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A measurement of the effect of technical change on the productivity of the Canadian agricultural sector… Carby-Samuels, Horace Raymond 1962

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A MEASUREMENT OF THE EFFECT OF TECHNICAL CHANGE ON THE PRODUCTIVITY OF THE CANADIAN AGRICULTURAL SECTOR:  1926-58  by  HORACE RAYMOND CARBI-SAMUELS B.S.A., U n i v e r s i t y o f Toronto, I960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AGRICULTURE  i n t h e Department of AGRICULTURAL ECONOMICS  We a c c e p t t h i s t h e s i s as conforming t o t h e r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA October, 1962  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study.  I further agree that permission  for extensive copying of this thesis for scholarly purposes may  be  granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for f i n a n c i a l gain shall not be allowed without my written permission.  Department of The University of B r i t i s h Columbia, Vancouver 8, Canada. Date  ABSTRACT This study i s designed to measure the amount, and character of the change i n the economic performance of the agricultural sector of the Canadian economy, over the period 1926 to 1958. The major hypothesis which i t examines i s that changes i n technology have had a positive effect on the productivity of factors used i n the agricultural sector of the Canadian economy. Technological change i s defined herein as any change which produces a shift i n the production function of the industry, and the concept of the relative shares going to each factor of production has been used to determine the shape of the aggregate production function. In the agricultural industry natural phenomenon such as weather, which are outside the control of management, are capable of causing significant variations i n annual output.  These fluctuations  in output make i t d i f f i c u l t to determine the permanent effects of technological change on input-output ratios.  However, the analysis  assumes that farmers take into account the possible effects of weather i n their decision-making processes, and also assumes that the effects of variations from this source w i l l be randomly distributed over the 33 year period of the study. The production functions were determined by f i r s t assuming that Euler s Theorem holds for the agricultural industry. 1  The relative  shares of each factor i n total inputs were then used as the estimates of the relative share of each factor i n total output.  By this method  the shape of the aggregate production function was determined with a minimum of distortions which may be due to the effects of exogeneous variables.  The d e t e r m i n i n g o f t h e aggregate p r o d u c t i o n f u n c t i o n s i n t h e manner used i s f e a s i b l e because o f t h e h i g h degree  o f c o m p e t i t i o n i n the  a g r i c u l t u r a l i n d u s t r y , w h i c h c o n t r i b u t e s t o a much l o w e r l e v e l o f p r o d u c t o r p r o c e s s d i f f e r e n t i a t i o n t h a n t h a t which e x i s t s i n o t h e r i n d u s t r i e s . The problems o f a g g r e g a t i o n o f p r o d u c t s a r e t h e r e f o r e i n t h i s  case  minimized. The l e v e l o f aggregate  output was determined by e x p r e s s i n g  as an i n d e x the v a l u e s e r i e s which was o b t a i n e d by d e f l a t i n g t h e t o t a l v a l u e o f each type o f p r o d u c t by an a p p r o p r i a t e p r i c e i n d e x which had a 1935-39 base.  The annual d e f l a t e d v a l u e s were aggregated;  and t h i s  output s e r i e s was t h e n e x p r e s s e d i n terms o f i t s v a l u e as a t 1926 b e i n g made e q u a l t o 100.  These i n d i c e s o f d e f l a t e d d o l l a r v a l u e s were u s e d  i n t h e p r o d u c t i o n f u n c t i o n as e s t i m a t e s o f t h e p h y s i c a l q u a n t i t y o f the output f o r t h a t p a r t i c u l a r y e a r . determine  A s i m i l a r p r o c e s s wa.s u s e d t o  t h e q u a n t i t y o f each p a r t i c u l a r f a c t o r i n p u t which was  i n c l u d e d i n the production f u n c t i o n .  The q u a n t i t y o f aggregate i n p u t s ,  however, was determined by a g e o m e t r i c a g g r e g a t i o n o f t h e i n d i c e s o f the f a c t o r i n p u t s . weighted  I n t h i s aggregate  t h e q u a n t i t y o f each f a c t o r was  by i t s r e l a t i v e share i n t h e aggregate i n p u t (hence  under t h e assumptions  output  o f the a n a l y s i s ) .  T h i s method o f geometric a g g r e g a t i o n o f i n p u t s g i v e s due r e c o g n i t i o n o f the f a c t t h a t changing m a r g i n a l r a t e s o f s u b s t i t u t i o n o f f a c t o r i n p u t s a r e p o s s i b l e i n the a g r i c u l t u r a l i n d u s t r y , and t h a t a t d i f f e r e n t l e v e l s o f output farmers may e f f e c t a change i n t h e m a r g i n a l r a t e s o f s u b s t i t u t i o n o f f a c t o r s without n e c e s s a r i l y producing a s h i f t o f the p r o d u c t i o n f u n c t i o n on which t h e y a r e o p e r a t i n g .  iv.  The d a t a f o r t h e a n a l y s i s were o b t a i n e d from D.B.S. m a t e r i a l , and t h e changes i n t h e o u t p u t - i n p u t r a t i o s were examined i n a model o f comparative  statics.  Hhen t h i s was done, i t was f o u n d t h a t when c a p i t a l  was measured i n c l u s i v e o f r e a l e s t a t e and o t h e r improvements t h e n e t change i n o v e r - a l l p r o d u c t i v i t y f o r the e n t i r e p e r i o d (1926-58), was not s u b s t a n t i a l l y d i f f e r e n t from t h a t which was c a l c u l a t e d when c a p i t a l was measured n e t o f the v a l u e o f t h e s e f a c t o r s .  Between 1926 and 1958,  the n e t change i n o v e r - a l l p r o d u c t i v i t y was 33 p e r c e n t when c a p i t a l was measured i n c l u s i v e o f r e a l e s t a t e , and 31 p e r cent when t h e v a l u e of  r e a l e s t a t e was removed.  Approximately  90 p e r cent o f t h i s  i n c r e a s e had been r e c o r d e d between t h e y e a r s 1946 and 1958.  observed  Over t h e  p e r i o d 1950 t o 1956 t h e d i f f e r e n c e i n the c a l c u l a t e d measure o f o v e r a l l p r o d u c t i v i t y from each method showed, however, d i f f e r e n c e s o f between 3 and 6 percentage  p o i n t s when compared t o t h e more f r e q u e n t l y  found d i f f e r e n c e o f 2 percentage  p o i n t s i n f a v o u r o f p r o d u c t i v i t y when  i t was d e r i v e d from d a t a which i n c l u d e d the value o f r e a l e s t a t e . T e c h n o l o g i c a l change between 1926 and 1958 has been a s s o c i a t e d w i t h an e s t i m a t e d d e c l i n e o f 28 p e r cent i n t h e q u a n t i t y of  l a b o u r i n use, a 15 p e r cent i n c r e a s e i n t h e q u a n t i t y o f t o t a l  c a p i t a l as compared w i t h a 4-3 p e r cent i n c r e a s e i n t he q u a n t i t y o f non r e a l e s t a t e c a p i t a l , and a 115 p e r cent i n c r e a s e i n t h e q u a n t i t y o f annual non-labour  expenses.  These expenses a r e c h i e f l y a s s o c i a t e d w i t h  the use o f farm machinery and t o a l e s s e r e x t e n t w i t h t h a t o f f e r t i l i z e r . Feed and seed were o m i t t e d from the c a l c u l a t i o n s i n o r d e r t o a v o i d the problems o f double  counting.  V.  The results of the analysis substantiate the main hypothesis of this study, i n that technological change has a positive effect on the productivity of factors used i n the agricultural sector of the Canadian economy.  ACKNOWLEDGEMENT  The writer takes this opportunity of acknowledging the assistance i n the preparation and presentation of this thesis, which was given by Professor W.J. Anderson of the Department of Agricultural Economics at the University of British Columbia} and also the advice, and assistance, which was given by Professors A.D. Scott, and J.J. RLchter, of the Department of Economics and Political Science, and the Department of Agricultural Economics, respectively.  L I S T OF TABLES TABLE I II  III  IV  V  VI  VII  VIII  IX  X  PAGE Factor  Shares, Canadian A g r i c u l t u r e , 1926-58  34-  I n d i c e s ; Output and Grouped I n p u t s , Canadian A g r i c u l t u r e , 1926-58; 1926 = 100  37  Percentage Annual C u r r e n t Non-Labour Costs from V a r i o u s S o u r c e s , S e l e c t e d Y e a r s , Canada, 1926-56 .  38  I n d i c e s ; Output, Composite Input, Composite and P a r t i c u l a r Output-Input R a t i o s , Canadian A g r i c u l t u r e , 1926-58; 1926 = 100  42  F a c t o r Shares, Net o f Land, Canadian Primary A g r i c u l t u r a l S e c t o r , 1926-58  4-7  I n d i c e s ; Output, Composite Input, Composite and P a r t i c u l a r Output-Input R a t i o s , Net o f Land, Canadian A g r i c u l t u r e , 1926-58; 1926 = 100 . . . .  4-9  R e l a t i v e s ; M a r g i n a l P h y s i c a l , and V a l u e Product o f F a c t o r I n p u t s , Canadian A g r i c u l t u r e , 1926-58; 1926 = 100 . . .  53  I n d i c e s ; Output-Input R a t i o s , A d d i t i o n a l S e l e c t e d Methods, Canadian A g r i c u l t u r e , 1926-58; 1926 = 100  76  Summary I n d i c e s ; Gross Output-Input R e l a t i o n s h i p s ; V a r i o u s S e l e c t e d Methods; Canadian A g r i c u l t u r e , 1926-58; 1926 = 100  77  R e l a t i v e Changes, M.P.P. F a c t o r Inputs, Canadian A g r i c u l t u r e , 1926-58; 1926 = 100  78  TABLE OF CONTENTS CHAPTER I  PAGE OBJECTIVES OF THE STUDY  1  The Concept of Technology II  2  REVIEW OF LITERATURE  6  The Joan Robinson Model  10 H  The Solow Model Points to Note i n the Solow Model The Urquhart Model  18  The Pasinetti Model  20  Studies Done on the Canadian Economy III  IV  17  .....  22  THE ANALYTICAL FRAMEWORK OF THE STUDY  26  Inputs  29  Output  30  The Production Function . . . . .  