Custom Daily Hired Work Labour 257.50 306.90 254.90 271 .00 257.50 306.90 257.50 306.90 246,60 318.20 257.50 306.90 246.60 318.20 257.50 306.90 246.60 318.20 257.50 306.90 246.60 318.20 236.10 343.00 236.10343.00 236.10 343.00 230.40 289.50 229.30 248.00 230.40 289.50 230.40 289.50 225.00 294.10 230.40 289.50 225.00 294.10 230.40 289.50 225.00 294. 10 230.40 289.50 225.00 294.10 221.40 326.20 221 .40 326.20 221.40 326.20 203.40 253 . 10 198.50 236.70 203.40 253.10 203.40 253.10 197.60 269.90 203.40 253.10 197.60 269.90 203.40 253. 1 0 197.60 269.90 203.40 253. 10 197.60 269.90 200.00 299.40 200.00 299.40 200.00 299.40 181.60 238.60 177.70 223.30 181 .60 238.60 181.60 238.60 182.80 246. 10 181.60 238.60 182.80 246.10 181.60 238.60 182.80 246.10 181.60 238.60 182.80 246.10 181 .20 287.50 181.20 287.50 181.20 287.50  (continued) Property Taxes 195.80 202.40 195.80 195.80 202.00 195.80 202.00 195.80 202.00 195.80 202.00 204.10 204. 10 204.10 172.20 171 .50 172.20 172.20 177.90 172.20 177.90 172.20 177.90 172.20 177.90 202.70 202.70 202.70 152.50 147.60 152.50 152.50 156.20 152.50 156.20 152.50 156.20 152.50 156.20 184.80 184.80 184.80 152.50 226.90 152.50 152.50 143.50 152.50 143.50 152.50 143.50 152.50 143.50 170.40 170.40 170.40  Interest 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 668.60 471 .40 471.40 471.40 471 .40 471.40 471 .40 471.40 471.40 471 .40 471.40 471 .40 471.40 471 .40 471 .40 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 398.30 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60 278.60  B. Year 1981  1980  1979  1978  Cross-sectional Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Data  Prices; Farm Rent 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 359.10 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 279.30 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 242.60 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10 236.10  By  Soil  Zone  CPI (1971= 100) 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 3 6 . 90 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 2 1 0 . 60 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 191 . 2 0 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20 1 7 5 . 20  (continued) Fencing Repa i r s 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 258.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 237.20 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 226.80 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30 202.30  213 B.  C r o s s - s e c t i o n a l Data By S o i l Zone  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Receipts: $ Custom Work 861196. 00 156959. 00 6714407. 00 15996818. 00 5988133. 00 858625. 00 2679761. 00 565223. 00 1929471 . 00 5196232. 00 3306930. 00 556710. 00 3412218. 00 940607. 00 228392. 00 478165. 00 4464154. 00 21873769. 00 2249517. 00 311003. 00 1708522. 00 363791 . 00 1449689. 00 3532707. 00 1300937. 00 1869534. 00 2210467. 00 1987664. 00 478165. 00 19548. 00 1521372. 00 25377328. 00 2273599. 00 30048. 00 2004649. 00 641867. 00 2787492. 00 2839443. 00 560720. 00 226554. 00 979395. 00 1201968. 00 360417. 00 385405. 00 1770757. 00 14701805. 00 1099474. 00 281170. 00 1305357. 00 201647. 00 1695629. 00 1136646. 00 1982675. 00 180598. 00 1038577. 00 389870. 00  (continued)  Total Agr i c u l t u r e 69004432 .00 20046976 .00 377858992 .00 618422546 .00 370194156 .00 100938891 .00 246416596 .00 123855889 .00 267709378 .00 554136776 .00 209836642 .00 106690231 .00 227176263 .00 53887773 .00 49181057 .00 20020827 .00 363462541 .00 568327306 .00 307794834 .00 9330801 6 .00 272034984 .00 109769488 .00 218840603 .00 442647642 .00 225512181 .00 83623172 .00 164794614 .00 61819410 .00 44434246 .00 11060588 .00 281807485 .00 558740318 .00 251528614 .00 75285114 .00 257857869 .00 87258228 .00 209446613 .00 368325851 .00 197905775 .00 60404321 .00 172185857 .00 45282841 .00 21928690 .00 10757768 .00 208307390 .00 452241930 .00 204888786 .00 67254294 .00 191627091 .00 54131506 .00 156057169 .00 242170413 .00 146831925 .00 46003016 .00 144626306 .00 37081924 .00  Grains 30060768. 00 4699093. 00 87652526. 00 243946834. 00 210853708. 00 42479732. 00 134755782. 00 40391130. 00 115052900. 00 232451039. 00 114442414. 00 56176697. 00 101855787. 00 12984888. 00 19341093. 00 5491368. 00 68505901. 00 190862782. 00 174460432. 00 28482517. 00 1 39815823.00 42324153. 00 99173629. 00 155266500. 00 102887047. 00 36094375. 00 68398128. 00 12631950. 00 10886191. 00 1716811. 00 63100491. 00 151528553. 00 12299201 1 .00 16992149.00 129746041. 00 30593476. 00 82432722. 00 120817725.00 83106868. 00 26600643. 00 60624769.00 7133268. 00 4902209. 00 3465771 . 00 37808449. 00 106880854. 00 94347162. 00 15084603. 00 106703979. 00 20223020. 00 74038060. 00 67389682. 00 70633576. 00 21600361. 00 46153713. 00 5797794. 00  214 B. Year 1981  1980  1979  1978  Cross-sectional Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Data  By  Soil  Zone  (continued)  Expenditure: $ Misc . Hired Labour 4 4 3 3 8 0 . 00 1305831.00 1 6 2 1 8 6 . 00 1059284.00 2 7 8 3 1 4 0 . 00 14650994.00 5 2 3 2 3 0 1 . 00 24513426.00 1 4 7 7 9 2 8 . 00 9667286.00 5 5 0 6 1 2 . 00 4244354.00 1 2 7 6 5 1 6 . 00 7077235.00 6 2 6 6 0 6 . 00 3773600.00 10684261.00 1 1 8 5 8 8 6 . 00 15325973.00 2 8 3 4 2 7 8 . 00 8065039.00 1 0 0 1 7 2 9 . 00 2873786.00 4 2 5 4 2 4 . 00 7099405.00 1 5 4 7 5 0 7 . 00 1986004.00 3 3 8 4 6 7 . 00 1 378821.00 3 8 0 5 0 9 . 00 1 1 70645.00 1 3 9 4 4 1 . 00 10646402.00 1 9 6 2 9 3 1 . 00 23128158.00 3 9 9 5 0 6 8 . 00 7614097.00 1 2 1 3 8 0 8 . 00 3860852.00 4 2 6 6 6 0 . 00 8738538.00 1 5 2 6 5 3 2 . 00 4692383.00 4 2 8 4 0 8 . 00 8390793.00 1 0 0 5 1 7 4 . 00 14494241 .00 2 2 9 6 7 4 1 . 00 5879082.00 1 3 3 3 7 1 5 . 00 2495535.00 3 0 6 4 7 6 . 00 3475056.00 7 0 1 2 0 9 . 00 2278024.00 2 6 2 2 7 7 . 00 837368.00 2 5 5 2 3 4 . 00 383482.00 1 1 6 3 1 3 . 00 5618449.00 1 6 7 4 3 2 4 . 00 21261629.00 4 0 9 6 0 6 7 . 00 5517396.00 1 2 2 7 3 7 4 . 00 2631056.00 4 0 0 9 8 7 . 00 6298019.00 1 0 8 4 5 5 2 . 00 2723029.00 5 0 9 6 8 4 . 00 6536701.00 1 0 3 1 0 9 0 . 00 8569875.00 1 8 6 3 6 6 4 . 00 4308817.00 8 8 3 8 2 7 . 00 1379469.00 2 6 4 4 3 0 . 00 3317466.00 1 0 6 0 8 6 3 . 00 1531350.00 1 8 3 8 3 8 . 00 713653.00 3 4 3 8 1 5 . 00 341106.00 1 5 6 6 6 5 . 00 1 5 1 5 3 5 5 . 00 6908217.00 3 0 9 9 6 0 0 . 00 20169432.00 9 2 3 1 8 3 . 00 5094319.00 2704260.00 3 6 5 9 7 3 . 00 5474556.00 1 2 9 7 2 3 0 . 00 1330699.00 4 1 8 6 5 1 . 00 4997709.00 7 7 5 0 0 4 . 00 5005076.00 1 6 6 0 0 7 5 . 00 3596033.00 861795.00 883811.00 3 5 2 2 0 3 . 00 4477823.00 9 7 9 4 8 6 . 00 1513999.00 2 0 8 1 1 4 . 00  Family Labour 433217.00 74260.00 6180814.00 4663250.00 3688391.00 1382691.00 2645176.00 1018535.00 3677490.00 5595321.00 3489641.00 1194850.00 1209994.00 605722.00 475594.00 53251.00 3153166.00 4766726.00 2932959.00 1 162350.00 2831016.00 1069858.00 2530416.00 3945450.00 2586376.00 1049612.00 845294.00 486690.00 157407.00 25571.00 1053110.00 1794692.00 1298789.00 279202.00 1917723.00 440703.00 1360652.00 1630880.00 1045586.00 228843.00 544669.00 195146.00 229915.00 149202.00 1703936.00 3174516.00 1756781.00 652417.00 2300708.00 473282.00 1424016.00 2188289.00 1683269.00 165597.00 534229.00 286586.00  Room + Board 78796.0 1 2 1 7 2 4 , ,0 3 9 6 7 8 2 , ,0 1 2 0 0 3 0 6 , ,0 2 7 0 8 3 3 , ,0 297663.0 179605.0 189090.0 549199.0 602252.0 1 5 3 6 6 0 , ,0 1 5 9 9 1 0 , ,0 2 5 9 4 8 3 , ,0 1 4 6 2 9 8 ,0 98078.0 168381.0 1103847.0 2372132.0 326117.0 197353.0 548928.0 188367.0 738971.0 1021537.0 280033.0 81679.0 231434.0 184062.0 74513.0 102302.0 7 3 0 8 8 0 , .0 1 3 7 3 4 1 7 ,,0 4 9 2 0 0 0 . .0 1 5 6 3 5 7 ,,0 2 7 0 9 5 3 , .0 9 3 4 3 3 , ,0 663814.0 795766.0 229977.0 9 0 6 5 0 ,.0 2 4 7 3 9 7 ,.0 1 2 6 1 0 3 ,.0 3 8 2 1 4 ,.0 3 0 6 8 6 ,.0 8 7 9 9 9 1 ,.0 1 5 8 7 0 8 8 ,.0 4 0 3 3 7 1 , .0 170084.0 345847.0 282552.0 522997.0 425415.0 257239.0 129616.0 339054.0 141714.0  B,  Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Expenditure: $ Pesticide 1075849. 00 120230. 00 5974791 . 00 11313184. 00 7197874. 00 1292502. 00 5882897. 00 1700626. 00 7443529. 00 15202173. 00 5908766.00 3486102. 00 8894202. 00 944390. 00 524546. 00 49032. 00 4672776. 00 9262628. 00 4189690. 00 725477. 00 4341050. 00 1 169084. 00 5567305. 00 10704360. 00 5127500. 00 2386046. .00 4434958. 00 712992. 00 399616. 00 71712. 00 4227998. 00 7023863, 00 3850644. 00 640434. 00 5390250. 00 726998. 00 4946248. 00 8007411. 00 4800323. 00 ' 2287752. 00 5067768. 00 548233. 00 277737. 00 240641. 00 3272177. 00 5117971 . 00 2870402. 00 438371 . 00 4419814. 00 456437. 00 5065210. 00 5679775. 00 3904248. 00 1683073. 00 4184923. 00 518297. 00  Zone  (continued)  Custom Work 1607579. 00 697567. 00 81 1 5454. 00 15145941. 00 6890977. 00 2664105. 00 4255609. 00 2194402. 00 4261261. 00 15158327. 00 3934396. 00 1646101 . 00 6063169. 00 1108648. 00 838755. 00 521656. 00 5268751. 00 11701593. 00 3798441. 00 1527836. 00 4925397. 00 994502. 00 5179575. 00 7734537. 00 3969964. 00 1649727. 00 3450473. 00 1346659. 00 865891. 00 234374. 00 5081446. 00 10759995. 00 2853852. 00 1365692. 00 3267434. 00 1438961. 00 2447162. 00 5808227. 00 2639491. 00 904997. 00 3384916. 00 613733. 00 785863. 00 222841. 00 2955327. 00 8299652. 00 3231379. 00 1277547. 00 2486168. 00 565259. 00 2531154. 00 3081527. 00 2175529. 00 598945. 00 2840056. 00 590355. 00  Feed + Supplements 3463687 .00 994182 .00 19767462 .00 73785600 .00 22769111 .00 9473521 .00 16296504 .00 8155861 .00 9516930 .00 27397437 .00 9925806 .00 3156532 .00 12279585 .00 3851327 .00 1994248 .00 790665 .00 24762689 .00 58438651 .00 16931331 .00 7897040 .00 20380444 .00 6207869 .00 7911963 .00 19078980 .00 16994164 .00 5075033 .00 17954261 .00 6463063 .00 1129487 .00 363548.00 22106413 .00 64857405 .00 10771106 .00 5526133 .00 11570493 .00 5395533 .00 6709134 .00 18114441 .00 7086903 .00 1651887 .00 9661447 .00 2663373 .00 826140 .00 267285 .00 15879192 .00 43821748 .00 8258080 .00 5474762 .00 7135760 .00 2708170 .00 5128369 .00 12614860 .00 3967830 .00 1535164 .00 88 1 1965 .00 2002284 .00  B. Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Zone Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Expenditure: $ Vet + A r t i f i c i a l Insemination 580809. 00 280534. 00 4090674. 00 5105883. 00 2218745. 00 579177. 00 2010782. 00 923140. 00 1759961. 00 4013219. 00 1647088. 00 623658. 00 1643325. 00 498070. 00 341531. 00 178746. 00 3073768. 00 3876794. 00 1594320. 00 621675. 00 2191901 . 00 790850. 00 1629934. 00 3246921. 00 1855515. 00 709174. 00 1315864. 00 539308. 00 548274. 00 74612. 00 2975098. 00 4545861 . 00 1515004. 00 366184. 00 2014192. 00 541599. 00 1710681. 00 2821272. 00 2196796. 00 332549. 00 1324132. 00 347718. 00 , 211422. 00 109720. 00 1886474. 00 3315453. 00 1084573. 00 398136. 00 1261172. 00 325233. 00 1108873. 00 1900751. 00 1266626. 00 280704. 00 986510. 00 325623. 00  (continued)  Interest on Loans 8012127 .00 3340005 .00 34442391 .00 63170463 .00 35787448 .00 7868979 .00 20875797 .00 10159465 .00 24292598 .00 57522760 .00 20080649 .00 8061884 .00 1692670 .00 470255 .00 6344059 .00 2973055 .00 30047549 .00 57600252 .00 24978997 .00 4742134 .00 23133223 .00 6229689 .00 16578166 .00 42382317 .00 17420689 .00 5904521 .00 16385148 .00 4445575 .00 5262112 .00 1098254 .00 17393725 .00 40612507 .00 16934334 .00 2920298 .00 16190059 .00 5689553 .00 14789414 .00 24223384 .00 14099012 .00 3852454 .00 12149390 .00 2567016 .00 61381 1 .00 4911 16 .00 4410485 .00 11526299 .00 3359640 .00 912735 .00 2822993 .00 1674767 .00 2677789 .00 6693003 .00 1582533 .00 997370 .00 3033420 .00 1001047 .00  Telephone 288825. 00 1 3357400 , 1355824. 00 1679451. 00 1334304. 00 254452. 00 861661. 00 407450. 00 792599. 00 1525427. 00 686671. 00 248059. 00 633540. 00 324887. 00 296253. 00 120198. 00 1379298. 00 1702931 . 00 1154092. 00 312984. 00 1210221. 00 446190. 00 865935. 00 1502702. 00 859665. 00 298169. 00 607349. 00 320357. 00 242954. 00 31288. 00 1215356. 00 1609256. 00 1040745. 00 196297. 00 915927. 00 444247. 00 880408. 00 1323024. 00 773031 . 00 204452. 00 558738. 00 195711. 00 228306. 00 89081 . 00 935546. 00 1410204. 00 819645. 00 216784. 00 738610. 00 320720. 00 588091. 00 1005271. 00 689164. 00 172167. 00 553704. 00 225225.00  217  B.  Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Expenditure: Electricity 708371. 00 227792. 00 3883668. 00 4165063. 00 2746130. 00 576393. 00 2077997. 00 958584. 00 1923441 . 00 3711765. 00 1717002. 00 859146. 00 1984133. 00 856537. 00 605697. 00 179429. 00 3863978. 00 4628779. 00 2628199. 00 613870. 00 2554128. 00 997624. 00 1882771 . 00 3278702. 00 2229450. 00 1009122. 00 1877526. 00 1012448. 00 512764. 00 53395. 00 3382126. 00 3757057. 00 2396389. 00 405046. 00 2476526. 00 868739. 00 2178373. 00 3070968. 00 2133703. 00 831314. 00 2079444. 00 742208. 00 546391. 00 140637. 00 2433042. 00 3880673. 00 2046965. 00 532088. 00 2090850. 00 643927. 00 1729119.00 2658040. 00 1834995. 00 794976.00 2193042. 00 770571 . 00  $  Zone  (continued) Fuel  401072. 00 160525. 00 2292300. 00 3218239. 00 1517827. 00 599205. 00 902674. 00 548098. 00 877424. 00 2705718. 00 669830. 00 324567. 00 694852. 00 202950. 00 485177. 00 180451. 00 3005743. 00 4188200. 00 1857003. 00 573119. 00 1875679. 00 584666. 00 1703860. 00 2709449. 00 1340910. 00 390726. 00 520608. 00 284627. 00 292450. 00 55020. 00 2457590. 00 3273086. 00 1770687. 00 437729. 00 1 46355100 . 535918. 00 1329108. 00 2233483. 00 1433053. 00 350459. 00 735224. 00 206997. 00 341981 . 00 9551 100 . 1678674. 00 2722565. 00 1374054. 00 381960. 00 1189058. 00 321 161 . 00 782592. 00 1759703. 00 1055985. 00 279257. 00 604783. 00 307702. 00  Insurance 1 103706. 00 159692. 00 6102282. 00 10846184. 00 7747274. 00 1998436. 00 6106082. 00 2831962. 00 4193868. 00 9505185. 00 5784475. 00 1735575. 00 4078125. 00 859805. 00 756468. 00 233717. 00 4372277. 00 8532114. 00 5773325. 00 1542297. 00 5982657. 00 2264338. 00 3539361. 00 6909279. 00 5342597. 00 1388918. 00 2613256. 00 845690. 00 627102. 00 68834. 00 3476782. 00 6633640. 00 5084049. 00 987233. 00 6004582. 00 1280702. 00 3584736. 00 4853653. 00 3817821. 00 1118121. 00 2818127. 00 394035. 00 448709. 00 170459. 00 2627636. 00 4945778. 00 4720179. 00 1068055. 00 5129566. 00 1067497. 00 2838098. 00 3828526. 00 4017323. 00 1072921. 00 2956014. 00 460082. 00  218 B.  C r o s s - s e c t i o n a l Data By S o i l  Year 1981  1980  1979  1978  Soil  Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 1 4 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Expenditure: $ Property Tax 844611. 00 176571. 00 5482938. 00 7833695. 00 9890461. 00 1210469. 00 5312501. 00 1878389. 00 4762849. 00 8046915. 00 5659376. 00 2469792. 00 5136627. 00 1395154. 00 681380. 00 187802. 00 4441520. 00 6655388. 00 8516039. 00 1952538. 00 6234212. 00 1856521. 00 4392774. 00 6656018. 00 5618518. 00 2171314. 00 4141422. 00 1112679. 00 545796. 00 116780. 00 3698704. 00 7091463. 00 7126074. 00 1097438. 00 5669892. 00 1110563. 00 4098901. 00 5138630. 00 4546930. 00 1666974. 00 3782190. 00 857879. 00 340326. 00 197961. 00 3219789. 00 5664297. 00 6183670. 00 1437642. 00 6286317. 00 1043297. 00 3733705. 00 4303791. 00 4550774. 00 1477306. 00 3606715. 00 1039502. 00  Zone  (continued)  Depreciation 9404018. 00 2100143. 00 63807431. 00 80115253. 00 62240864. 00 14325780. 00 50329652. 00 19965125. 00 36493448. 00 82233441. 00 36614591. 00 14772700. 00 29195733. 00 8701976. 00 9461013. 00 2386745. 00 65470742. 00 ' 73875804. 00 54720894. 00 14100925. 00 48503163. 00 18871472. 00 37236810. 00 71267927. 00 40722480. 00 13919459. 00 26690584. 00 10958829. 00 10853578. 00 1294554. 00 52476355. 00 59189042. 00 49940628. 00 8928490. 00 50116086. 00 17428486. 00 37652794. 00 58289337. 00 36160541. 00 9197278. 00 25848705. 00 6465004. 00 4150089. 00 1849368. 00 38761244. 00 57744467. 00 43680584. 00 12968795. 00 41906773. 00 11910413. 00 26632151. 00 35984272. 00 28805626.00 7945392. 00 20768491. 00 5809655. 00  Building Repairs 891819.00 164059. 00 5280290. 00 7906551. 00 2824674. 00 774101. 00 2315565. 00 1389963. 00 2453299. 00 5455804. 00 1979636. 00 952967. 00 2264886. 00 497675. 00 619209. 00 196324. 00 4531329. 00 6469924. 00 2864026. 00 748786. 00 2360119. 00 883780. 00 2068957. 00 3732038. 00 2328207. 00 1005960. 00 1876444. 00 781732. 00 465070. 00 66505. 00 3965410. 00 6013242. 00 2573873. 00 522093. 00 2451967. 00 768030. 00 2227948. 00 4466204. 00 2168989. 00 725770. 00 1776189. 00 564120. 00 457737. 00 250118. 00 2825116. 00 3987440. 00 2284152. 00 862852. 00 2461868. 00 564507. 00 1656865. 00 4030321.00 1767566. 00 712647. 00 1914019. 00 676916. 00  219  B. Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7' 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Expenditure: $ Rental 2347930. 00 465432. 00 1 1713816. 00 22732692. 00 13839929. 00 2719929. 00 11639316. 00 4350344. 00 9387737. 00 23799645. 00 8569584. 00 3640208. 00 7290640. 00 2032495. 00 1336184. 00 362542. 00 12690743. 00 26577998. 00 16600326. 00 2001858. 00 15309897. 00 4263367. 00 .9667148. 00 16025937. 00 9368233. 00 3541224. 00 6785140. 00 1521068. 00 479605. 00 339303. 00 8865101. 00 19772871 . 00 9513101. 00 1635130. 00 12453306. 00 3101739. 00 8740839. 00 12742865. 00 5231367. 00 1753542. 00 8679488. 00 1563871. 00 373922. 00 491837. 00 6997168. 00 15023742. 00 8960997. 00 1927452. 00 8762352. 00 1704573. 00 6427456. 00 10256784.00 5992353. 00 1942862. 00 7041289. 00 1258924. 