31  RESULTS OF THE STUDY  32  Measuring Technological Change Inclusive of Land Capital  32  Output-Input Relationships Inclusive of Land  .  39  Measuring Technological Change When Land i s  1<A  Excluded Output-Input Relationships Net of Land  ....  46  An Evaluation of the Two Methods  50  Summary  54  BIBLIOGRAPHY APPENDIX  .  56 61  I  OBJECTIVES OF THE S T U D Y  This study i s aimed at measuring the effects of technological change on the output-input relationships of the primary agricultural sector over the 33-year period of 1926 to 1953. It seeks to measure the extent of the changes which have been due to advances i n the ability of the Canadian farm sector to convert input into output by analyzing the changes which have occurred in factor-factor and factorproduct relationships. An estimate of the amount of change which has been due to technology facilitates a better evaluation of the use that the agricultural industry has made of that portion of society's resources which have been associated with i t s productive activities.  In making  policy decisions affecting the future allocation of resources, a knowledge of the past performance of the agricultural industry furnishes a better guide for future decision-making. The hypothesis is that technological change has had a positive effect on the productivity of the factors used in primary agriculture. Various theoretical models for measuring technological change may be found in economic literature. Many of these models are designed to meet particular objectives such as to make measurements for the whole economy or for a particular firm. The data used in this study, and the objectives, required the modification of the available models, which are analyzed later i n this study. Although change i s a dynamic process in dealing with which dynamic theory i s needed, the results of change may be viewed, however, in term3 of static analysis. Samuelson has also pointed out that "... i n order for the comparative statics analysis to yield fruitful  2. r e s u l t s we must f i r s t d e v e l o p a t h e o r y o f dynamics".^  I n t L i s study a  model o f comparative s t a t i c s i s u s e d w i t h t h e assumption t h a t t h e p r i m a r y a g r i c u l t u r a l s e c t o r a d j u s t s each y e a r i n t h e l i g h t o f p a s t e x p e r i e n c e and f u t u r e e x p e c t a t i o n s .  The i n p u t - o u t p u t  data f o r the  a g r i c u l t u r a l s e c t o r a r e a l s o c o l l e c t e d and compiled on a n annual b a s i s . 5br t h e s e r e a s o n s t e c h n o l o g i c a l change w i l l be measured from one y e a r t o the next.  The  Concept o f Technology I n t h i s s t u d y t e c h n o l o g i c a l change has been d e f i n e d as any  change which makes t h e a d o p t i o n o f a new p r o d u c t i o n economically  feasible.  T h i s means (a) t h e e s t a b l i s h m e n t  e q u i l i b r i u m p o s i t i o n a t a p o i n t on a t r a n s f o r m a t i o n economically  function o f an  curve n o t  f e a s i b l e under p r e v i o u s l y e x i s t i n g c o n d i t i o n s , o r (b) a  change i n t h e p o s i t i o n o r t h e shape o f t h e t r a n s f o r m a t i o n These s h i f t s o f t h e p r o d u c t i o n transformation  function.  function o r of the  f u n c t i o n a r e d i s t i n g u i s h e d from changes i n f a c t o r  combinations which a r e a s s o c i a t e d w i t h d i m i n i s h i n g m a r g i n a l p r o d u c t i v i t y as o u t p u t i s i n c r e a s e d .  These changes are e f f e c t e d a s a r e s u l t o f  p r o d u c e r d e c i s i o n s t o s u b s t i t u t e those i n p u t s which have a l a r g e r marginal product a t a given marginal product-cost  ratio.  c o s t f o r t h o s e which have a  smaller  They may a l s o be i n d u c e d as t h e r e s u l t o f  physical scarcities of certain factors.  The new e q u i l i b r i u m p o s i t i o n  may a l s o produce a p h y s i c a l s a v i n g o f f a c t o r s . S h i f t s i n the transformation its  f u n c t i o n as w e l l a s changes i n  shape cause changes i n the m a r g i n a l r a t e s o f s u b s t i t u t i o n o f  ^ P.A. Samuelson, Foundations o f Economic A n a l y s i s , U n i v e r s i t y P r e s s , 1955), pp. 262-63.  (Cambridge:  Harvard  3. factors.  These shifts also cause changes i n the shape and position of  the cost functions.  Some of these cost effects are due to changes i n the  relative scarcity of factor inputs, while other effects may be due to changes i n scale.  One such scale effect for example, i s a shift i n the  transformation function which encourages the development of large-scale production, and this may enable these enlarged farm-firms to purchase more efficient machinery from the non-farm sector.  At the same time a  change i n the relative scarcity of factors also results  from the reduced  demand for certain factors as the number of firms are reduced.  The  adoption of new production methods may also increase the demand for the products of the farm machinery industry without necessarily encouraging large-scale farming.  Having more efficient machinery available tends to  free labour time which may be utilized i n complementary enterprises, or i n shorter hours of work, or which may be transferred to non-farm enterprises. These changes i n technology may be induced by innovations which have been developed directly within the sector, as well as by those improvements i n the factors of production such as machines, which are purchased from other sectors.  Because of the small size of firms, the  research for primary agriculture i s paid for out of public funds.  This  basis for research eliminates patents and other practices which restrict the use of the results of research to certain firms.  Thus the results  of research tend to be quickly adopted by the entire farm sector through the process of  competition.  Heady discusses technological innovations i n the following terms: In a purely physical and firm sense i t i s possible for an innovation to be either factor-saving, factor-using, or output-increasing. The change may also combine factorusing or factor-saving features with output-increasing features ....  While the n o t i o n o f i n n o v a t i o n s which are s i n g u l a r l y f a c t o r - u s i n g may seem a b i t f a r f e t c h e d , t h e r e i s no r e a s o n why t h i s s h o u l d be so . . . . D i s t i n c t i o n between t e c h n o l o g i c a l improvements which are o u t p u t - i n c r e a s i n g and those w h i c h are f a c t o r - s a v i n g may a p p l y t o an i n d i v i d u a l i n d u s t r y o r f i r m but do not e x i s t s i m i l a r l y on an economy-wide b a s i s . The b a s i c n a t u r e o f t e c h n o l o g i c a l improvement i s always the same i n the economy as a whole. Aside from the u n c e r t a i n t y e x c e p t i o n n o t e d elsewhere, a l l t e c h n o l o g i c a l improvements are o u t p u t i n c r e a s i n g f o r given resources, or conversely, inputd e c r e a s i n g f o r a g i v e n o u t p u t . An i n n o v a t i o n i s always o u t p u t - i n c r e a s i n g i n the aggregate s i n c e a l t h o u g h i t may r e s u l t i n the same output from a s m a l l e r r e s o u r c e i n p u t by a given f i r m o r i n d u s t r y , i t f r e e s resources f o r output e x p a n s i o n i n o t h e r i n d u s t r i e s . In t h i s sense a l l i n n o v a t i o n s are l i k e l y t o extend economic p r o g r e s s r e g a r d l e s s o f the i n d u s t r y t o which t h e y a p p l y . The g r e a t e s t p o r t i o n o f t e c h n i c a l i n n o v a t i o n s i n a g r i c u l t u r e have been o f an o u t p u t - i n c r e a s i n g n a t u r e t o the e x t e n t t h a t t h e y have lowered the average p e r u n i t c o s t o f p r o d u c i n g farm p r o d u c t s and o f a f a c t o r u s i n g n a t u r e i n the sense t h a t the lovrer m a r g i n a l c o s t s have caused farm f i r m s t o employ more r e s o u r c e s (and a l s o t o i n c r e a s e o u t p u t f o r the l a t t e r r e a s o n ) . Changes i n t e c h n o l o g y w i l l n o t o n l y s h i f t i s o - p r o d u c t toward t h e o r i g i n but w i l l p o s s i b l y a l s o change t h e i r shape. shift will shift  a l l isoquants  i n the same p r o p o r t i o n , w h i l e  n e u t r a l s h i f t w i l l change b o t h the p o s i t i o n and the shape o f  curves  A neutral a  non-  the  isoquants. The  concept o f t e c h n o l o g i c a l change which w i l l be u s e d i n  •a t h i s a n a l y s i s i s e s s e n t i a l l y Schumpeterian.  J  In the  Schumpeterian  system an i n n o v a t i o n i n c o n t r a s t t o a f a c t o r adjustment i s r e g a r d e d S.O. Heady, The Economics o f A g r i c u l t u r a l P r o d u c t i o n and Resource (Inglewood C l i f f s , New J e r s e y : P r e n t i c e H a l l , 1952) pp. 803-04.  Use.  3 F o r a d i s c u s s i o n o f the Schumpeterian System see R i c h a r d V. Clemmence, and F r a n c i s S. Doody, The Schumpeterian System. (Cambridge 42, Mass: A d d i s o n Wesley Press I n c . , 1950;.  5. as the "setting up of a new production process", i . e . one based on t  technical coefficients that did not exist previously.  Clemmence and  Doody point out that innovation i s thus an internal factor from the point of view of the Schumpeterian System} and that innovation with i t s effects, and with the response of the economy of these effects, i s responsible for the process of economic evolution.^5  The outlook adopted by Schultz  was essentially Schumpeterian,  because he associated economic progress with the opening up of new production pos s i b i l i t i e s.^ Schumpeter did not mention the special case i n which the setting up of a new production process does not change the shape of the production function.  Hicks called this one a "neutral  7  technological change".  This study recognizes that either neutral or  non-neutral technological changes can occur.  