00  Zone  (continued)  Machinery 1 1629733 .00 3960682 .00 54469821 .00 55066901 .00 44677252 .00 9609172 .00 36295873 .00 14530497 .00 33353259 .00 69539964 .00 32513981 .00 14626929 .00 31692508 .00 12217437 .00 7679156 .00 2901372 .00 40678179 .00 50318434 .00 36666662 .00 7728612 .00 35442041 .00 13379886 .00 29027273 .00 51907738 .00 30130893 .00 12784197 .00 20831451 .00 1 0700942 .00 7445386 .00 1480204 .00 31877822 .00 40033928 .00 28530972 .00 5754439 .00 28735014 .00 8260422 .00 27279265 .00 36548830 .00 22294831 .00 7841970 .00 17656406 .00 7089774 .00 5117505 .00 2236662 .00 23809977 .00 34701066 .00 25436049 .00 6497354 .00 24775190 .00 6838602 .00 22574849 .00 30629209 .00 22591510 .00 7015729 .00 18552040 .00 7664000 .00  Seed 1 1 48700 .00 514625 .00 5440749 .00 4523363 .00 2284540 .00 633015 .00 2383136 .00 597873 .00 4566410 .00 6675581 .00 3670806 .00 1706099 .00 4912247 .00 1157480 .00 618540 .00 192249 .00 4206984 .00 5228461 .00 2167987 .00 717305 .00 3563111 .00 546233 .00 3692527 .00 5088342 .00 3533218 .00 1660840 .00 4431883 .00 917594 .00 722602 .00 171023 .00 4039767 .00 3954920 .00 1 393377 .00 505943 .00 2167864 .00 536389 .00 3263364 .00 3842261 .00 2978549 .00 1304156 .00 3242914 .00 633643 .00 453639 .00 177927 .00 3124300 .00 3566643 .00 1094443 .00 591631 .00 1977139 .00 377817 .00 2607439 .00 3528819 .00 2708063 .00 1105228 .00 2975987 .00 745151 .00  220 B. Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Expenditure: $ Fencing Repairs 527412.00 196614.00 3728656.00 2444183.00 2330619.00 458409.00 1377066.00 907886.00 1821189.00 3705807.00 1765525.00 485036.00 1197332.00 486797.00 378899.00 125401.00 2968528.00 2388589.00 2063117.00 660644.00 1586456.00 889599.00 1207505.00 3758887.00 1212891.00 562376.00 1025385.00 587705.00 253964.00 27204.00 2604099.00 2298418.00 1610484.00 467513.00 1322442.00 990720.00 1390158.00 2973527.00 1347174.00 399192.00 748957.00 513465.00 290455.00 104656.00 2067523.00 2211783.00 1709433.00 517867.00 1424005.00 540709.00 1113805.00 2505078.00 1218230.00 436692.00 870294.00 540510.00  Zone  (continued)  Twine + Wi re 396087.00 99933.00 1842548.00 1351417.00 997619.00 189291.00 823146.00 255660.00 1021408.00 1422058.00 900222.00 357162.00 931080.00 403534.00 346845.00 125158.00 1856414.00 1668076.00 1345151.00 255066.00 1235600.00 325001.00 1064476.00 1 478389.00 1 146714.00 458419.00 808605.00 382968.00 247992.00 38084.00 1628234.00 1479584.00 1136218.00 219785.00 1045935.00 264666.00 1 205464.00 1650951.00 1096802.00 247922.00 831049.00 279647.00 187252.00 73497.00 1094196.00 1330471.00 931264.00 292859.00 692418.00 205766.00 905951.00 1 184119.00 870863.00 253422.00 766312.00 220822.00  Hardware 634740.00 151301.00 3762318.00 3750614 00 2921449 00 595253 00 2009052 ,00 954933 00 1655078.00 3746062.00 1514295 00 668013 00 1692670 00 470255 00 701435 00 267023 00 3019576 00 3995113 00 2338613 00 690515 00 2491761 00 954035 00 1556174 00 3137159 00 1729529 00 624482 00 1104541 00 493317 00 368886.00 59141.00 2777170.00 3509112.00 2159882.00 471 100.00 21 31926.00 781110.00 1835759.00 2552728.00 1301576.00 445777.00 930861.00 433496.00 344976.00 114444.00 2158975.00 2322071.00 1727931.00 489983.00 1707562.00 608737.00 1293068.00 2131257.00 1 153705.00 340333.00 959935.00 411809.00  221  B. Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Zone  (continued)  Expenditure: $ Fertilizer  Irrigation  4552104.00 823422.00 23615482.00 33679644.00 6068933.00 2571543.00 7728924.00 1400715.00 17264488.00 46615041.00 8700811.00 8488230.00 17697486.00 3384426.00 2670252.00 650134.00 19908746.00 28489907.00 4861713.00 1403622.00 9484002.00 1545929.00 14996368.00 29293798.00 9063718.00 6333442.00 13222369.00 2546440.00 2847228.00 458543.00 17600494.00 27527427.00 3791746.00 1221637.00 10639665.00 1685671.00 13853248.00 22436217.00 8387632.00 5074812.00 13125254.00 1726562.00 1222735.00 1201406.00 12956492.00 22321693.00 2252895.00 1057444.00 7041243.00 834009.00 10403566.00 15906005.00 6506594.00 3368362.00 12252735.00 1795427.00  0.0 0.0 27782.00 1894672.00 164295.00 253963.00 120329.00 10528.00 13202.00 0.0 166.00 0.0 0.0 0.0 17976.00 302.00 15312.00 1825600.00 478884.00 261382.00 1 1 1256.00 19000.00 0.0 1000.00 37394.00 0.0 0.0 0.0 0.0 0.0 87724.00 1709615.00 405621.00 288143.00 21849.00 10505.00 0.0 1164.00 54586.00 11026.00 5077.00 5304.00 0.0 248.00 0.0 1504437.00 90627.00 222387.00 46082.00 0.0 10.00 0.0 60902.00 0.0 7282.00 14095.00  Other 144072.00 11376.00 210692.00 407911.00 177847.00 93979.00 219181 .00 44801.00 69135.00 155284.00 282052.00 27848.00 275676.00 9946.00 51595.00 30427.00 261059.00 378766.00 191131.00 78881.00 511022.00 117086.00 44235.00 166338.00 288839.00 93980.00 262306.00 35378.00 82809.00 99864.00 886962.00 671589.00 119792.00 11648.00 189591.00 142827.00 312403.00 302792.00 349827.00 214407.00 336670.00 11513.00 9496.00 232449.00 1844156.00 1169044.00 289189.00 378963.00 1268367.00 260854.00 864482.00 760206.00 641835.00 143366.00 600265.00 68453.00  222 B. Year 1981  1980  1979  1978  C r o s s - s e c t i o n a l Data By S o i l Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Acres: T o t a l of 7 Grains 366516.00 61813.00 1128662.00 2036666.00 1939235.00 371369.00 1534546.00 721953.00 1361581.00 2599305.00 1310021.00 541365.00 1050914.00 205689.00 303664.00 58561.00 1 148531.00 2276044.00 1954909.00 373166.00 1876436.00 . 696805.00 1299791.00 2155027.00 1615616.00 516540.00 839094.00 160447.00 205029.00 27970.00 986992.00 1960517.00 1781996.00 247220, 00 1916560, 00 639581, 00 1354552, 00 1813940, 00 1340634, 00 389251, 00 913779.00 154242.00 198269.00 37802.00 940820.00 1998755.00 1821287.00 247210.00 1842131.00 635609.00 1285825.00 1809310.00 1306365.00 399543.00 919077.00 133307.00  Zone  (continued)  Tame Hay 246379.00 86079.00 890095, 00 361252. ,00 281699. ,00 49199, ,00 192683.00 1 1 3725.00 392292.00 609789.00 180547, 00 127898, 00 287454, ,00 214659, 00 178011, ,00 74973, ,00 902697.00 378104.00 306079.00 76022.00 391560.00 1 4 1 356.00 302216.00 516909.00 235453, ,00 158073, ,00 311528, ,00 184584, ,00 193343, ,00 29575, ,00 883254, ,00 483148, ,00 334786.00 53166, 00 297157, 00 130085, 00 437657, 00 598017, ,00 234042, 00 104549.00 259084.00 157903.00 199467.00 28481.00 846848, ,00 495001, 00 331717, ,00 56893, 00 284896.00 129418.00 435042.00 544089.00 234027.00 98638.00 272869.00 153249.00  Rented Land 428117. 00 138157. 00 1356160. 00 1922621. 00 4075988. 00 1290770.00 1257266. 00 3247162. ,00 1997421.,00 1848443. ,00 763202. ,00 377094. ,00 784954. ,00 1208652. ,00 415210, .00 67474,.00 1355732, .00 2788536, .00 3822595, .00 2106745, .00 1693780, .00 2310534, .00 2261031,.00 2421534, .00 897107..00 443380, .00 697142, .00 1216744, .00 250868, .00 94351,.00 1474954, .00 2836234, .00 3503472, .00 1508371,.00 1 47281.00 1 , 3377117, .00 2403749.00 2849089.00 81 1406, 00 249966, ,00 813751, ,00 1051217, ,00 298725, ,00 84833, ,00 1585269, ,00 1936623, ,00 3200173, ,00 2124811, ,00 1458498, 00 2507702, ,00 1663632. 00 2015509. 00 783637.00 269535.00 748389.00 1356211.00  223 B.  (  Year 1981  1980  1979  1978  - s e c t i o n a l Data By Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  S o i l Zone  Acres: Other Crops 5013.00 3396.0.0 12228.00 18834.00 35107.00 1 1774.00 26859.00 31690.00 42523.00 67140.00 23141 .00 10287.00 87378.00 15569.00 10807.00 4480.00 19744.00 33773.00 26704.00 4444.00 32401.00 29586.00 62777.00 44689.00 22435.00 10093.00 61879.00 24282.00 1646.00 1092.00 32718.00 48425.00 6050.00 12141 .00 11403.00 10027.00 37250.00 60088.00 13856.00 15190.00 56267.00 24590.00 4350.00 898.00 36816.00 30185.00 2846.00 10605.00 5469.00 13026.00 38500.00 65682.00 11997.00 7670.00 50951 .00 21157.00  (continued)  Summer Fallow 73738.00 10059.00 102417.00 705764.00 1597981.00 316856.00 1071744.00 529902.00 433763.00 611109.00 703899.00 178490.00 156996.00 74862.00 57206.00 6693.00 108511.00 809748.00 1637048.00 306214.00 1384961.00 564682.00 451951.00 560383.00 932225.00 171383.00 142059.00 71792.00 77324.00 13203.00 135548.00 931985.00 1588606.00 211905.00 1463123.00 478093.00 590999.00 577315.00 813314.00 161591.00 248425.00 63880.00 66600.00 13912.00 162901.00 877233.00 1571502.00 210597.00 1439288.00 496514.00 617265.00 554771.00 803564.00 162834.00 259652.00 90484.00  All  Crops  691648.00 161348.00 2133404.00 3122516.00 3854023.00 749199.00 2825833.00 1397272.00 2230160.00 3887344.00 2217609.00 858041.00 1582744.00 510781.00 549690.00 1 44708.00 2180308.00 3524075.00 3927799.00 768878.00 3694295.00 1432681.00 2128709.00 3283519.00 2819239.00 858191.00 1391321.00 441106.00 477364.00 71841 .00 2041902.00 3431954.00 3711799.00 527150.00 3692061.00 1260198.00 2428242.00 3052205.00 2408464.00 672909.00 1 488020.00 400617.00 468687.00 81095.00 1991682.00 3410528.00 3728125.00 528165.00 3575820.00 1278349.00 2376654.00 2976714.00 2359698.00 670665.00 1510064.00 398449.00  224 B.  Cross-sectional  Year 1981  1980  1979  1978  Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Data  By  Soil  Acres: Improved Pasture 130850.00 39415.00 809562.00 355059.00 284947.00 73825.00 213637.00 33478.00 217595.00 432334.00 84240.00 66232.00 149335.00 75305.00 91123.00 46212.00 731709.00 433338.00 311828.00 119270.00 195680.00 326177.00 210325.00 444834.00 105031.00 61731.00 134598.00 67838.00 83050.00 39009.00 622863.00 355487.00 239726.00 135544.00 212188.00 39652.00 209796.00 359956.00 105692.00 45803.00 99677.00 39098.00 82292.00 26874.00 616785.00 361377.00 242169.00 135945.00 212262.00 37169.00 197966.00 341905.00 101281.00 44705.00 98629.00 40765.00  Zone  (continued)  Other Land 639899.00 244037.00 1561368.00 31 1 6 6 5 0 . 0 0 4792648.00 1861749.00 1214000.00 3399936.00 2232206.00 2643988.00 988919.00 504479.00 938787.00 1603743.00 610722.00 198575.00 1769527.00 3604241.00 4561596.00 2883523.00 1779249.00 2301072.00 2563920.00 3141 1 0 5 . 0 0 1232324.00 497132.00 966269.00 1652187.00 521621.00 119467.00 1899734.00 3784770.00 4598845.00 21 1 2 1 4 0 . 0 0 1451628.00 3171785.00 2698639.00 3703648.00 1229224.00 382080.00 1046660.00 1426311.00 542512.00 164355.00 1790317.00 3299509.00 4414048.00 3017786.00 1554200.00 2508684.00 1960810.00 2730624.00 1 178466.00 417513.00 1 100462.00 1656460.00  Total Land 1462398.00 444801 .00 4504304.00 6594267.00 8931642.00 2684774.00 4253470.00 4830689.00 4679921.00 6963617.00 3300744.00 1428718.00 2670833.00 2189820.00 1251588.00 389496.00 4681626.00 7560743.00 8801403.00 3771679.00 5669660.00 4059973.00 4903681.00 6869108.00 4156976.00 1417260.00 2492291.00 2161155.00 1081716.00 230318.00 4564475.00 7570275.00 8550185.00 2774774.00 5356756.00 4475693.00 5335943.00 7115632.00 3743257.00 1099941.00 2634248.00 1866027.00 1009498.00 338061.00 4183813.00 6667722.00 8463786.00 3774398.00 5305498.00 3698592.00 4670373.00 6021560.00 3795182.00 1088939.00 2736500.00 2173945.00  B. Ye,ar 1981  1980  1979  1978  Cross-sectional Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 1 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Data  By  Soil  Quantity: bu. Wheat Fed 16698.00 5000.00 354360.00 369325.00 147205.00 11504.00 194578.00 90015.00 124443.00 126954.00 176393.00 31495.00 212508.00 62147.00 7800.00 8245.00 305441.00 523811.00 322138.00 99409.00 643057.00 143943.00 165261.00 547709.00 375332.00 20638.00 195463.00 166311.00 12207.00 1102.00 786406.00 729531.00 363665.00 45596.00 653177.00 445190.00 212397.00 297135.00 448233.00 55678.00 316866.00 198754.00 0.0 5000.00 109177.00 326823,00 200954.00 16613.00 123874.00 54703.00 70219.00 174275.00 43697.00 35161.00 101555.00 100280.00  Zone Oats  (continued) Fed  1245911.00 356161.00 7081003.00 4038434.00 3780700.00 539549.00 4561345.00 2143672.00 5038804.00 9581151.00 5566290.00 2267197.00 4236258.00 1143004.00 712737.00 315310.00 7148308.00 4156520.00 3613506.00 947405.00 6312505.00 2138215.00 5761057.00 11085495.00 6072486.00 2313272.00 3235551.00 712793.00 777578.00 131516.00 6717466.00 8663249.00 3493138.00 766051.00 5039493.00 2224130.00 7081495.00 10903683.00 7399882.00 1709414.00 4790867.00 1433088.00 816190.00 191159.00 4919108.00 3660538.00 3172032.00 837497.00 4508700.00 1143515.00 3842927.00 8309804.00 6021379.00 1435637.00 4930447.00 1151222.00  Barley Fed 763209.00 187486.00 10439811.00 17138253.00 3659549.00 1310703.00 4033252.00 1523881.00 5138179.00 14392678.00 3182063.00 1712565.00 3693021.00 843604.00 926485.00 170202.00 11976537.00 18833405.00 2660482.00 1491555.00 5174275.00 1095456.00 5079747.00 10468848.00 3593482.00 2171996.00 3890880.00 902912.00 1 141256.00 106196.00 12548101.00 31827757.00 2505093.00 1025086.00 5589703.00 1060958.00 4675395.00 8600299.00 4101385.00 1402629.00 3536518.00 1070440.00 557845.00 633435.00 8254304.00 16112848.00 1590180.00 1512718.00 3468570.00 977384.00 3636065.00 6111956.00 1632991.00 873601.00 2891279.00 592231.00  B.  (  Year 1981  1980  1979  1978  - s e c t i o n a l Data By Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 ' 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  tr  S o i l Zone  Q u a n t i t y : Head Calves Born 68906.00 20916.00 330090.00 325742.00 272700.00 65276.00 132479.00 1 14822.00 165736.00 309558.00 137818.00 63729.00 135035.00 91473.00 51923.00 19902.00 331554.00 306492.00 261451.00 101077.00 188946.00 90296.00 192338.00 307069.00 169293.00 62726.00 128730.00 86969.00 56211.00 7835.00 331456.00 331345.00 241312.00 72132.00 168493.00 116324.00 190642.00 297564.00 155874.00 48475.00 126565.00 62018.00 45-1 33.00 14505.00 306890.00 320727.00 278438.00 78052.00 185045.00 85822.00 164573.00 259152.00 163552.00 47173.00 134147.00 88071.00  (continued)  Beef Cows 78740.00 24848.00 375585.00 357753.00 299056.00 69926.00 153619.00 122615.00 185753.00 352425.00 154327.00 69864.00 151788.00 101810.00 57246.00 22382.00 369101.00 343525.00 286365.00 108394.00 517091.00 105411.00 212577.00 328066.00 188051.00 70162.00 145105.00 99762.00 64789.00 9269.00 369122.00 356713.00 268980.00 80021.00 185766.00 126472.00 221094.00 322718.00 178381.00 54240.00 139657.00 73590.00 50768.00 15188.00 345208.00 360773.00 307327.00 87797.00 204244.00 96538.00 181648.00 291510.00 180521.00 52356.00 148887.00 97748.00  Replacement Hei f e r s 11886.00 4797.00 67594.00 59345.00 36520.00 13221.00 25360.00 15164.00 25293.00 47438.00 20856.00 10208.00 26980.00 24405.00 14172.00 5386.00 65633.00 57300.00 41692.00 20445.00 39245.00 15967.00 34668.00 56623.00 33356.00 12114.00 23237.00 15164.00 10268.00 3413.00 60687.00 66066.00 42587.00 12719.00 33887.00 23647.00 41228.00 51644.00 31475.00 6820.00 27489.00 13775.00 13809.00 3448.00 93897.00 98130.00 53782.00 23881.00 35743.00 26258.00 31788.00 79291.00 31591.00 14921.00 42433.00 27858.00  227 B. Year 1981  1980  1979  1978  Cross-sectional Soil Zone 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14  Data  By  Quantity: Steers  Soil  Zone  (continued)  Head  Slaughter Hei fers 7970.00 1766.00 4507.00 1996.00 8263 1 . 0 0 4 7 0 0 1 . 0 0 146540.00 64988.00 43681.00 17373.00 26883.00 12134.00 39960.00 17275.00 15502.00 14176.00 39149.00 28621.00 62887.00 62089.00 42420.00 17313.00 17456.00 9784.00 39569.00 22749.00 16961.00 7967.00 7069.00 2434.00 2634.00 476.00 106139.00 51727.00 134313.00 68023.00 30401.00 7064.00 16007.00 5470.00 29230.00 13256.00 16709.00 7370.00 32804.00 12905.00 75804.00 62554.00 38143.00 11578.00 16503.00 5648.00 34360.00 20203.00 11820.00 3877.00 13327.00 2408.00 2899.00 332.00 76989.00 36968.00 142411.00 52711.00 33320.00 18584.00 14602.00 3719.00 28859.00 12785.00 13685.00 4749.00 39765.00 10160.00 74820.00 39234.00 34894.00 9156.00 9729.00 3683.00 37767.00 15419.00 14424.00 4061.00 17016.00 0.0 3007.00 0.0 115645.00 0.0 120859.00 0.0 40874.00 0.0 29412.00 0.0 27165.00 0.0 32340.00 1978 24159.00 I n c l u d e d i n 97656.00 R e p l a c e m e n t 24009.00 H e i f e r s 15969.00 45411.00 29813.00  Calves 6 6 4 5 3 , 00 2 1 0 6 6 , 00 3 2 7 4 6 9 , 00 3 1 3 3 2 8 , ,00 2 5 7 0 6 5 , ,00 61504.00 130261.00 1 12251 . 0 0 162323.00 297943.00 135411.00 62603.00 132534.00 90039.00 48521.00 19467.00 328773.00 309296.00 263558.00 99609.00 190526.00 96358.00 191096.00 301540.00 165045.00 64112.00 132066.00 89588.00 52475.00 7650.00 333924.00 318259.00 243440.00 72324.00 163342.00 108509.00 192540.00 298272.00 157048.00 49797.00 125474.00 62659.00 45640.00 13426.00 310342.00 324335.00 209904.00 78930.00 138886.00 86788.00 124066.00 262067.00 123296.00 45079.00 128192.00 84161.00  Cattle + Calves 170794.00 58684.00 926546.00 974962.00 669184.00 188117.00 376887.00 287581.00 452647.00 848417.00 380474.00 174486.00 383289.00 247362.00 132022.00 57472.00 944256.00 943673.00 643089.00 256145.00 507055.00 247163.00 497860.00 851344.00 445873.00 175631.00 366046.00 229587.00 146606.00  24569.00 908259.00 969452.00 620321 .00 189115.00 439299.00 284137.00 518671.00 807909.00 422165.00 128243.00 357652.00 172409.00 91431.00 30552.00 727402.00 973918.00 443235.00 171271 . 0 0 398189.00 151077.00 385017.00 598284.00 347438.00 106413.00 331732.00 172030.00  228 C. Year  Time-Series Prices  Data  and E x p e c t e d P r i c e s  Steer*  Expected Steer  Heifer  1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982  16.10 16.85 21 .90 23.08 19.90 20.50 24.20 23.25 20.70 21 .95 24.90 26.40 26.40 31 .25 32.40 33.80 37.84 49.89 42.64 36.84 36.62 40.54 66.53 92.46 82.01 76.58 74.64  15.77 17.34 23.72 21 .57 18.10 22.01 25.52 21 .38 20.01 23.49 25.64 25.86 25.81 33.27 30.96 33.93 38.98 53.35 34.82 37.28 38.83 42.27 75.89 93.05 67.35 78.44 81 .37  12.10 1 2.87 18.93 19.32 16.71 16.68 20.25 20.47 17.83 18.33 20.30 22.00 22.50 2 6 . 45 27.05 27.80 32.32 43.15 35.78 30.77 31 .97 34.52 58.86 88.99 75.86 72.36 6 9 . 14  * Cattle  prices  in  units  cwt.  Expected Heifer 11.91 13.36 20.53 17.61 1 5.80 17.46 21 .34 1 9.46 1 6.97 19.28 20.74 21 .92 22. 1 4 27.49 26.04 27.85 33.46 45.06 30.29 31 .48 33.84 34.93 65.45 90.75 62.80 75.26 77.20  Cow 10.40 1 1 .40 15.84 16.55 14.87 15.05 16.60 16.55 14.75 13.90 17.95 18.50 18.45 21 .70 22.20 22.20 25.85 33.91 26.06 21 .30 22.91 24.99 40.27 58.27 51 .77 48.52 46.39  Expected Cow 9.99 12.06 16.97 15.19 14.05 15.71 17.05 15.98 14.17 1 4.26 19.61 17.23 18.24 22.80 21 .20 22.02 27.07 35.29 20.54 22.53 2 5 . 16 25.11 44.63 58.80 4 3 . 14 49.77 51.35  C.  Time-Series  Year  1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1 979 1980 1981 1982  Prices  Data  (cont.)  and E x p e c t e d  Prices  Calf  Expected Calf  Grain Index  C.P.I.  Interest Rate  10. 40 1 140 . 15. 84 16. 55 14. 87 15. 05 16. 60 16. 55 14. 75 13. 90 17. 95 18. 50 18. 45 21 . 70 2 2 . 20 2 2 . 20 2 5 . 85 3 3 . 91 2 6 . 06 21 . 30 2 2 . 91 2 4 . 