Since change i s taking  place over time i t cannot be judged a priori what i s the nature and the extent of the change.  The study, therefore, examines the data and  formulates a model based on economic theory and on the structure of the agricultural industry.  The purpose i s to measure the changes i n  factor-product conversion ratios that have occurred.  I  b  i  d  * t  P»  36  ^ T.W. Schultz, The Economic Organization of Agriculture (New York: McGraw-Hill Book Company, Inc., 1953). 6  Ibid., pp. 99-124  7  J.R. Hicks, Theory of Wages, (London: MacMillan and Co., Limited,  1932), pp. 121-22.  II  REVIBf OF LITERATURE  In a recently published paper Lok mentions two approaches to measuring changes i n p r o d u c t i v i t y , ( l ) the production function method, and (2) the constant dollar method. Domar has presented a more  2 comprehensive classification.  He points out that i n measuring  technological change the practise has been to impute to i t that portion of productivity which cannot be imputed to changes i n the quantity of factor inputs.  The factors contributing to the change, he  goes on, are technological progress i n the narrow sense, economies of scale, external economies, improved health, education and s k i l l of the labour force, better management, changes i n the product mix, other non-specific factors.  and  He calls the parameter derived from this  method of measurement, which involves taking the differences between actual production and that which i s mathematically determined from a fixed production function a "Residual". The Residual has been calculated i n different ways. Domar mentions the f i r s t four-* of the following:  (l) It i s the difference  between the values of outputs and of inputs calculated at constant prices by Hiram S. Davis.^  (2) It i s the ratio between arithmetic  Siepko H. Lok, An Enquiry into the Relationships Between Changes i n Over-All Productivity and Real Net Return Fer Farm and Between Changes i n Total Output and Real Gross Return. Canadian Agriculture 1926-57. (Ottawa: " Technical Publication, Canada Department of Agriculture,  Oct., 1961), pp. 14-21.  S.D. Domar, "On the measurement of technological changes," Economic Journal, Volume LXXI (December 1961), pp. 709-29. 3  I b i d  « » P«  7 1  The  °-  ^ Hiram S. Davis, Productivity Accounting (Philadelphia: of Pennsylvania Press, 1955)•  University  i n d i c e s o f output and i n p u t i n the works o f S c h m o o k l e r ,  5  Abramovitz ,  and K e n d r i c k ; and t h i s Domar c a l l s t h e S.A.K. method.  (3)  I t has a l s o  been c a l c u l a t e d as a r a t i o between an aggregate a r i t h m e t i c i n d e x o f output and i n p u t s embodied i n a l i n e a r and homogeneous p r o d u c t i o n function.  T h i s method was u s e d by Solow.^  (4)  The  relative  percentage r a t e o f growth o f the w e i g h t e d a r i t h m e t i c average o f i n p u t c o e f f i c i e n t s between two p o i n t s i n time as d e r i v e d by L e o n t i e f from h i s input-output  s t u d i e s has a l s o been u s e d as a measure o f the r a t e o f  growth o f t h e R e s i d u a l . ^  Domar c a l l s a t t e n t i o n t o t h e f a c t t h a t i n a  l a r g e s l o w l y grovring economy t h e s e methods are l i k e l y t o y i e l d s i m i l a r r e s u l t s ; but t h a t i n r a p i d l y growing s e c t o r s and i n d u s t r i e s , and i n problems i n v o l v i n g i n t e g r a t i o n and a g g r e g a t i o n o f i n d u s t r i e s , b o t h the d i f f e r e n c e s i n the r e s u l t s from, and the arguments method, may become more s i g n i f i c a n t .  about each  T h i s i s because the d i s t o r t i o n s  p r e s e n t e d by the s m a l l amount o f s h i f t i n the t r a n s f o r m a t i o n  function  Jacob Schmookler, "The Changing E f f i c i e n c y o f t h e American Economy: 1869-1938," The Review o f Economics and S t a t i s t i c s , Volume XXXIV, (August, 1952), pp. 214.-31. Moses Abramovitz,, "Resource and Output Trends i n the U n i t e d S t a t e s S i n c e 1870," The American Economic Review, Papers and P r o c e e d i n g s , Volume XLVT, (May 1956), pp. 5-23, r e p r i n t e d as a N a t i o n a l Bureau o f Economic Research, O c c a s i o n a l Paper 52, (New York, 1956). John W. K e n d r i c k , " P r o d u c t i v i t y T r e n d s : C a p i t a l and Labour," The Review o f Economics and S t a t i s t i c s , Volume XXXVII, (August 1956), pp. 248-57, r e p r i n t e d as a N a t i o n a l Bureau o f Economic Research, O c c a s i o n a l Paper 53, (New York: 1956).  g Robert M. Solow, ""Technical Change and the Aggregate P r o d u c t i o n Function, The Review o f Economics and S t a t i s t i c s , Volume XXXIX, (August 1957), pp. 312-20. 11  W a s s i l y L e o n t i e f e t . a l . . S t u d i e s i n the S t r u c t u r e o f the American Economy, (New York: O x f o r d U n i v e r s i t y P r e s s , 1952), pp. 27-35.  8. i n the slowly growing economy are not large enough to significantly change the results from each method.  (5) In agricultural economics  research the residual has been calculated by the use of the production function.  The relative changes between the output derived from the  function and actual output, have been regarded as measurements of the change i n productive capacity.- 1  Solow method.  0  This approach i s an off-shoot of the  (6) The constant dollar method which Lok describes as  having been used also i n agricultural economics research i s a modification of the method which Domar ascribes to Davis.  Quantity  indices constructed from deflated value series of inputs and outputs are compared by expressing them as a ratio of each other.  Those  measurements which express as a ratio input factors to gross output i n a growing economy, however, may not measure technological change because factor-factor ratios may change under conditions of constant technology.  The result i s that single-input-output ratios are mis-  leading as measures of changes i n technology.  Salter points out that  the only significance that can be given to these output-single-inputratios i s that " . . . they are indications of what may be termed 'growth i n depth as distinct from 'extensive growth'- growth which 1  merely reproduces a given situation.  They are measures which crystallize  out changes i n content as distinct from changes i n amount. But because changes i n depth are as highly inter-related as other forms of economic change, individual productivity measures, such as labour productivity, have l i t t l e direct significance unless we can relate them to the  The production function may be linear or non-linear. The Solow method applies to non-linear production functions. For an application of the production function method i n agricultural economics research C f . Vernon W. Ruttan, "The Contribution of Technological Progress to Farm Output: 1950-75, The Review of Economics and Statistics. Volume XXXVIII, (1956), pp. 61-69. n  9. complex p r o c e s s o f change o f which t h e y a r e a p r o d u c t . * . .  We  cannot d i v o r c e changes i n the p r o d u c t i v i t y o f one f a c t o r from the p r o d u c t i v i t y o f o t h e r f a c t o r s , o r i n d e e d from a l l the elements i n an i n t e r - r e l a t e d economic system. "-^ The o b j e c t i v e o f t h i s s t u d y i s t o measure i n q u a n t i t a t i v e terms the e f f e c t s o f change which have been due t o t e c h n o l o g y .  Thus a  r e v i e w o f some o f the models which have been u s e d f o r measuring changes i n technology i s appropriate.  Significant contributions to this  subject  have been made by Joan R o b i n s o n , ^ Champerowne,-^ P a s i n e t t i , ^ Urquhart,^-' and  Solow.  Some s t u d i e s which r e l a t e t o the Canadian economy w i l l  a l s o be examined.  W.E.G. S a l t e r , P r o d u c t i v i t y and T e c h n i c a l Change, U n i v e r s i t y P r e s s , I 9 6 0 ) , p. 3.  (London:  Cambridge  12 Joan Robinson, "The P r o d u c t i o n F u n c t i o n and t h e Theory o f C a p i t a l , " The Review o f Economic Studies," Volume XXI, (1953-54-), pp. 81-103. c f . a l s o Volume X X I I I (1955-56) p. 24-7. 13 D.G. Champerowne, "The P r o d u c t i o n F u n c t i o n and t h e Theory o f C a p i t a l : A Comment," The Review o f Economic S t u d i e s . Volume XXI, (1953-54.), pp. 112-35. I n c o n j u n c t i o n w i t h R.F. Khan he a l s o wrote a m a t h e m a t i c a l addendum t o Mrs. Robinson's a r t i c l e op. c i t . , pp. 107-11. L u i g i L . P a s i n e t t i , "On Concepts and Measures o f Changes i n P r o d u c t i v i t y , " The Review o f Economics and S t a t i s t i c s . Volume X L I , (August, 1959), pp. 270-82. See a l s o h i s "Reply" i n the same p u b l i c a t i o n , pp. 285-86. 15 M.C. U r q u h a r t , " C a p i t a l Accumulation, T e c h n i c a l Change and Economic Growth," The Canadian J o u r n a l o f Economics and P o l i t i c a l S c i e n c e , Volume 25, Number 4-, (November 1959), pp. 411-30. Solow, op. c i t . See a l s o R.M. Solow "The P r o d u c t i o n F u n c t i o n and the Theory o f C a p i t a l , " The Review o f Economic S t u d i e s . Volume X X I I I , (1955-56), pp. 101-08: a l s o , "On Concepts and Measures o f Changes i n P r o d u c t i v i t y : Comment," The Review o f Economics and S t a t i s t i c s , Volume XLI, (August, 1959), pp. 282-85: a l s o , "Reply" The Review o f Economics and S t a t i s t i c s , Volume XL, (November, 1958), pp. 411-13.  10.  Since Charaperowne's papers were closely associated with Joan Robinson's model, the contributions of both authors w i l l be discussed together. The Joan Robinson Model In Joan Robinson's model, the various levels of technology were derived from capital measured i n wage units, i.e., real capital, expressed as a ratio to man hours.  