99 4 0 . 27 5 8 . 27 51 . 77 4 8 . 52 4 6 . 39  9. 99 12. 06 16. 97 15. 19 14. 05 15. 71 17. 05 15. 98 14. 17 14. 26 19. 61 17. 23 18. 24 2 2 . 80 21 . 20 2 2 . 02 2 7 . 07 3 5 . 29 2 0 . 54 2 2 . 53 2 5 . 16 25. 1 1 4 4 . 63 5 8 . 80 4 3 . 14 4 9 . 77 51 . 35  9 8 . 80 9 2 . 40 9 4 . 90 9 7 . 70 102. 80 118. 50 124. 90 121 . 40 122. 30 120. 90 125. 80 123. 30 110. 50 98. 90 9 9 . 80 100. 00 117. 10 2 2 3 . 00 311. 40 2 9 8 . 40 2 4 5 . 30 2 1 3 . 00 2 2 9 . 90 2 8 5 . 60 357. 60 3 7 7 . 00 3 2 5 . 30  6 8 . 50 7 0 . 70 7 2 . 60 73. 40 74. 30 7 5 . 30 7 5 . 907 7 . 20 7 8 . 60 8 0 . 50 8 3 . 50 8 6 . 50 9 0 . 00 94. 10 9 7 . 20 100. 00 104. 80 112. 70 1 2 500 . 138. 50 148. 90 160. 80 175. 20 191 . 20 210. 60 236. 90 2 6 2 . 50  5. 04 5. 58 5. 27 5. 62 5. 75 5. 60 5. 71 5. 75 5. 75 5. 77 6. 00 5. 92 6. 92 7. 96 8. 17 6. 48 6. 00 7. 65 10. 75 9. 42 10. 04 8. 50 9. 58 12. 90 14. 25 19. 29 15. 81  Labour Index 4 8 . 90 51 . 90 5 4 . 10 5 6 . 50 5 8 . 30 5 9 . 60 6 0 . 90 6 2 . 40 6 5 . 30 6 9 . 70 7 6 . 80 8 3 . 50 8 8 . 30 9 2 . 70 9 4 . 90 100. 00 108. 50 1 2 410 . 1 4 810 . 176. 30 2 0 3 . 40 2 2 5 . 80 2 3 9 . 90 254. 10 2 7 2 . 30 291 . 10 3 0 9 . 90  C.  Time-Series  Year  (cont.)  Prices Capital Index  1 956 1 957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1 972 1 973 1974 1 975 1976 1 977 1978 1979 1980 1981 1982  Data  6 3 . 40 6 7 . 50 71 . 30 7 4 . 60 7 6 . 40 7 8 . 50 7 9 . 70 81 . 80 8 3 . 50 8 4 . 50 8 6 . 80 8 9 . 60 9 3 . 20 9 5 . 10 9 7 . 30 100. 00 1 0 360 . 1 0 790 . 121. 10 1 4 030 . 1 5 310 . 1 6 480 . 1 7 650 . 193. 90 221 . 90 2 6 0 . 70 2 8 7 . 60  Cattle Materials Index 74. 30 7 5 . 50 7 6 . 80 7 8 . 80 8 0 . 50 81 . 80 8 8 . 50 8 7 . 80 8 7 . 40 8 7 . 40 91 . 00 94. 90 9 6 . 20 9 8 . 70 9 7 . 60 100. 00 103. 10 109. 60 121 . 10 136. 50 150. 10 161. 10 172. 70 190. 10 207. 50 244. 60 268. 40  Inventories  End-of-Feriod Steer Hei fer 749. 8 838. 4 659. 8 614. 0 668. 2 791 . 6 737. 0 795. 0 945. 0 943. 0 995. 1 950. 0 939. 0 921 . 0 984. 0 980. 0 1039. 0 1038. 0 1277. 0 1428. 0 1410. 0 1 199. 0 1119. 0 1096. 0 998. 0 988. 0 998. 0  1615. 8 1667. 0 1773. 0 1852. 0 1911. 0 2016. 8 2037. 0 21 52. 0 2292. 0 2399. 0 2377. 9 2305. 0 2236. 0 2197. 0 2363. 0 2555. 9 2706. 0 2883. 0 3073. 0 31 3 5 . 0 3027. 0 2862. 0 2677. 5 2626. 0 2733. 5 2796. 0 2683. 0  (,000)  Cow 1 530 .3 1 602 .0 1633 .0 1 720 .0 1776 .3 1921 .4 1989 .0 2105 .0 2333 .0 2528 .0 2517 .4 2514 .0 2444 .0 2428 .0 2597 .0 2866 .4 3047 .0 3341 .0 3658 .0 3747 .0 3362 .0 3265 .0 3017 .0 2964 .0 301 3 .0 2937 .0 2845 .0  Calf 537. 7 569. 5 520. 7 520. 5 538. 8 586. 4 581 . 0 665. 0 778. 0 806. 0 735. 8 771 . 0 721 . 0 708. 0 836. 0 901 . 4 1024. 0 1023. 0 1 1 22 0. 1 164. 0 1261. 0 1119. 0 1060. 0 1043. 0 1025. 0 1024. 0 1009. 0  C.  Time-Series  Year  Cattle  Data  (cont.  Inventories  (,  Beginning-of-Period Steer Heifer Cow 1956 1957 1958 1959 1960 1961 1962 1 963 1964 1965 1 966 1 967 1 968 1969 1 970 1 971 1 972 1973 1974 1975 1976 1 977 1978 1979 1980 1 981 1 982  669. 0 749. 8 838. 4 659. 8 614. 0 668. 2 791 . 6 737. 0 795. 0 945. 0 943. 0 995. 1 950. 0 939. 0 921 . 0 984. 0 980. 0 1039. 0 1038. 0 1 2 7 70. 1428. 0 1410. 0 1 199.0 1119. 0 1096. 0 998. 0 988. 0  1490. 0 1615. 8 1667. 0 1773. 0 1852. 0 1911. 0 2016. 8 2037. 0 2152. 0 2292. 0 2399. 0 2377. 9 2305. 0 2236. 0 2197. 0 2363. 0 2555. 9 2706. 0 2883. 0 3073. 0 3135. 0 3027. 0 2862. 0 2677. 5 2626. 0 2733. 5 2796. 0  1 3 4 50. 1 5 3 03. 1 6 0 20. 1 6 3 30. 1720. 0 1776. 3 1 9214. 1989. 0 2105. 0 2333. 0 2528. 0 2517. 4 2514. 0 2444. 0 2428. 0 2597. 0 2866. 4 3047. 0 3341 . 0 3658. 0 3747. 0 3362. 0 3265. 0 3017. 0 2964. 0 3013. 0 2937. 0  Quant i t y Calf 494. 0 537. 7 569. 5 520. 7 520. 5 538. 8 586. 4 581 . 0 665. 0 778. 0 806. 0 735. 8 771 . 0 721 . 0 708. 0 836. 0 901 . 4 1024. 0 1023. 0 1 122.0 1 164.0 1 2610. 1119. 0 1060. 0 1043. 0 1025. 0 1024. 0  Calves Born 21 4 8 . 6 2351 . 0 2375. 9 2322. 0 2401 . 4 2500. 5 2509. 0 2616. 0 2775. 0 3001 . 0 2921 . 0 2830. 0 2725. 0 2714. 0 2851 . 0 3149. 0 3462. 0 3626. 0 3837. 0 3889. 0 3518. 0 3553. 0 3357. 0 3213. 0 3239. 0 3239. 0 3170. 0  Grain Index 86.3 47.8 51.3 55.0 67.3 22.9 87.4 109.3 80.5 95. 1 124.9 80.2 102.2 105.9 55.7 100.0 84. 1 94.6 74.6 111.1 151.2 134.3 131.4 97.0 123.0 172.8 183.8  D.  Regression Results Functional  F o r m s : Almon Lag P r i c e  The r e s u l t s multi-output, that  obtained  expectation  prediction prices  of  prior  be w r i t t e n  cattle of  to  an  can be  Almon  lag  in  this  process  defines  year.  of  function  prices  reported  the c u r r e n t  estimation  profit  a polynomial d i s t r i b u t e d  the  assuming  represented  (Almon  1965)  appendix. expected p r i c e  l a g model of  This prediction  as  the  annual  own  model  can  as:  (D.1)  n  = a +  ^1  The  l  (P  Vt-i  =Q  relationship  prices  between  degree  W  = E  i  B,  k=0 Equation  (W^)  constrained  lie  p  lag  + 1  of  ^  a n <  n  ^  P  a s t  periods  on a p o l y n o m i a l  of  , n> q .  k  (D.1)  is  b a s e d on a n n u a l five  used to g e n e r a t e Data  used to  observations  a u c t i o n markets  an e x p e c t e d p r i c e  estimate  of  in western  prices  the  polynomial  from 1946 t o  Canada  as  for  1983,  described  in  Four.  In  order  to  generate  alternative  specifications  degree  the  of  l e n g t h of final  to  ^ ^  k  each animal c a t e g o r y .  Chapter  prices  q: q  are  expected  ) can be d e s c r i b e d by a f i n i t e  fc  with lagged weights  for  of  predictions  expectation process are This  variable  expectations  by t h e  Predictions  from e c o n o m e t r i c  multi-input  farmers'  exactly  u s i n g C o b b - D o u g l a s and T r a n s l o g  the  model  of  the the  best  model were  p o l y n o m i a l was v a r i e d  l a g was v a r i e d  from  was  on  selected  fit  to  basis  the  data,  attempted.  from one t o  two the  to  five of  f o u r and  the  years.  The  R - v a l u e s and 2  The  t-  s t a t i s t i c s for the estimated c o e f f i c i e n t s . A p o l y n o m i a l of provided  the  estimated Calgary other  best  fit  market  market  are  areas  equation  is  for  are  expected in  in  each  In  animal  of  Table  five  D.I,  the  for  the  category  The e c o n o m e t r i c  This  the  prices  results  generated  Table D.2.  follow  period.  coefficients  data.  length  for  the  similar.  reported  one  with a lag  the  reported.  predicted prices  within  three  to  coefficients  An example of  that  degree  actual is  first  This  by  table  prices  and  i m p l i e d by t h e  year  as  the  steer  illustrates  are  dampened  large  estimated  compared  to  other  coef f ic i e n t s . The  prices  transformed Chapter  predicted  into  expected  Four.  These  w i t h t h e main d a t a  for  each  gain  animal  variables  expected  category  as  described  gain v a r i a b l e s  base t o a l l o w  econometric  were in  were c o m b i n e d  estimation  of  the  as  an  model. The C o b b - D o u g l a s f u n c t i o n a l initial  specification  variable  profit  ( D  '  three-input,  was  postulated  multi-output,  This  functional  multi-input form f o r  one-fixed-factor  case  can  the be  as:  n = a FP Jl  2 )  l  where a l l except  the  f u n c t i o n model.  three-output, written  of  form  a l  P "  variables  that  6 2  2  P  are is  a3 3  P  a4 4  as  P  a 5 5  P  a 6 6  n A ^ D b  6 1 x  previously  generated  n D  6 2 2  n D  6 3 3  ,  defined  u s i n g an Almon l a g  (Table  4.3)  expectation  process. It  is  interesting  to note  that  for  input  prices,  the  234 TABLE  D.1  Estimated Price Prediction Equations P o l y n o m i a l D i s t r i b u t e d Lag Time P e r i o d  using a  Steer  Calves  Cows  Heifers  t  .988 (. 1 6 4 ) *  1 .09 ( . 173)  1 .05 ( . 163)  .941 (.167)  t-1  -.174 (.181)  -.327 ( .206)  -.173 ( . 180)  -.124 ( .184)  t-2  -.207 (.081 )  -.192 (.084)  -.196 (.091)  -.192 (.091)  t-3  .242 (.191)  .386 ( .228)  .229 (.190)  .224 ( .200)  t-4  .530 ( .250)  .298 (.256)  .346 (.240)  .610 ( .280)  1.38  1.26  1.26  1.46  Sum Of L a g g e d Coefficients r  .9108  2  .8766  .  .8656  .8926  D e g r e e of Polynomial  3  3  3  3  Durbin-Watson  1.98  1.86  2.04  2.09  *  standard error  in  parentheses  TABLE Example Year  Observed Value  D.2  of P r e d i c t e d P r i c e s , Steer Equation Predicted Value  Calculated Error  1960  22.62  18.50  4.110  1 961  20.16  20.82  -0.662  1962  20.75  17.11  3.638  1963  23.45  19.62  3.833  1964  22.65  25.74  -.3090  1965  20.40  24.49  -4.098  1966  21 .40  20.69  0.707  1967  24.70  23.21  1 .494  1968  26.40  27.99  -1.598  1969  26.75  27.93  -1.177  1970  31 .50  26.34  5. 1 56  1971  33.20  31 .96  1 .242  1972  33.55  34.90  -1.354  1973  38.60  34.96  3.642  1974  48.98  40.88  8. 104  1975  42.03  5 3 . 12  -11.088  1976  34.25  44.39  -10.137  1977  35.44  3 7 . 17  -1.728  1978  38.77  46.33  -7.564  1979  65.35  54.85  10.503  1980  91 .08  74.72  16.360  1981  7 9 . 