In such a model the larger the  number of man hours which i s used i n conjunction with a given capital measured i n wage units, the lower i s the level of technology. If the economy to which her method of measurement i s applied i s i n equilibrium, the value of capital goods i s the present value of the future earnings of the capital discounted as the prevailing rate of interest. Since her model i s macro-economic, i t might appear that i t i s necessary that the labour which i s spent on consumption goods and services should be isolated from that which i s spent on the making of producer goods. However, since she was considering an economy i n equilibrium, and since equilibrium requires that the stock of capital equipment be maintained, the age composition of the stock i n equilibrium i s such that the amortization funds provided by the stock as a whole are continuously being spent on replacement.  Under these  conditions with the stock of capital goods i n balance there i s no need to examine whether the particular worker i s engaged i n the production of capital goods, or of consumer goods, since the whole economy i s geared to producing a stream of f i n a l output for both the present and for the future.  11,  There are several weaknesses involved i n the Joan Robinson model which Ohamperowne and Solow have pointed out.  These weaknesses  are associated with (a) the problems which arise when attempts are made to compare two stationary states which have different rates of time preference, and (b) from the presence of factors which have rates of increase that are not necessarily associated with the level of economic activity i n the "stationary state . 0  The rate of population  increase i s an example of one such factor. Because of these problems i f comparisons are made between two stationary states, the following erroneous results are l i k e l y to appear,  (a) Identical quantities of physical capital goods and labour  producing each the same quantity of output w i l l appear as different real capital to labour ratios i f there are differences i n the rates of interest existing between both states.  Each of the stationary states  w i l l thus appear to be operating at a different level of technology even though they differ only i n time preference.  Conversely, i t i s  possible to find two stationary states with the same quantity of labour but with different techniques.  Differing rates of interest w i l l be  capable of causing each such stationary state to appear as being operated at the same level of technology,  (b) If the level of  technology i s regarded as being a determinant of the shape of the production function, two states though operating on the same production function w i l l appear under Joan Robinson's criterion as having two different levels of technology.  The nature of the production function  as well as time preference determines the equilibrium level of interest, therefore, to say that interest i n the Joan Robinson model i s an  12  additional variable would not solve the problem,  (c) $hen one measures  the ratio of capital measured i n wage units to labour hours i n the same stationary state at different points i n time, one i s actually comparing the relative rates of accumulation of capital and  population.  Furthermore, i f food supply i n the stationary state i s not a limiting resource and wages are not at a subsistence level, the increase i n population may be greater than the increase i n capital accumulation. The stationary equilibrium i s thus shifted: but this shift need not affect the customary pattern of conversion of non-labour resources into output.  It i s for these reasons that Joan Robinson's model w i l l have to 17  be regarded as being applicable only to a completely stationary state, (d) In Joan Robinson's model,assuming that no change i n the total quantity of labour hours has occurred, and assuming no change i n the rates of interest, her higher level of technology i s one which i s more capital intensive than others.  If under conditions of constant rates of  interest and fixed supply of labour an innovation occurs which has the effect of shifting some of the labour force from the commodity industries into the service industries i n which case less labour i s needed for production and maintenance of the existing physical capital stock or for a given level of physical output, this shift i n the resources i s not registered i n the model used.  This condition arises because the  Joan Robinson model cannot register such structural changes which have been effected i n the economy. It does not recognize the criterion that 17  The writer once saw this comment i n a paper by Solow but has been unsuccessful i n relocating the source. This stationary state must be one which i s completely so over time. Autonomous factors would have to be absent.  13. more leisure time as a legitimate output for the economy as a whole. The demand for new services present also problems of measurement i n any Indexed series, and thus also exist i n Joan Robinson's model.  The  above weaknesses, therefore, force one to eschew a model which gives labour an especial place i n a general equilibrium system where substitution of factor inputs i s possible. The basic d i f f i c u l t i e s presented by the Joan Robinson model involve problems associated with attempts at measuring the quantity of capital, and also problems of indexing.  An alternative approach  which seems to avoid some of the above problems i s suggested by Ohamperowne. A natural method by which to construct an index of quantity of capital i n a historical sequence would be to form a chain index, increasing the index at each step by the proportion i n which the cost of the capital at current wage and interest rates at the end of the step exceeded the cost of capital at the beginning of the step calculated at the same wage and interest rates. By shortening the steps, the distortion due to choosing wage and interest rates at the end of each step could be made as small as we pleased. The same method can be used to construct an index of quantity of capital i n a sequence of stationary states, and provided these are arranged i n order so that the difference between the one and the next i s always a small step the distortion due to the method can again be reduced to negligible proportions. The method has the advantage that changes of cost merely due to changes i n the interest rate do not affect this measure of the quantity of capital.18 Champerovme's suggested method i s consistent with measurement attempting to quantify change through a system of comparative statics.  Ohamperowne, "Comment," p. 115»  u. Solow, however, pointed out that as Champerowne was aware the use of h i s chain index does not dispel a l l the d i f f i c u l t i e s .  The  problem of measuring c a p i t a l Solow asserts, other than i n the circumstance where c a p i t a l i s regarded as abstract purchasing power uncommitted to a s p e c i f i c form, (hence i n value u n i t s ) comes not from physical d i v e r s i t y of c a p i t a l goods but pomes from the inter-twining of the past, the present, and the future.  The measurement problem i s such  a d i f f i c u l t one to handle that although a theory of c a p i t a l b u i l t on the assemption of perfect foresight seems unreasonable, present theory provides no equally precise and d e f i n i t e assumption to take i t s p l a c e . ^  The Solow Model The Solow model may be regarded as one of the chief examples of the production function method.^ cussed the premises of t h i s model.  Hogan,^1 and Bomar^ have d i s The s t a t i s t i c s i n h i s model  comprise,  Q = Index of the quantity of output. K = A measure of the index of quantity of c a p i t a l goods. L = Index of labour input i n physical u n i t s , t = Time. Solow postulated that the production function was of the following form. Q = F(K, L ; t)  (1)  19 Solow "The Production Function, e t c . Volume XXIII, (1955-56), pp. 101-02. n  The Review of  Economic-Studies.  on Solow, "Technical Change" e t c . ^ Warren P. Hogan, "Technical Progress and Production Functions," The' Review of Economics and S t a t i s t i c s , Volume XL (1958), pp. 4-07-11. See also Solow" s reply to Hogan, pp. 411-13. 22 Domar, Loc. c i t .  15.  In his model with neutral changes i n technology the Marginal Rates of Substitution (M.R.S.) remain unchanged.  In this case the production  function takes on the special form;  Q = A (t) £ (K,L)  (2)  A (t) i s a multiplicative factor which measures the cumulative effects of shifts of the production function over time. Solow was seeking to measure the rate of change of technology and not the amount of change which has occurred. An examination of a section of the development of his technique of measurement i s nevertheless f r u i t f u l . To get the rate change of Q over time, i t *ras necessary to express additional output as a ratio of the amount i n the base period. Each preceding year was used as a base for that succeeding.  Q, there-  fore, was differentiated with respect to time and the result divided through by Q. • ^ = A ^I . . dt (dK  dK dt  (  +  ££  gt  dL ) + dt )  f  ( dA ) ( dt )  Solow l e t the derivitives of each factor with respect to time be Q, . . . A, K, L, respectively.  =  cL£  £>K  = ^f  £  f  + ^£ bL  I» + f A f Yk  K A + ^ f L _ A f A £>L £ A  +  f i f~A  ,  v  Ub)  [ i c\ ^ '  16  = 4 £ K = ^QK  K K  Q K  3K  L  + ^ Q L 51  is Q =  a_f  + A  +  ^ «> L  +  A  +  A  (/D) /.v  I  A  U  L L + Q L  A  .  = ^ J K K + ^ Q L L + A dK E § S>L L Q  A  K  E  4  ;  1  J  o_\ A  ^  In the above system of equations i t can be noted that K, Q, L, are identifiable factors.  The gross rate of change of output i s seemed  to be made up of the weighted sum of the rates of change i n the input factors (equation 4g). identifiable.  That due to technology i s made explicit and  That portion of the gross change which cannot be  allocated to identifiable changes i n the other measurable inputs i s thus allocated to technology. In order to further isolate the identifiable changes Solow defines the following quantities: W  K  L  =  K  (5)  =  L  (6)  I  These quantities are the relative shares of each factor which are also equal to the elasticities of production for each factor input (marginal product divided by average product). In terms of inputoutput analysis using a linear and homogeneous production function the relative share i s the ratio marginal product to the average product.  17.  The' v a l u e s o f e q u a t i o n s 5 and 6 were s u b s t i t u t e d e q u a t i o n 4g*  g  t h i s produced t h e f o l l o w i n g e q u a t i o n :  -  q The  into  + W L L L  V K KK  +  / N  A A  7  K  '  change i n output i s t h e r e f o r e observed t o be t h e weighted  the r a t e s o f change o f the components.  W  sum o f  i s r e g a r d e d as b e i n g e q u a l  L to  (1 - ^g).  I n terms o f a p r o d u c t i o n f u n c t i o n S o l o w s model t h e r e f o r e 1  c o n s i s t s o f a p r o d u c t i o n f u n c t i o n which i s l i n e a r and homogeneous o f degree  unity. Rearrangement o f e q u a t i o n 7 produces t h e f o l l o w i n g e q u a t i o n  which e x p r e s s e s t h e r a t e o f change i n t e c h n o l o g y .  A A  -  g  ®  -  W K - W_ L K  P o i n t s t o Note i n t h e Solow Model  L  L  .  A  I t must be o b s e r v e d t h a t A (which i s a measure o f t h e r a t e o f change i n t e c h n o l o g y ) i s a r e s i d u a l and n o t a dynamic prime mover.  It  absorbs l i k e a sponge, Domar says, a l l i n c r e a s e s i n o u t p u t n o t accounted f o r by t h e growth o f e x p l i c i t l y r e c o g n i z e d i n p u t s .  He goes on t o p o i n t  out t h a t A i s t h u s n o t an i n p u t i n t o t e c h n o l o g i c a l p r o g r e s s ; so t h e  A  .  model does n o t measure t h e n a t u r e and t h e magnitude o f i n p u t s which would r e s u l t i n a g i v e n increment o f A .  A  The magnitude o f t h e  t e c h n o l o g i c a l change i s t h u s d i v o r c e d from c a p i t a l a c c u m u l a t i o n . accumulates  Capital  b u t does n o t serve as an i n s t r u m e n t f o r the i n t r o d u c t i o n o f  t e c h n o l o g i c a l change i n t o t h e p r o d u c t i v e p r o c e s s . These c r i t i c i s m s o f Solow's model which Domar has advanced appear t o be s t r o n g .  A, however, i s d e r i v e d from e q u a t i o n 2, which i s  18, a special form of equation 1.  That being the case, with technology  assumed neutral, any changes i n the level of technology  are assumed  to leave shares constant as well as to leave marginal rates of substitution unchanged.  This i s because of the way Solow defines a  neutral technological change. The model does not preclude changes i n technology which may be due to changes i n the quality or the quantity of capital goods as capital accumulation proceeds. It must also be bourne i n mind that the isolation of capital formation from technological progress i s empirically impossible.  It  should also be noted that the deflation methods tend also to understate the case for capital formation, i n that changes i n the quality of capital are not measured i n the indexed time series data.  The rate of  change of capital formation ( § ) and also of labour i n use ( h ) are K L therefore understated.  The result i s that the residual i s overstated.  If the measured amount of technological change i s not to be overestimated any attempts to use a model based on the production function approach must find a means whereby errors due to this indexing problem are minimized. 23 The Urquhart Model This model uses a linear and homogeneous production function .73 .18 .09 of the form Q = L  C  T  where L, C, and T, are indices of  labour capital and land respectively.  Technological change i s a  residual calculated i n a manner different from that of Solow. Urquhart's definition of a neutral change i n technology was also different. Since 23  Urquhart, op. c i t .  19. his neutral change was one i n which the shape of the production function was l e f t unchanged he did not preclude changes i n the Marginal Rates of Substitution of factors, given that the original factor relationships were non-linear. Over-all productivity was obtained by solving the production function for each year given the levels of each category of input,  and  the composite index derived from solving the production function was divided into the index of observed output. The effects of technology on the productivity of individual categories of inputs were obtained i n the following manner. Urquhart kept two of the factor inputs constant at the base year quantities. The production function was then solved for each year using the observed quantity of the third input which was allowed to vary. repeated for another factor input.  The process  was  The effect of technology on the  productivity of a factor input held invariant at the base period level of input was determined by taking the unweighted product of the indices which had been derived by solving the production function i n the manner just described. This method of determining the effect of technology on the productivity of the individual factor i s superior to that which i s calculated by dividing the individual indices of factor inputs into output, because i t makes allowances for the effects of the increases i n co-operating input factors, and does not merely record the effects of relative changes i n the rates of increase of individual inputs as compared to gross output.  Since the quantity of the input whose  productivity response i s being measured i s kept at the base period quantity, however, Urquhart's method does not cope with technological change which accompanies simultaneous increases i n a l l factors.  20. Changing price cost relationships were removed from the data by using price indices to deflate current values of input and output.  Returns  to scale were assumed to be held constant since he used a Cobb-Douglas function.  Changes i n the ratio of actual output to the calculated joint  input were then ascribed to changes i n technology. The Pasinetti Model ^ 2  Pasinetti emphasized that input-output data were usually limited to one point on the production function.  This fact made i t  d i f f i c u l t to distinguish a change i n the level or shape of the function from a movement along i t .  production  He preferred to avoid making  assumptions as to the nature of the particular production function, or postulates as to ways different functions at different points of time are related to each other, and instead gave up the distinction between the change of the production function and a movement along i t .  Solow  criticized him for this with the following comment: The notion of a production function i s not simply a matter of formality or convenience. It i s meant to express the fact ( i f i t i s a fact) that at any time the firm or industry or economic system i s faced with a range of technological alternatives any one of which might be chosen, and that given enough time any previously made choice can be changed without appealing to new knowledge . . . . Nobody has yet proposed giving up the distinction shifts or and movements along demand and supply curves although a l l we ever observe for one market at any one time i s one p and one q . . . By abandoning the production function Mr. Pasinetti has i n effect abandoned the possibility of substituting capital for labour as of given technical knowledge. If  Pasinetti, op_. c i t .  a. t e c h n o l o g y were r e a l l y l i k e t h a t no one c o u l d complain. But t o b e l i e v e t h i s seems t o be t o be f o l l y , e s p e c i a l l y f o r p e r i o d s as l o n g as a decade.^5 What P a s i n e t t i d i d was t o abandon t h e H i c k s i a n d e f i n i t i o n o f a n e u t r a l t e c h n i c a l change. output to f a c t o r i n p u t s .  I n s t e a d he compared t h e r a t i o s o f  H i s n e u t r a l change was one i n which t h e  o u t p u t - i n p u t r a t i o s o f a l l f a c t o r s o r more s p e c i f i c a l l y o f a composite K and L changed i n the same p r o p o r t i o n .  His labour saving e f f e c t  was  one i n which the change o f the r a t i o g was g r e a t e r t h a n t h e change i n K the r a t i o £J. The converse was a c a p i t a l s a v i n g e f f e c t . He r e g a r d s L the a n a l y s i s by Solow which has j u s t been p r e s e n t e d as b e i n g " r o u g h l y along these l i n e s . 0  his.  2 0  Solow d e n i e d t h a t t h i s method was  similar to  Solow a l s o p o i n t e d o u t the b a s i c weakness i n v o l v e d i n the  attempt t o use r a t i o s r a t h e r t h a n s h a r e s ; and t h i s he s t a t e d as f o l l o w s . "Suppose t h a t changes i n K and L o v e r time r e f l e c t e x c l u s i v e l y o r p r i m a r i l y i m p u l s e s from the s i d e o f the s u p p l y o f s a v i n g and the growth of population.  Then whatever happens t o Q, P a s i n e t t i ' s  judgement  about the n a t u r e o f t e c h n i c a l change w i l l i n f a c t r e f l e c t  nothing  about t e c h n o l o g y b u t o n l y the r e l a t i v e speeds a t w h i c h p o p u l a t i o n and 27 c a p i t a l accumulate."  T h i s c r i t i c i s m i s s i m i l a r t o one o f those which  has been made e a r l i e r i n t h i s t h e s i s about the Joan Robinson model.  R.M. Solow, "Concepts and Measures o f Change i n P r o d u c t i v i t y , " The Review o f Economics and S t a t i s t i c s , Volume XLI, (August, 1959), p . 283. 2  ° P a s i n e t t i , o j % c i t . , p. 272.  27  Solow, "Concepts", e t c . , p. 283.  22. S t u d i e s Done on the Canadian Economy The  s t u d i e s done by Hood and S c o t t , ^ A n d e r s o n , ^ and  Lok,-^  have been chosen f o r c l o s e r e x a m i n a t i o n . The  s t u d y by Hood and S c o t t , was  w i t h i n which the measures o f p o p u l a t i o n ,  d e s i g n e d to f o r e c a s t the  ranges  labour f o r c e , output, c a p i t a l  c e r t a i n o f t h e i r c o n s t i t u e n t elements might be e x p e c t e d t o l i e . ^ study a l s o contains  and  Their  a d i s c u s s i o n o f the p r i n c i p l e s and the problems o f  measurement t h a t are a s s o c i a t e d w i t h the economic a n a l y s i s o f a growing economy.  