10  91.01  -11.910  1982  74.66  70.63  4.029  1983  73.26  71 .22  2.039  236 convexity  conditions  are  satisfied  in Equation  monotonicity  c o n d i t i o n s are  satisfied.  that  j=4,5,6,  this  &j < 0,  convexity the  is  satisfied.  second order  input  and  Convexity  = -a. (a.-l)P.II  requires  n  = =  satisfied  if  For  fi..  sufficient  Equation  of  Equation  by  (D.2) ±  ±  (D.2)  ensures  that  examining  with respect  to  of  sufficient Keeping  that  Casual reveals  in  the  Furthermore,  >  the  order  that  the  is  regression  of  the  0,  is  not  i=1,2,3)  satisfied. order  T h i s can derivative  be of  prices:  the in  to  all  of  i.  's  satisfy  in are  the  profit,  but  prices. the  this  convexity  is the  necessary  d e f i n e d as  share  of  restriction  in output  prices,  i must be g r e a t e r  than  farm.  sample d a t a  used  in  c o n d i t i o n s would n o t  Cobb-Douglas results  condition  Consequently,  output  each output  by t h e  this  c o n d i t i o n s are  total  for  > o but  n_ _  for  convexity  multi-output  satisfaction  second  convexity  received  observation  is  to output  1,  i  received  that  condition  i = 1,2,3.  to ensure  profit  >  the m o n o t o n i c i t y  output  revenue total  i  the  convexity  i n mind t h a t  from  indicates  that  requires fi  This  j .  examining  if  j .  (i.e.,  ±  only  all  however,  - a (0^-1)^11  satisfaction  revenue  all  with respect  convexity  satisfied  > 0 for  prices  to ensure  np P  for  also  requires  j = 4,5,6.  conditions  demonstrated  Again,  < 0 for  output  monotonicity  the  restriction  the  i  j  the  Monotonicity  T h i s can be d e m o n s t r a t e d by  derivatives  if  prices: n_ „  not  (D.2)  for  this be  profit  Equation  (D.2)  study  satisfied function. supported  237 this  conclusion. To c i r c u m v e n t  Cobb-Douglas  this  problem,  specification  an a g g r e g a t e  output  price  form  1977).  The  (Fuss  restrictions  on  the  it  was d e c i d e d t o m a i n t a i n  on the  input  index u s i n g translog  revenue  side  a  but  to  translog  generate  functional  f u n c t i o n does not  shares  in  order  a  require  to  satisfy  convexity. The t r a n s l o g p r i c e (D.3)  lnP  where are  Pj  = InB  I  T  is  o  ± = 1  (D.3),  the .  i  =  where  i  B  is  +  E  B  ik  output  V  i's  + e  l  k  =  B . InP InP , ij i j  1  i n d e x and a l l  Applying share  i  i  =  revenue  to  e q u a t i o n s c a n be d e f i n e d  as:  X  ' ' ' 2  3  share  in t o t a l  estimation  all  of  Equation  coefficients  InBo.  Consequently,  d e f i n e d o n l y up t o a c o n s t a n t  Dummy v a r i a b l e s (D.4) data  used  Furthermore, constraints  are  added  account in  prior  Estimates equations  to  are  revenue  of  derived  to  for  (D.3)  scaling  the  the  to e s t i m a t i o n ,  will  the aggregate  estimating  imposed on the  (D.4)  in Equation  (InPj.)  series  variables Lemma  term,  Equation  other  Hotelling's  intercept is  as:  and  e  A  term.  Econometric of  l n  =  3 Z  price  revenue  k=l  a random e r r o r  estimates  ±  defined.  (D.4) S  3 B InP + JjE i i  the aggregate  as p r e v i o u s l y  Equation  is  3 +2  i n d e x c a n be w r i t t e n  generate except  price  intercept  share  index  factor. term  cross-sectional,  the  the  in  time-  equations.  symmetry and t h e  adding-up  model.  the parameters  of  using Z e l l n e r ' s  the (SUR)  three  revenue  regression  share  procedure  are  reported  in Table D.3.  Five  iterations  were r e q u i r e d  for  convergence. Own  output  statistically necessary price  price  significant  condition  for  coefficients  percent  eigenvalues  variables  of  are  5 percent  positive  level  statistically  and  which  Furthermore,  all  is  a  remaining  significant  constant,  checked  by  at  the  computing  of  were d e t e r m i n e d a t  t h e means of  of  Measures  are  the H e s s i a n m a t r i x  and e q u a l l e d  Hessian matrix  5  of  the  .332, price  output  the p r i c e  . 1 0 2 , and index  .001.  function  substitution,  index the  the  function.  endogeneous  Therefore,  is  the  convex.  holding total  output  c a n be g e n e r a t e d u s i n g t h e e s t i m a t e d c o e f f i c i e n t s  Table D.3.  In  elasticities  T a b l e D.4 are  the  supply e l a s t i c i t i e s the  substitute  relationship  Using aggregate  price  (D.3).  This  single  output  are  supply  This  table  positive  cross  price  between o u t p u t  estimated index  and p r o f i t  cross  indicates  that  „Ji „ «  variables  Applying H o t e l l i n g ' s  own In  suggest a  pairs. in  Table  D.3,  can now be g e n e r a t e d t h r o u g h  A"5  in  price  inelastic.  elasticities  rewrite Equation  n o r m a l i z e d Cobb-Douglas p r o f i t  if if if  and  and  coefficients  i n d e x c a n be u s e d t o  II - a where p r i c e  estimated  the  output  presented.  addition,  input  the  convexity.  conditions  values  output  at  are  level.  Convexity  These  coefficients  an  Equation  (D.2)  as  a  function:  „«3, are  n o r m a l i z e d by Pj .  lemma t o E q u a t i o n  demand e q u a t i o n s can be d e f i n e d  as:  (D.5),  the  derived  , TABLE Regression Results: Share  D.3  Translog Price  Prices Cattle  Index  Dummy V a r i a b l e s  Inven. *  Crops C o n s t .  1981  1980  1979  R  2  .0001 --.056 .513 (.006) (3.3)  Cattle  .421 -.230 ( 5 . 4 ) * * (6.5)  -.191 (3.3)  .595 (6.4)  .056 (3.6)  Inven.  -.23 (6.5)  -.095 (2.2)  .652 (10.)  •-.037 (1.9)  .014 (.81)  .023 .556 (1.0)  .286 •- . 2 4 7  -.019  -.014  .033  Crops  -.191  .325 (6.6) -.095  Inventories  t-statistics  in  parentheses  TABLE  D.4  O u t p u t S u p p l y and C r o s s P r i c e E l a s t i c i t i e s H o l d i n g T o t a l O u t p u t C o n s t a n t , Mean of t h e E x o g e n e o u s V a r i a b l e s , 1981 Quantity  Prices Cattle  Cattle  ,623  Inventories  , 1 27  Crops  ,827  Inventorles  Crops  -.200  -.424  .147  -.020  -.062  .889  (D.6)  = -<*.,n/j?  x  where X  is  j  the  jt-h  Efficient  symmetry  parameters  are  coefficients  are  are  are  Equation  estimating  using  Equation  imposed.  Zellner's  exhibited  These  in Table D.5.  that  c a n be  (D.5)  (SUR)  and s t a t i s t i c a l l y  indicating  (D.5)  estimated regression  Own i n p u t  significant  monotonicity  and  and  price at  the  convexity  satisfied.  measures and  of  estimated  coefficients  own p r i c e  elasticities,  elasticities  values are  with  reported  With respect elasticity  is  to  measurements  indicate  pairs.  functional  own  positive  are  input  respect  in Table  elasticities  used  to  compute  elasticities,  fixed  factor.  aggregate  and e l a s t i c .  result  is  These  output  whereas The  supply  input  cross  demand  elasticity  r e l a t i o n s h i p between  imposed  all  by t h e C o b b - D o u g l a s  form.  price  cross  output  the  inelastic  the p r e s e n t a t i o n  account  to  a complementary  This  be  cross price  prices,, and  negative  can  D.6.  To c o m p l e t e  component  and are  for  positive  reported  price  supply of  results but  "output-constant"  the Cobb-Douglas r e s u l t s ,  elasticities  effect  individual  indicate  larger  of  in Table D.7.  the a d d i t i o n a l  on t h e  These are  of  restrictions  negative  level,  These  own  estimates  derived  and  5 percent  quantity,  simultaneously  with  procedure  input  parameter  g e n e r a t e d by (D.6)  j = 4,5,6,  of  the  output  These e l a s t i c i t i e s changes  in  now  aggregate  outputs.  that  in magnitude  elasticities  for  output than  reported  supply the in  elasticities corresponding  Table  D.4.  In  241  TABLE Joint  Variable Profit  D.5  E s t i m a t i o n : Normalized Cobb-Douglas P r o f i t F u n c t i o n and Net I n p u t Demand E q u a t i o n s Parameter  Estimated  Coefficients  Function  Constant Labour  lna a. 1  Capital Materials  a  2  a  3  Begin ing Inventories  2.46 (7.4) -.059 (16.8) -.055 (16.8) -.114 (12.6) 1 .06 (39.28) .237 (3.9)  1981 = 1 1980 = 1  . 151 (2.6)  1979 = 1  -.041 (.686)  Net I n p u t Equations -.059 (13.3)  Labour Capital Mater i a l s  2  -.055 (16.8)  a  -.114 (12.6)  a  3  TABLE D.6 Own Price E l a s t i t i c i e s , Cross Price E l a s t i t i c e s , and E l a s t i t i c i e s With Respect To the Fixed Factor: Cobb-Douglas Profit Function Quantity  Price Aggregate Output  Aggregate Output  .228  Labour  Beginning Inventories  Capital  Materials  -.059  -.055  -.114  1  .02  -.055  -.114  1  .02  -.114  1  .02  -1.114  1  .02  Labour  1  .228  -1.059  Capi t a l  1  .228  -.059  Mater i a l s  1  .228  -.059  -1  .055  -.055  TABLE D.7 Total Supply E l a s t i c i t i e s : Output Component Output  Prices Cattle  Crops  —^97  ^7084  -.386  Inventories  -.049  .263  .018  Crops  -.753  .054  .927  C a  ttle  Inventories  243  addition, altered crops  accounting the  for  apparent  were  imposed a p r i o r i which  acheive  this  specified profit this  However,  by t h i s  allow  f u n c t i o n model.  