They measured output i n d o l l a r s p e r man  the u n i t o f measurement i s output p e r c a l e n d a r Hhereas the  study o f Hood and  economy, t h a t by Anderson was  hour.  For t h i s  year.  S c o t t encompassed the  Canadian  p r i m a r i l y concerned w i t h the p r o d u c t i v i t y  o f l a b o u r i n a g r i c u l t u r e as compared w i t h i t s p r o d u c t i v i t y . i n the a g r i c u l t u r a l sector. i n v o l v e d i n the use  study  non-  Anderson, though r e c o g n i z i n g the l i m i t a t i o n s o f the r e s i d u a l method f o r the  c a l c u l a t i o n of f a c t o r  p r o d u c t i v i t y , p o i n t s out t h a t the absence o f a more p r e c i s e method made the procedure a p p r o p r i a t e The  f o r the t a s k a t hand.  s t u d y by Lok  a g r i c u l t u r a l sector.  and  t h i s present  Lok's study was  c a l c u l a t i o n s o f the p r e s e n t  study apply to  published  a f t e r most o f  s t u d y were completed.  s t u d i e s t o a l a r g e e x t e n t use  the same d a t a ,  the the  Since b o t h these  i t i s appropriate  that  the  ^ Wm. C. Hood, and Anthony S c o t t , Output. Labour and C a p i t a l i n the Canadian Economy, (Ottawa: Queen's P r i n t e r , 1957). T h i s study i s a p a r t o f r e p o r t o f the Royal Commission on Canada's Economic P r o s p e c t s . 29 W.J. Anderson, " P r o d u c t i v i t y o f Labour i n Canadian A g r i c u l t u r e , " Canadian J o u r n a l o f Economics and P o l i t i c a l S c i e n c e , Volume XXI, (May,' 1955), pp. 228-36.  30  Lok,  31  loc. c i t .  Hood and S c o t t , op.  c i t . , i n t r o d u c t i o n p. i .  23.  sources of the differences i n the results should be made clear. The objectives of each study are dissimilar and so too are the models used.  The best statement of this fundamental difference i s found i n  the following statement by Lok.  "It i s not the purpose of this study  to describe, and interpret f u l l y the relative changes over time i n the input and output and the output structure of Canadian Agriculture.' One of the aims of this present study i s to make this interpretation. Lok's study demonstrates the weight period bias which i s a part of the index number problem. Lok shows the differences which arise between the different indices which were calculated.  Four of  these were fixed base indices, and the two variable base indices were calculated on the bias of the Paasche and the chain index number formulae.  The weight periods used were 1935-39, 194-0-44-, 194-5-4-9, and  1950-54-.  Lok'a fixed base quantity index formulae were of the form Vn / In / Iw Vo / lo / Iw ; where Vn = Aggregate current value. In = Price index number of the commodity i n year n. Io = Price index of the commodity i n the base year (1926). Vo = Aggregate value of output i n the base year. Iw = The average price index number i n the base period of the quantity index. Lok's calculated output index series for the 1935 to 1939 fixed base period differs from the gross output index calculated i n this study.  32  These differences arise from the price indices used to  Lok, op. c i t . , p. 68.  24. deflate output and from the method i n which feed and seed were treated i n each study.  Lok recognizes that farm price indices rather than oo  wholesale price indices should be used to deflate output.  The  unavailability of farm price indices before 1935 prompted his decision to make two sets of calculations:  one using farm price  indices from 1935, and another using wholesale price indices from 1926.  These two sets of calculations were presented i n his study. In  this study an index farm price was calculated for the years 1926-34 by linking the wholesale price index to the farm price index. Lok also recognized the problem of intermediate products i n 0/  a production function.  Feed and seed as an example were mentioned.  In his study feed and seed were included i n input and not removed from output.  In the present study feed and seed are recognized as an  intermediate product by neglecting the value on the input side and removing i t from the output product.  In this manner only f i n a l output  of the agricultural sector was considered. If the proportion of livestock i n the agricultural economy i s changing, i n view of the manner i n which the quantity indices were calculated, the method which includes feed and seed and that which excludes i t , produce each different results.  The major difference,  however, i s the method of aggregation of inputs. Lok used a linear function to add together input quantities weighted by prices of the base period. In this study a linear and homogeneous production function Lok, op. c i t . , p. 61. op. c i t . , pp. 59 & 63*  25.  was used.  T h i s made i t p o s s i b l e t o add g e o m e t r i c a l l y  indices of  f a c t o r i n p u t s and t o a r r i v e a t a measure o f g r o s s i n p u t which i s a g e o m e t r i c aggregate i n which t h e exponents  are t h e weights  T h i s method f a c i l i t a t e s t h e use o f s t o c k c o e f f i c i e n t s r a t h e r f l o w e s t i m a t e s , and so a v o i d s some o f t h e problems  used. than  o f measurement  a s s o c i a t e d w i t h t h e d e t e r m i n i n g o f t h e amount o f c a p i t a l i n u s e . - ^ I n s e e k i n g t o t e s t h i s h y p o t h e s i s Lok's method p o s s e s s e s h i g h degrees o f a u t o - c o r r e l a t i o n , because productivity to r e a l net return.  he was r e l a t i n g o v e r - a l l  Productivity i s a function of  o u t p u t , and n e t r e t u r n i s a l s o a f u n c t i o n o f o u t p u t j t h e r e f o r e , Y, as used i n t h i s a n a l y s i s , i s i n v o l v e d on b o t h t h e h o r i z o n t a l and t h e v e r t i c a l axes.  That b e i n g the case, t h e r e l a t i o n s h i p s which Lok was  t e s t i n g were b o t h f u n c t i o n a l s o f o u t p u t . cannot be r e g a r d e d as b e i n g independent  The changes i n p r o d u c t i v i t y of r e a l net return.  I n t h i s a n a l y s i s i n p u t i s c a l c u l a t e d independent o f the c a l c u l a t i o n s made f o r output; and a l t h o u g h some amount o f a u t o c o r r e l a t i o n i s i n v o l v e d i n a l l measurements o f p r o d u c t i v i t y , composite i n p u t s  because  a r e a r r i v e d a t by t h i s g e o m e t r i c a g g r e g a t i o n , and  because no e x p l i c i t r e g r e s s i o n o r c o r r e l a t i o n methods w i l l be attempted, it  i s hoped t h a t many o f t h e problems  o f a u t o - c o r r e l a t i o n w i l l be  avoided.  35 c f . , John ¥ . K e n d r i c k , "Some T h e o r e t i c a l Aspects o f C a p i t a l Measurement," The American Economic Review: Proceedings and Papers, Volume L I , (May, 1961),, 102-11.  Ill  THE ANALYTICAL FBAMEHORK OF THE STUDY  In a study such as this one which seeks to measure the changes which have occurred i n the position and the shape of the production function, a major problem i s the determining of the production function from the limited amount of information availablej since without making any assumptions as to the nature of the production function,the available annual data furnishes information about a point on the production function rather than the whole function. On the basis of the theory that a family of isoquants may be derived from each production function, and the twin assumption of diminishing marginal productivity of factor inputs under conditions of constant technology, and of the condition that factors are paid as wages an amount equal to the value of their marginal product, a means of deriving the production function for the agricultural industry i s available.  This means u t i l i z e s the concept of factor shares. The concept of a single production function for the industry  as a whole represents a simplification of the conditions of production operating i n the industry, and the derivation of a function for the industry as a whole presents problems of aggregation. A further assumption as to the type of production function i s necessary. Under conditions of constant technology agricultural production i s characterized by diminishing marginal rates of substitution of factors and diminishing returns; therefore the production function i s non-linear.  For this study i t i s assumed that a Cobb-  Douglas type production function characterizes the agricultural industry.  27. This type of function has the advantage of allowing for diminishing returns and changing marginal rates of substitution. Since i t i s linear i n a logarithmic form, the computation methods which are applied a linear production function may be readily adopted to the data when they are expressed i n a logarithmic form.  This type  of function i s also homogeneous, so that returns to scale are held constant. Other conveniences conveyed by the use of the Cobb-Douglas type function arose from the fact that the exponents of the function are estimates of both the elasticity of production coefficients, and the relative share of the particular factor.  It i s thus possible to  determine the function from time-series data i n which only one observation of factor combinations i s given for each year, because the exponents can be determined by calculating the relative share of each factor. The production function used i n this study assumes that the total wage payments to a l l identifiable factors would exhaust total production i f there were no changes i n technology.  But the total  output of the agricultural industry i s influenced to a large extent by weather and other exogeneous variables.  Consequently, the variability  i n agricultural output w i l l at times be due to the influence of the exogeneous variables rather than to the influence of the prevailing level of technology. With the assumption that the total product i s exhausted i n wages to factors under conditions of constant technology, the aggregate wage payments to factors may be used as an alternative means of measuring output.  In this event the difficulties which the  interaction of the exogeneous variables and changes i n technology  28  p r e s e n t i n the way  o f d e t e r m i n i n g the s h o r t - r u n p r o d u c t i o n f u n c t i o n  are e l i m i n a t e d ; s i n c e under c o n d i t i o n s o f c o n s t a n t t e c h n o l o g y when the p r o d u c t i o n f u n c t i o n i s o f the Cobb-Douglas t y p e , and f a c t o r s are p a i d t h e v a l u e o f t h e i r m a r g i n a l p r o d u c t , the v a l u e o f t o t a l i n p u t i s e q u i v a l e n t t o what the v a l u e o f t o t a l o u t p u t would be u n d e r the e x i s t i n g l e v e l o f t e c h n o l o g y and market c o n d i t i o n s .  Divergences o f  the v a l u e o f t o t a l i n p u t from t o t a l o u t p u t would be the r e s u l t o f (a) exogeneous v a r i a b l e s , o r (b) changes i n t e c h n o l o g y which r e s u l t i n the i n c r e a s i n g o f the gross o u t p u t from the a v a i l a b l e f a c t o r s . t h e s e c i r c u m s t a n c e s , r e a l i z e d g r o s s p r o d u c t may  be as a r e s u l t  from a n t i c i p a t e d t o t a l p r o d u c t a r r i v e d a t on the b a s i s o f the  In different initial  production function. The values.  s h a r e s were c a l c u l a t e d on the b a s i s o f c u r r e n t d o l l a r  However, s i n c e changing p r i c e - c o s t e f f e c t s w i l l  influence  the t o t a l v a l u e o f i n p u t s and o u t p u t , and s i n c e t e c h n o l o g i c a l change d e a l s w i t h the changes i n the c o n v e r s i o n r a t i o s between g i v e n q u a n t i t i e s o f p h y s i c a l i n p u t s and o u t p u t s , the p r i c e - c o s t  effects  were removed from the aggregate v a l u e s e r i e s by measuring  the  as i n d i c e s o f d e f l a t e d (1935-39) d o l l a r i n p u t s i n which the v a l u e as a t 1926  was  set at  The r e l a t i v e  quantities  deflated  100.  shares o f t h e c u r r e n t d o l l a r v a l u e o f  p a r t i c u l a r f a c t o r i n p u t s i n aggregate  i n p u t (aggregate o u t p u t u n d e r  c o n d i t i o n s o f c o n s t a n t t e c h n o l o g y and i n a system f r e e o f exogeneous v a r i a b l e s ) , may  be s a t i s f a c t o r i l y u s e d as the share o f the f a c t o r i n  the e x p e c t e d l e v e l o f aggregate o u t p u t i f t e c h n o l o g y remains  constant.^  A more p r e c i s e development o f the model u s e d i n t h i s t h e s i s i s p r e s e n t e d i n Appendix A.  29  Inputs Three independent variables were included i n the production function used; namely, capital (C), current inputs (K), and labour (L). In this analysis capital was treated as a stock.  The value of capital  goods as at any point i n time was regarded as being determined by the expected value of the, future stream of production discounted at some rate of interest (not necessarily the prevailing market rate). Those inputs other than labour whose claims on output must be met from current production were regarded i n this study as current inputs.  This category included depreciation, and operating expenses  which were incurred for items which were not the intermediate products of agricultural industry. Feed and seed were thus excluded from this category; and for the third input category, D.B.S. data on the agricultural labour force were used. Because of the problems associated with the inclusion of land inputs (which constitute a major portion of the value of agricultural capital), two sets of calculations were carried out. In one set of calculation the value of land was included, i t s value being excluded from the other set.  Because many of the characteristics  which make agricultural land technologically productive are produced capabilities, the arguments for the inclusion of agricultural land as a capital good, are very substantial. In a manner similar to that which was used by Lok capital was also measured as.an indexed series of the flow of interest payments to capital stock.  However, i n this study, since depreciation on  capital stock has already been charged to current inputs the use of an  i n d e x o f the aggregate  i n t e r e s t payments as an i n d i c a t o r o f the l e v e l o f  c a p i t a l i n p u t does n o t recommend i t s e l f .  T h i s i s because o f the  t h a t the market r a t e o f i n t e r e s t o f i t s e l f  fact  depends upon time p r e f e r e n c e  as w e l l as upon t h e m a r g i n a l e f f i c i e n c y o f c a p i t a l , and a l t h o u g h b e i n g a means o f measuring  the e q u i l i b r i u m l e v e l o f n e t i n v e s t m e n t ,  i s thus  an u n s a t i s f a c t o r y measure o f the q u a n t i t y o f c a p i t a l i n use a t  any  given l e v e l of technology. A l l these i n p u t s were c a l c u l a t e d i n terms o f i n d i c e s o f the t o t a l v a l u e o f the u n i t s f o r each y e a r .  The i t e m s i n each  were d e f l a t e d by the a p p r o p r i a t e p r i c e i n d e x (1935-39 d e f l a t e d v a l u e o f each c a t e g o r y was  =  category  100).  The  summed, and t h i s aggregate  t r a n s f o r m e d i n t o an i n d e x e d s e r i e s 1926  = 100.*  p r o c e s s removes those e f f e c t s due t o p r i c e  S i n c e the  was  deflation  ( w i t h i n the l i m i t a t i o n s o f  the i n d e x number problem) t h e i n d e x o f t o t a l d e f l a t e d v a l u e may r e g a r d e d as b e i n g e q u i v a l e n t t o an i n d e x o f p h y s i c a l  be  quantities.  Output Output i n c l u d e s cash farm income as w e l l as income i n k i n d . Each c a t e g o r y was  t r e a t e d i n the same manner as were i n p u t s .  i n d i v i d u a l c a t e g o r y o f output o f the farm s e c t o r was appropriate p r i c e index.  Each  d e f l a t e d by i t s  The d e f l a t e d v a l u e s were aggregated;  and the  q u a n t i t y i n d i c e s o f the t o t a l output were o b t a i n e d by a p r o c e s s to  t h a t used i n c a l c u l a t i o n o f the i n d i c e s o f i n p u t . 3  The  similar  composite  o u t p u t f i g u r e , however, r e p r e s e n t e d an a r i t h m e t i c a g g r e g a t i o n o f d e f l a t e d d o l l a r v a l u e s , r a t h e r than a geometric aggregation o f the components. The d e t a i l s o f the i t e m s i n each c a t e g o r y and the i n d i c e s u s e d are i n c l u d e d i n Appendix A.  2  3  Ibid.  The Production Function The Cobb-Douglas function which i s used i n this study i s of the form 1 = X Q Xg X^ where X Q , Xg , and X^ , represented the indices of capital, current inputs, and labour inputs respectively, and where Y i s an index of the quantity of gross farm output. <x , /3  t  The exponents  and-tf , represent the calculated shares of capital current  inputs and labour respectively, and the sum of the exponents equals unity. These wage payments were determined from the data. The aggregate annual wage payment to labour was estimated by the product of the annual wage rate and the size of the farm labour force.  The monthly  farm wage rate without board as at May 15 was used i n this analysis to determine the estimate of the annual wage rate.  This wage rate was  chosen because the D.B.S. estimate of the annual farm labour force refers to this period. The aggregate of the wage payments to other current inputs was determined from the annual expenditures on the items which make up this input category. 4The wage payment of capital inputs was determined by the product of the aggregate current dollar value of farm capital (in one case inclusive of land and i n the other case exclusive of land) and the current market rate of the rate of interest on farm mortgages. The share of each factor was then determined by the ratio that the wage payment to each, i s of the aggregate wage payments to a l l factors.  In this manner the share going to each factor was determined  net of many of the effects that are produced by exogeneous variables and additional shifts i n technology. ^ The details are included i n Appendix A .  IV  RESULTS OF THE STUDY  In this section the results of the study w i l l be examined within the framework of the model which has been developed. The results of technological change which economic resource use would lead one to expect are associated with the producing of a larger quantity of output from a given stock of resources.  The innovation  which this study has introduced i s the method of determining the shape of the production function and from i t the quantity of resources being used at any point i n time. Changes i n the product mix, and i n the input mix, are also associated with changes i n technology; but within the framework of the model which has been developed for use i n this study the major step i s the determining of the production function; and from this point the other steps follow. The results of the study w i l l be presented i n a sequence which involves the presentation of the derived production functions i n the one case using capital resources inclusive of land and i n the other case using capital resources exclusive of land.  Those calculations  which were made from the production functions i n which the quantity of capital was measured as an index of the annual flow of interest payments w i l l be presented i n the Appendix. Measuring Technological Change Inclusive of Land Capital Table 1 , indicates the relative shares which were calculated from data i n which the value of land and buildings was included i n the value of capital stock (C ). Examination of the table shows that the 5  33. relative  shares o f the f a c t o r s had been changing o v e r t i m e .  