Five  which  are  expectations. coefficients statistics  expectation  Table  5.6  translog  to  that  on  is  the worth  i n T a b l e D.8  own p r i c e  process, are  and c r o s s  are  is of  Five.  quite  inferior  to  structure.  To  functional  form  multi-input  variable  followed  to  in  in  Table  those  assumption noting  of  price  similar  those  price  that  the  lower  elasticities  to  Chapter  ARIMA  in Chapter  in Table D.9.  These  in  have  to the  Four.  D.8.  however,  generally  is  estimating  reported  computed s u b j e c t  presented  generally  in Chapter  and  restrictions  d e s c r i b e d in Chapter  reported  similar  p r o d u c t i o n , which are  estimates  it  than the c o r r e s p o n d i n g e s t i m a t e s  Finally, calf  based  reported  has  specification  the  flexibility a  are  quite  It  form,  The p r o c e d u r e  identical  are  of  the m u l t i - o u t p u t ,  The e s t i m a t e d p a r a m e t e r s coefficients  output  inventories  Cobb-Douglas  functional  flexibility,  is  between  because  greater  to r e p r e s e n t  model  aggregate  to complements.  obtained using a  satisfactory.  models  in  relationship  from s u b s t i t u t e s The r e s u l t s  changes  t-  Five. for  cow-  Almon  lag  Again,  these  reported  in  Table D.8 Estimated Parameters, Translog P r o f i t  Function;  Almon Lag Price Expectations Share  Cattle  Prices Cattle  Inventories  Crops  Labour  .849  -.246  -.328  -.074  (8.2)* Inventories  -.246 (7.7)  Crops  -.328 (5.2)  Labour  -.074 (4.3)  Capital  .077 (4.9)  Materials  Dummy Variables  -.279  (7.7) .299 (7.0)  (5.2) -.105  (4.3) .012  (2.3)  (2.3)  .320  .013  (2.3)  (4.8)  (1.3)  .012  .013  .021  (2.3)  (1.3)  (2.6)  -.105  -.011  -.038  -.007  (2.1)  (3.8)  (1.4)  .051  .139  .035  * t - s t a t i s t i c s i n parentheses  Capital .077 (4.9) -.011 (2.1) -.038 (3.8) -.007 (1.4) -.017 (2.9) -.003  Materials -.279 (5.9) .051  Constant  1981  1980  1979  .037  .761  .144  .002  -.145  (5.3)  (6.1)  (6.9)  (.19)  (6.9)  .016  .031  (1.0)  (1.4)  Stock  -.036  (4.3)  (3.4)  .139  .01  (5.9)  (.88)  .035 (2.1) -.003 (.29) .057  -.002  1.09 (8.1) -.578 (3.7) -.092  -.046 (2.7) -.046 (2.1) -.018  (1.7)  (3.7)  (4.7)  .002  .054  .016  (1.5)  (2.5)  (4.5)  -.011  -.235  -.05  -.009  .055  (.56)  (2.1)  .002  .02  (1.4)  (5.8)  -.003 (2.4) -.004  -.012 (3.8) .051  R  2  .6947  .6395  .4554  .6081  .5174  245 TABLE  D.9  Price E l a s t i t i c e s , Cross Price E l a s t i t i c e s Translog P r o f i t F u n c t i o n , Mean of E x o g e n e o u s V a r i a b l e s 1981, Almon P r i c e E x p e c t a t i o n s Quantity  Prices Cattle  Cattle Inventories Crops Labour Capital Materials  Inventories  Crops Labour C a p i t a l  Materials  1 .380 ,  -.028  -.604  -.211  .154  -.710  i.023  .094  -.046  -.022  -.041  .015  -1 ,.760  -.167  1 .290  .044  -.274  .851  2,.160  .280  - . 1 52 - 1 . 5 3 0  . 143  -.893  - 3 ,.220 4..110  1 .080 -.111  1 .960 -1 .680  .291  -.211  .068  -.509  .019  -1 .830  246 E.  Estimated  Parameters:  ARIMA M o d e l s  The e s t i m a t e d c o e f f i c i e n t s each a n i m a l Regina,  category  for  i n e a c h market  Saskatoon,  and  the ARIMA(2,1,0)  model  location  Edmonton,  Winnipeg)  are  (i.e., reported  in  for  this  appendix. The A R I M A ( 2 , 1 , 0 )  s p e c i f i c a t i o n can be w r i t t e n  AP. . = ch.AP. + cp-.AP. + e. ijt Ij ijt-1 2j ijt-2 ijt where A P  = is  'j $  indicates the  the  1J  •+$  first  price  jth  series  is  of  the  = 1...4,  is  a random e r r o r  reported  in Table  Except Regina,  for  all  significant  necessary  Moreso, at  in each e s t i m a t e d If  the  residuals  the p l o t s  should  each  of  for  each  for  in  the  model  the the  heifer  equation  are  statistically  10 p e r c e n t  or  95 p e r c e n t  confidence  stationarity  $i +$  5 percent  <  2  models have  are  correctly  1  level  level  is  for  of the  satisfied  independent  and  specified, identical  T h i s c o n d i t i o n can be e v a l u a t e d  and  each o b s e r v a t i o n .  for  ARIMA(2,1,0)  coefficients  the a u t o c o r r e l a t i o n  equation  condition  equation.  ARIMA  distributions.  a necessary  parameters  either  condition  in  term.  estimated  significance.  category  E.1.  the  at  animal  and  The e s t i m a t e d c o e f f i c i e n t s are  ith  location,  stationarity, ejj  j = 1 ,...,*»,  differences,  market  < 1 ,j  2j  as:  checking T a b l e E.2  function  the  of  the  statistical  reproduces  the  by  the normal  examining  residuals  significance  for of  autocorrelation  247  function for each equation along with intervals symbol  on  for  statistically  percent  confidence  each observation, which are denoted by the  both  confidence  95  sides  intervals  of  the  indicate  vertical that  axis.  each  The  large  observation  i n s i g n i f i c a n t l y different from zero.  is  TABLE E . l Estimated Parameters:  ARIMA(2,1,0)  Market Locat ion  Animal Category  Edmonton  Steers S.E.  .4027** (.165)  -.3856** ( . 1632)  .0171 ( .232)  Calves S.E.  .4333** ( . 1602)  -.5040** ( . 1631 )  -.0707 ( .228)  Cows S.E.  .3747** (.1661)  -.3814** (.1659)  -.0066 (.235)  Hei f e r s S.E.  .2731* (.1734)  -.2856* (.1727)  -.0125 (.245)  Steers S.E.  .2508* (.172)  -.2865* (.170)  -.0357 ( .242)  Calves S.E.  .4972** (.1615)  -.5361** (.1698)  -.0389 ( .234)  Cows S.E.  .2955** ( .1702)  -.3272** (.1689)  -.0317 (.239)  Hei f e r s S.E.  . 1 565 (.177)  -.2181 (.175)  -.0616 (.249)  Steers S.E.  .3313** (.1691 )  -.3289** (.1668)  .0024 (.238)  Calves S.E.  .4757** (.1579)  -.5400** (.1628)  -.0643 (.227)  Cows S.E.  .3146** (.170)  -.3450** (.1693)  -.0304 (.239)  Hei f e r s S.E.  .2823* (.1744)  -.2753* (.1730)  .007 ( .224)  Steers S.E.  .3680** (.1677)  -.3553** (.1665)  .0127 ( .236)  Calves S.E.  .2402* (.170)  -.3787** (.1738)  -.1385 ( .243)  Cows S.E.  .3282** (.1684)  -.3608** (.1681)  -.0326 ( .238)  Hei f e r s S.E.  .3508** (. 1714)  -.3206** (.1706)  .0302 (.242)  Regina  Saskatoon  Winnipeg  * **  s i g n i f i c a n t at s i g n i f i c a n t at  E s t i m a t e d Coef f i c i e n t s  »i  t h e 10 p e r c e n t l e v e l o f s i g n i f i c a n c e the 5 p e r c e n t l e v e l of s i g n i f i c a n c e  249  TABLE E.2  Edmonton M a r k e t  Plots o f the /Autocorrelation Function of the Residuals  Steers  Calves  PLOT OF AUTOCORRELATIONS -1.0  LAO t 2 3 4 3 6 7 6 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 23 26 27 28 29 30  -0.8 -0.6  -0.0T2 -0.126 0.0S3 -0.223 -0.003 0. 180 -0.036 0.052 0.007 0.020 0.009 O.OSI -0.048 -0.020 -0.038 -0.019 -0.034 -0.003 -0.074 0.063 0.011 0.001 0.033 -0.104 -0.133 -0.047 -0. 126 0.215 -0.026 •0.063  PLOT OF AUTOCORRELATIONS -0.4 -0.2  0.0  I XXI xxxi IX XXXXXXI I ixxxx XI IX I I I IX XI XI XI i XI I XXI IXX I I IX xxxi XXXI XI XXXI IXXXXX XI XXI  • •  4 4 •  4 * * * • • • •  * * •  * *  * 4 * •  0.4  0.2 •  • • • •  4 • • •  fr 4 • •  4 • • •  4 .  •  4 4 •  4 4 4 •  4 4  Cows  1 2 3 4 9 6 7 8 9 10 11 12 13 14 IS 16 IT 18 19 20 21 22 23 34 35 26 27 28 29 30  1 2 3 4 5 6 7 8 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 23 26 27 28 29 30  -1.0 -0.6 -0.6 -0.4 -0.032 -0.153 0.044 -0.157 -0.114 0. 136 0.060 -0.029 0.028 0. 1 14 -0.033 0.053 0.001 -0.073 -0.016 -0.006 -0.108 0.085 -0.089 0.019 0.073 0.047 •0.O99 -0.091 0.032 -0.137 -0.099 0. 192 -0.103 -0.026  -0 2  4 4 4 4 •  4 4 4 4 •  4 4 4 4 4 4 4 4 4 4 4 4 •  4 4 4 4 4 4 4  0.0  0.2  I XI XXXXI IX XXXXI XXXI IXXX • IX XI IX IXXX XI IX 1 XXI 1 I XXXI IXX XXI I IXX IX XXI XXI IX XXXI XXI IXXXXX XXXI XI  0.  * 4 4 * * 4 • •  4 4 4 4  fr 4 4 4 4  Hei f e r s  PLOT OF AUTOCORRELATIONS LAG  LAO  -1.0 -0.8  PLOT OF AUTOCORRELATIONS  -0.6 - 0 . 4  - 0.2  0.0  0.2  0.' LAG  -0. 040 -0. 144 0. 039 -0. 201 -0. 141 0. 202 0. 038 -0. O i l -0. 008 0. 092 -0. 058 0. 097 -0. 008 -0 129 0. 058 -0. 051 -o 094 0 081 -0 054 0 032 -0 003 0 147 -0 103 -0 130 -0 035 -0 148 -0 086 0 222 -0 029 -0 026  • •  4 4 4 4 • •  4 4 4 4 4 4  •  • •  4 4 •  4 4 4 4 •  4 4 4 4  I 4 XI • XXXXI • IX 4 XXXXXI XXXXI 4 4 ixxxxx IX * 4 I 4 I • ixx 4 XI 4 IXX 4 I 4 XXXI 4 IX • XI XXI * IXX 4 4 XI 4 IX 4 I 4 ixxxx 4 XXXI 4 XXXI • XI • XXXXI 4 XXI 4 IXXXXXX XI XI  1 2 3 4 5 6 7 a 9 10 11 12 13 14 IS 16 17 18 19 20 2 1 22 23 34 23 26 27 28 29 30  -1.0 -0.8 -0.6 -0.4 -0.069 -0.086 -0.056 -0.179 -0.07 1 0. 182 -0.023 0.030 0.021 0.029 -0.002 0.054 -0.023 -0.077 -0.021 -0.013 -O.TJIJ -0.030 -0.036 0.054 0.012 0.035 -0.035 -0.091 -0.076 -0.079 -0.086 0.236 -0.031 -0.021  -0 2  4 •  4 4 4 4 4 4 4 4 •  4 4 4 4 4 4 4 4 4 4 4 •  4 4  •  4 4 4  0.0  0.2  0  4 XXI 4 XXI • XI 4 XXXXI 4 XXI 4 IXXXXX XI 4 IX • IX IX 1 IX • XI XXI • XI 1 I XI XI 4 • IX I IX • XI • XXI XXI XXI • XXI • IXXXXXX XI XI  fr fr fr fr fr fr fr fr fr fr fr fr  TABLE E.2 (cont.) Plots of the Autocorrelation Function of the Residuals  Saskatoon Market Steers  Calves  PLOT OF AUTOCORRELATIONS LAC 1 3 3 4 S 6 7 S 9 10 11 12 13 14 13 16 17 18 19 20 21 22 23 24 33 26 27 28 39 SO  PLOT OF AUTOCORRELATIONS  -1.0 -0.8 -0.6 -0.4 -0.2 -0.033 -0.140 0.083 -0.268 0.021 0. 176 -0.034 0.073 -O.OIS 0.016 0.005 0.043 -0.035 -0.034 -0.031 -0.031 -0.007 -0.043 -0.035 O.OSO -0.021 0.026 0.036 -0.142 -0.038 -0.119 •0.094 0. 183 0.002 •0.068  •  •  0.0  0.2  I XI XXXXI IXX XXXXXXXI IX 1XXXX XI IXX I I I IX XI XI XI XI I XI XI IX XI IX IX XXXXI XI XXXI XXI IXXXXX 1 XXI  4 4  4 •  4 •  4 4 4 •  4  * 4 •  4 •  4 4 •  4 4 4 4 4 4 4  0.4 LAG •  4 4 4  . 4 4 4 *  • •  4 4 4 4 4 4 4 4 4 4  .  4 4 4 4 4 4 4 4  Cows  1 2 3 4 3 6 7  a  9  to  11 12 13 14 IS 16 17 18 19 20 21 22 23 24 23 26 27 28 29 30  I  4 XI 4 XXXXXI 4 IXXX 4 XXXXXI 4 XXI 4 IXXX 4 IXX 4 XXI 4 I XX 4 I XX 4 XI ,•  4 4 4 4 4 4 4 •  4 4 4 4 4 4 4 4 4 4  0.4  0.2 • •  •  • * • • •  •  •  IX I XXI XI I xxt IX xt IX IX IX xxt XXXXI I XX XXXXI XXI IXXXX XI XI  •  • • • • • • •  * • •  •  •  •  PLOT OF AUTOCORRELATIONS  -1.0 -0.8 -0.6 -0.4 -0.2 CORR. 44 4 4 4 -O.OSO -0.131 0.027 -0.240 -0.091 0. 191 0.033 0.002 0.001 0.034 0.006 0.034 -0.003 -0.103 0.055 -0.039 -0.065 0.017 -0.022 0.037 -0.038 0. ISO -0.078 -0.133 •0.038 -0.160 -0.065 O. 188 -0.034 0.008  -0.033 -0. 190 0. 123 -0.206 -0.O63 0. 1 16 0.076 -0.073 0.063 0.063 -0.032 0.033 0.011 -0.068 -0.027 0.006 -0.092 0.053 -0.031 0.023 0.044 0.022 -0.069 -0.131 0.092 -0.173 -0.086 0. 148 -0.043 -0.027  0.0  Hei fers  PLOT OF AUTOCORRELATIONS LAO  1 2 3 4 5 6 7 8 9 10 11 12 13 14 13 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  -1.0 -0.8 -0.6 -0.4 • 0.2  0.0 0.2 0.4 4 -4 I 4 4 XI 4 4 XXXI • 4 IX • XXXXXXI • 4 XXI 4 4 IXXXXX 4 4 IX 4 4 I 4 4 I 4 IX 4 4 4 I 4 4 IX 4 4 I 4 4 XXXI 4 4 IX 4 4 XI 4 4 XXI 4 4 I 4 4 XI 4 4 IX 4 4 XI  4 4  •  4 4 4  . 4 4  ixxxxx  XXI XXXI XI XXXXI XXI IXXXXX XI I  4 4 4 4 4 4 4 4 4  LAO 1 2 3 4 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  • -1.0 -0.8 -0.6 -0.4 -0.2 -0.042 -0.116 0.046 -0.263. -0.O49 0. 161 -0.021 0.058 -0.016 0.040 -0.009 0.047 -0.011 -0.075 -0.025 0.022 -0.063 0.008 0.012 -0.014 0.028 0.052  -o.oao  -0.089 -0.035 -0.147 -O.0S7 0. 193 -0.022 -0.013  0.0  0.2  I XI XXXI IX •XXXXXXXI XI 4 . 4 IXXXX 4 XI 4 IX 4 1 4 IX 4 I 4 IX 4 I 4 XXI 4 XI 4 IX XXI 4 • I 1 4 1 4 4 IX 4 IX xxt 4 XXI 4 4 XI XXXXI 4 4 XI • IXXXXX 4 XI 4 1  4 4 4  0.  4 4 •  4 4 •  * 4 4 4 4 4 4 4 4 4 4 4 4 4 4 •  •  4 4 *  251  TABLE E.2 (cont.) Plots of the Autocorrelation Function of the Residuals Regina Market Steers  Calves  PLOT OF AUTOCORRELATIONS LAO 1 2 3 4 9 6 7 6 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 2S 26 27 28 29 30  PLOT OF AUTOCORRELATIONS  -1.0 .-0.8 -0.6 -0.4 -0. 3  0.0  0.4  0.3  LAO -0.057 -0. 113 0.031 -0.276 0.072 0. 124 0.007 0.055 -0.009 0.006 -0.020 0.054 -0.036 -0.036 -0.033 -0.013 -0.030 -0.032 -0.035 0.044 -0.005 0.013 0.051 -0. 138 •0.063 -0.101 -0. 11S 0.305 -0.013 •0.054  1 • XI * XXXI • IX •XXXXXXXI • IXX • IXXX • I • IX • I • 1 • XI IX XI • XI • XI I • XI • XI • XI • IX I • I • IX • xxxi XXI 4 XXXI 4 XXXI • IXXXXX 4 I 4 XI  • • • • • • • • •  4 • • • • • • • •  4 •  •  4  •  • • •  Cows  1 2 3 4 5 6 7 6 9 10 11 12 13 14 IS 16 17 18 19 30 21 32 23 24 35 26 27 28 29 30  • • • •  * •  4 4 * 4 • • •  * 4 • • • • •  • •  0.0  0.3  0.4  I XXI XXI XI XXXI I IX IXXX xxt IXX IX I I I xxt XI I XXI IX XXI IX I IX XI XXXXI IXXX XXXXXXI XI IXX I XI  PLOT OF AUTOCORRELATIONS  -1.0 -0.8 -0.6 -0.4 -0.3 CORR. • • • • • -0.056 -0.098 -0.020 -0.219 -0.055 0. 108 0.061 0.010 -0.022 0.058 0.007 0.050 0.013 -0.139 0.036 -0.027 -0.076 0.040 -0.039 0.056 •0.024 0. 116 -0.005 -0.184 -0.031 -0.128 -0.133 0.255 -0.034 0.005  -0.083 -0.066 -0.031 -0.117 -0.001 0.053 0. 108 -0.088 0.062 0.035 0.018 0.000 0.010 -0.061 -0.021 -0.015 -0.065 0.047 -0.068 0.049 0.012 0.022 -0.042 -0.170 0. 101 -0.227 -0.025 0.071 0.017 -0.043  -0.2  Heifers  PLOT OF AUTOCORRELATIONS LAG  1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 39 30  -1.0 -0.8 -0.6 -0.4  4 4 •  4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4> 4 4 4 4 4 4 4 4 4 4  0.0 0.2 0.4 » 1 4 XI 4 XXI • XI 4 XXXXXI 4 XI 4 IXXX 4 IXX 4 1 4 XI 4 IX 4 I 4 IX 4 I 4 XXXI 4 IX 4 XI 4 XXI 4 IX 4 XI 4 IX • XI 4 IXXX 4 I 4 XXXXXI 4 XI 4 XXXI 4 XXXI 4 IXXXXXX XI 4 4 I  LAG 1 2 3 4 3 6 7 8 9 to 11 13 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  -1.0 -0.8 -0.6 -0.4 -0. 2 -0.044 -0. 103 0.000 •0.394 -0.011 0. 141 0.004 0.047 -0.036 0.062 -0.010 0.036 -0.014 -0.051 -0.022 -0.027 -0.029 -0.018 -0.028 0.069 0.014 0.042 0.002 -0.137 -0.044 •0.086 -0.093 0. 187 -0.009 -0.044  0.0  I XI XXXI I •XXXXXXXI 4 1 • IXXXX 4 1 4 IX 4 XI 4 IXX 4 I 4 IX 4 I • XI 4 XI XI 4 4 XI 4 1 4 XI IXX *4 1 4 IX 4 1 4 XXXI 4 X! 4 XXI 4 XXI IXXXXX 4 4 I 4 XI  4 4 4  0 .4  0.3  4 4  •  4  4 4 4 4 •  4  252  TABLE E.2 (cont.) P l o t s o f the /Autocorrelation Function of the Residuals  Winnipeg Market Steers  Calves  PLOT OF  PLOT OF  -1.0 -0.8 -0.6 -0.4 -0.2  LAG 1 2 3  4 S 6 7 8 a  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  AUTOCORRELATIONS  -0.050 -0.151 0.082 -0.220 -0.070 0.216 -0.013 0.045 -0.019 0.044 0.017 0.030 -0.022 -0.032 -0.023 -0.035 -0.022 -0.023 -0.031 0.034 -0.032 0.083 -0.002 -O. 140 -0.023 -0.108 -0.136 0. 193 -0.019 -0.061  0.0  0.4  0.2  I XI XXXXI 4 IXX 4 XXXXXXI 4 XXI 4 IXXXXX 4 I • IX • I 4 IX 4 I 4 IX 4 XI • XI 4 XI 4 XI 4 XI 4 XI 4 XI 4 IX 4 XI • IXX • 1 XXXI * XI XXXI xxxi * IXXXXX • I • XXI •  4  *  •  •  4 4 4 • •  4 4 4  4 4 4  4 4 4 4 4 4 4 4  4 4  4 4 .4 4  LAO 1 2 3 4 3 6 7 8 9 10 « 1 12 13 14 15 16 17 18 19 20 21 22 23 24 23 26 27 28 29 30  -0.034 -0.114 -0.047 -0.171 -0.144 0. 137 0.031 0.029 -0.032 0.110 0.005 0.021 0.013 -0.058 -0.032 -0.040 -0.033 0.019 -0.053 0.011 0.099 0.033 -0.019 -0.079 -0.046 -0.059 -0. 170 0. 170 -0.002 -0.035  -0.4 -0.2 •  4 4 4 4 4 4 4 4 4 4 4 4 4 •  4 4 4 4 4 4 4 4 4 •  4 4 4 4 4  0.0  0.4  0.2  1 XI XXXI XI XXXXI XXXXI IXXX IX IX XI IXXX 1 IX 1 XI XI XI XI 1 XI 1 IXX IX 1 XXI XI XI XXXXI IXXXX 1 XI  • •  4 4 4 4 4 4  *  4  * 4 4 4 4 * »  4 •  4 4 4 • •  * 4 4 4 4  Heifers  Cows PLOT OF  -1.0 -0.8 -0.6  LAG 1 2 3 4 5 6 7 a 9 10 11 12 13 14 IS 16 17 18 19 20 21 22 23 24 29 26 27 28 29 30  AUTOCORRELATIONS  PLOT OF  AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 - 0.2  -0.036 -0. 113 -0.009 -0.163 -0. 113 0. 165 0.056 -0.016 -0.011 0.068 0.003 0.054 0.004 -0.109 0.037 -0.033 -0.093 0.054 -0.059 0.043 -0.008 0. 146 -0.062 •0.126 -0.053 -0.139 -0.107 0.222 -0.039 -0.009  4 4 4 4 4 4 4 4 4 •  4 4 4 4 4 4 •  4 4 4 4 4 4 4 4 4 4 4 4  0.0  fl  0.2  1 XI XXXI I XXXXI XXXI IXXXX IX I I IXX I IX I XXXI IX XI XXI IX XI IX I IXXXX XXI XXXI XI xxxi XXXI IXXXXXX XI I  0.4  4 4 4 4 4 4 •  4 4 4  4 4 4 •  4 * •  4 *.  4 4 4 4 4 4 4 4 4 4  LAG 1 2 3 4 3 6 7 8 9 10 11 12 13 14 13 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  AUTOCORRELATIONS -1.0 -0.8 -0.6 -0.4 - 0.2  -0.058 -0.110 0.007 -0.197 -O.095 0. 193 -0.021 0.066 -0.033 0.040 ' 0.015 0.034 -0.025 -0.022 -0.036 -0.028 -0.031 -0.011 -0.041 0.061 0.021 0.046 -0.033 -0.103 -0.051 -0. 109 -0.096 0.213 -0.036 -0.020  4 4 4  *  4 4 4 4 4  4  * 4  4 4 4 •  + •  4 4 4 4 •  4 4 4 4 4 4 4  0.0  0.2  I XI xxxi I XXXXXI XXI IXXXXX XI IXX XI IX I IX XI XI XI XI XI I XI IXX IX IX XI XXXI XI XXXI XXI IXXXXX XI XI  0 •  4  4 4  4 4 4  4 4 *  4  *4  4 4 4  4 4 4 4 •  4  •  4 4  •  F. Year 1981  1980  1979  1978  Price Predictions: Soil Zone 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14  ARIMA Models  Steer 77.49 77.49 77.49 78.44 79.40 78.44 78.55 78.44 78.55 77.49 79.40 75.36 75.36 75.36 64.35 64.35 64.35 67.35 66.46 67.35 66.24 67.35 66.24 64.35 66.46 65.88 65.88 65.88 91.19 91.19 91.19 93.05 93.39 93.05 91.82 93.05 91.82 91.19 93.39 89.21 89.21 89.21 74.77 74.77 74.77 75.89 70.04 75.89 70.91 75.89 70.91 74.77 70.04 67.73 67.73 67.73  Calf 76.31 76.31 76.31 74.20 70.21 74.20 7 5 . 12 74.20 7 5 . 12 76.31 70.21 76.36 76.36 76.36 67.72 67.72 67.72 71 . 3 9 74.31 71 . 3 9 68.34 71 . 3 9 68.34 67.72 74.31 68. 1 1 68. 1 1 68. 1 1 106.31 106.31 106.31 99.81 96.97 99.81 102.29 99.81 102.29 106.31 96.97 106.44 106.44 106.44 86.82 86.82 86.82 98.32 101.80 98.32 94.86 98.32 94.86 86.82 101.80 64.70 64.70 64.70  Hei f e r  Cow  71 . 5 0 71 . 5 0 71.50 75.26 73.26 75.26 73.04 75.26 73.04 71 . 5 0 73.26 69.53 69.53 69.53 59.83 59.83 59.83 62.80 6 2 . 13 62.80 61 . 5 5 62.80 61.55 59.83 62.13 58.76 58.76 58.76 9 0 . 17 9 0 . 17 9 0 . 17 90.75 87.62 90.75 87.23 90.75 87.23 90. 1 7 87.62 83.74 83.74 83.74 6 2 . 15 6 2 . 15 6 2 . 15 65.44 60.36 65.44 63.50 65.44 63.50 6 2 . 15 60.36 60.57 60.57 60.57  46.56 46.56 46.56 49.77 46.53 49.77 48.98 49.77 48.98 46.56 46.53 48.55 48.55 48.55 43.06 43.06 43.06 4 3 . 14 42.40 43.14 45.06 4 3 . 14 45.06 43.06 42.40 44.35 44.35 44.35 5 6 . 19 5 6 . 19 5 6 . 19 58.80 54.62 58.80 55.84 58.80 55.84 5 6 . 19 54.62 57.09 57.09 57.09 43.82 43.82 43.82 44.63 41 . 8 8 44.63 44.58 44.63 44.58 43.82 41 . 8 8 44.01 44.01 44.01  

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