I t followed  from t h e method chosen t h a t these changes must i n d i c a t e changes which have t a k e n p l a c e i n the shape o f the p r o d u c t i o n f u n c t i o n .  Since  n e u t r a l changes are those i n which s h i f t s o f the p r o d u c t i o n f u n c t i o n do not i n v o l v e changes i n i t s shape, i t f o l l o w s t h a t the t e c h n o l o g i c a l changes which had been adopted were n o n - n e u t r a l . Examination  o f t h e d a t a o f Table 1 shows t h a t t h e r e i s no  c o n s i s t e n t t r e n d i n the changes o f the s h a r e s . c a p i t a l d u r i n g the p e r i o d 1928 then d e c l i n e d s t e a d i l y p e r cent i n 1958. relative  t o 1932  The r e l a t i v e  share o f  r o s e from 30 t o 33 p e r  t o 14 p e r cent i n 1946,  cent,  and r o s e a g a i n t o  Although t h e r e has been an upward tendency  share o f c a p i t a l s i n c e 1946,  t h e share i n 1958,  19.6  i n the  was  still  s u b s t a n t i a l l y l o w e r t h a n i t s share o f a p p r o x i m a t e l y 29 p e r cent i n the p r e - d e p r e s s i o n e r a . The p r o p o r t i o n o f t o t a l expenses r e p r e s e n t e d by c u r r e n t i n p u t s f o l l o w s by a s i m i l a r i n c r e a s e d from 21.8 d e c l i n e d t o 22.6 by  p a t t e r n to t h a t of c a p i t a l . t o 28.2  The r e l a t i v e  p e r cent o v e r the p e r i o d 1926  p e r cent i n 1945,  and i n c r e a s e d t o 38.6  to per  share 1932,  cent  1958. Although the r e l a t i v e share o f c u r r e n t i n p u t s had d e c l i n e d  i n t h e immediate post-war y e a r s o f 1944 p o i n t o f i t s 1926  had i n 1926;  percentage  l e v e l , the subsequent i n c r e a s e i n the most r e c e n t  y e a r s o f the a n a l y s i s was it  and 194-5 t o w i t h i n 1  s i g n i f i c a n t l y above the r e l a t i v e  h a v i n g i n c r e a s e d from 21.8  p e r cent t o 38.6  When t h i s i n c r e a s e i s compared w i t h t h a t o f the r e l a t i v e  share which per cent.  share o f  capital  TABLE I FACTOR SHARES, CANADIAN AGRICULTURE, 1926-58  Including Land (Oo)  Year  Capital  < 2) Current Inputs K  ( 2) L  Labour  1926 1927 1928 1929 1930  .298 .292 .300 .301 .294  .218 .221 .229 .237 .255  .484 .487 .471 .462 .451  1931 1932 1933 1934 1935  .316 .333 .332 .317 .300  .262 .282 .277 .277 .271  .422 .385 .391 .406 .429  1936 1937 1938 1939 1940  .270 .248 .227 .223 .199  .267 .266 .271 .272 .251  .463 .486 .502 .505 .544  1941 1942 1943 1944 1945  .190 .180 .172 .158 .151  .264 .256 .236 .228 .226  .546 .564 .592 .614 .623  1946 1947 1948 1949 1950  .140 .145 .147 .153 .161  .230 .245 .2a .280 .312  .630 .ao .592 .567 .527  1951 1952 1953 1954 1955  .175 .172 .177 .176 .184  .327 .341 .353 .3a .376  .498 .487 .470 .463 .440  1956 1957 1958  .185 .184 .196  .384 .370 .386  .431 .437 .418  35.  i t must be observed c a p i t a l s i n c e 1946 o f 29.8  per  t h a t the most r e c e n t and l a r g e s t r e l a t i v e share i s s t i l l 10.2  percentage  p o i n t s belot* i t s 1926  of  share  cent.  The r e l a t i v e share o f l a b o u r has v a r i e d from a low o f p e r cent i n 1932 the r e l a t i v e  t o a h i g h o f 63 p e r cent i n 1946.  38.5  S i n c e the t o t a l o f  shares i s 100 p e r cent, l a b o u r ' s share has v a r i e d i n v e r s e l y  t o t h a t o f the o t h e r two  factors.  d e c l i n e d t o 38.5  p e r cent i n 1932,  d e c l i n e d t o 41.8  p e r cent i n  From 48.4  p e r cent i n 1926,  r o s e t o 63.0  the  p e r cent i n 1946,  share and  1958.  S i n c e t h e s h a r e s a r e dependent on the m a r g i n a l o f t h e f a c t o r as w e l l as the q u a n t i t y o f the f a c t o r the  productivity changing  r e l a t i v e s h a r e s i n d i c a t e the changing r e l a t i v e importance o f f a c t o r s i n the p r o d u c t i o n o f output.  The i n c r e a s i n g r e l a t i v e share o f c u r r e n t  i n p u t s r e p r e s e n t s the i n c r e a s e d importance o f s h o r t - t e r m c a p i t a l t o the industry.  T h i s i s r e f l e c t e d i n the i n c r e a s e d l e v e l o f use o f c u r r e n t  inputs. An e x a m i n a t i o n  o f the changes i n the q u a n t i t y o f the v a r i o u s  i n p u t s as compared t o the changes i n the r e l a t i v e shares i n d i c a t e s the type o f adjustment which changes i n t e c h n o l o g y have r e q u i r e d . These adjustments t o c a p i t a l , c u r r e n t i n p u t s , and l a b o u r r e s p e c t i v e l y , may  be observed i n Columns 2, 3 and 4 o f Table I I , which r e v e a l an  o v e r - a l l g r a d u a l i n c r e a s e i n the q u a n t i t y o f c a p i t a l i n use,  a  s u b s t a n t i a l i n c r e a s e i n t h e l e v e l o f c u r r e n t i n p u t s , and a l e s s s u b s t a n t i a l but n o t i c e a b l e d e c l i n e i n the q u a n t i t y o f l a b o u r i n u s e .  36. The 1926; 1958  q u a n t i t y o f c u r r e n t i n p u t s has more t h a n d o u b l e d s i n c e  however, from Table was  I , i t can be o b s e r v e d t h a t the share as a t  l e s s t h a n double i t s share as at 1926.  observations  Other s t r i k i n g  are the f a c t s t h a t a l t h o u g h the q u a n t i t y o f l a b o u r i n use  as a t 1958  had d e c l i n e d by n e a r l y 4-0 p e r c e n t , i t s share had  by o n l y 14  p e r c e n t , and t h a t the q u a n t i t y o f c a p i t a l had i n c r e a s e d  15 p e r cent, w h i l e i t s share had d i f f e r e n c e s between the  d e c l i n e d by 34  per cent.  declined by  The  changes i n the f a c t o r shares as compared t o  changes i n f a c t o r q u a n t i t i e s r e f l e c t some o f the e f f e c t s o f t e c h n o l o g i c a l change on the p r o d u c t i v i t y o f the f a c t o r s u s e d i n the a g r i c u l t u r a l i n d u s t r y , and the n a t u r e o f some o f the s t r u c t u r a l adjustments which had  taken place.  M i e n the q u a n t i t y o f c u r r e n t i n p u t s i s broken down i n t o i t s main components (Table I I I ) i t becomes e v i d e n t t h a t  significant  i n c r e a s e s have o c c u r r e d i n the p r o p o r t i o n o f annual cash expenses which are a s s o c i a t e d w i t h farm m e c h a n i z a t i o n and w i t h on  expenditures  fertilizer. On f u r t h e r e x a m i n a t i o n the reduced p r o p o r t i o n o f farm cash  expenses a s s o c i a t e d w i t h d e p r e c i a t i o n and i n c r e a s e s i n the a b s o l u t e  r e p a i r s showed s i g n i f i c a n t  c o s t o f farm machinery d e p r e c i a t i o n  r e p a i r s as w e l l as t h a t o f b u i l d i n g d e p r e c i a t i o n and r e p a i r s . i n the presence o f a d e c r e a s e d p r o p o r t i o n one  concludes t h a t  and Thus the  i n c r e a s e s i n the o t h e r o p e r a t i n g expenses have been g r e a t e r t h a n the i n c r e a s e s i n those expenses a s s o c i a t e d w i t h d e p r e c i a t i o n and r e p a i r s .  TABLE I I  INDICES: OUTPUT AND GROUPED INPUTS, CANADIAN  AGRICULTURE, 1926-58;  1926 = 100 (1)  Year 1926  (I) Output  (2)  (c ) 2  Capital  (3)  (4)  (K) Current Inputs  Labour  (L)  100.0 101.2  100.0 107.2 112.6 89.4 96.0  100.0 104.7 107.8 110.5 111.6  100.0 108.8 115.1 119.5 121.4  114.4 114.9  113.0 103.8  1933 1934 1935  77.9 100.0 88.8 91.0 99.6  113.9 114.7 112.6  100.7 100.4 100.8  106.2 106.2 110.2 110.9 113.5  1936 1937 1938 1939 1940  92.3 85.2 102.2 129.5 127.6  108.6 107.1 110.7 101.4 101.9  99.7 100.1 103.0 106.7 107.0  114.7 114.8 118.0 117.9 116.5  1941 1942 1943 1944 1945  112.1 161.8 113.5 137.2 109.2  96.4 99.8 102.6 102.0 104.2  110.1 116.1 121.7 127.0 135.3  99.8 91.9 88.2 99.2 99.1  1946 1947 1948 1949 1950  116.7 118.7 130,0 125.8 119.7  103.6 103.5 101.5 102.7 105.5  146.0 154.4 159.7 166.3 181.3  103.3 97.5 95.2 93.7 89.7  1951 1952  153.3 160.1  1953 1954 1955  163.4 129.3 149.6  107.5 108.7 109.2 110.6 110.8  190.7 193.9 204.3 206.4 211.9  81.5 77.0 75.2 76.0 70.9  1956 1957 1958  167.3 140.1 150.6  111.4 111.0  221.1 213.7 214.6  67.3 66.0 61.7  1927 1928 1929 1930  1931 1932  115.4  101.4 102.7 102.5  TABLE III  PERCENTAGE ANNUAL CURRENT NON-LABOUR COSTS FROM VARIOUS SOURCES, SELECTED YEARS, CANADA, 1926-56  Years Source  1926  1931  1936  1941  1946  1951  1956  (Percentages) Depreciation and repairs on farm buildings and" machinery  44.7 43.2  42.9  37.1  41.0  39.3 37.7  Tractor, truck, auto engine and combine expenses  17.1  21.2  22.4 27.2  23.9  28.3 28.8  Taxes  21.2  21.8  21.0 16.7 14.6 13.1' H - 6  .•  2.0  3.2  2.9  Miscellaneous expenses ..  15.0  10.6  10.8  Fertilizer cost  Source:  3.9  5.0  5.0  4.7  15.1 15.5 14*3' 14.2  Handbook of Agricultural Statistics Part II, Farm Income 1926-1957 (Revised Edition Reference paper No. 25-Part II), D.B.S., Agricultural Division, Farm Finance Section, pp. 68-69.  39.  The percentage declined. 1941  o f farm cash expenses made up o f t a x e s has a l s o  M i s c e l l a n e o u s expenses have been r e l a t i v e l y c o n s t a n t s i n c e  a t t h e i r 1926 l e v e l o f a p p r o x i m a t e l y 15 p e r cent, b u t d u r i n g t h e  d e p r e s s i o n m i s c e l l a n e o u s expenses were down t o 10 p e r cent o f c u r r e n t expenses.  Changes i n t e c h n o l o g y i n the a g r i c u l t u r a l s e c t o r , t h e r e f o r e ,  have been a s s o c i a t e d w i t h i n c r e a s e s i n t h e use o f f e r t i l i z e r and machinery.  The g r e a t e r i n c r e a s e o f o p e r a t i n g expenses r e l a t i v e t o  d e p r e c i a t i o n a l s o r e f l e c t s t h e i n t e n s i f i c a t i o n o f t h e use o f farm machinery.  Output-Input  R e l a t i o n s h i p s I n c l u s i v e o f Land  The d a t a from which the o u t p u t - i n p u t r e l a t i o n s h i p s may be c a l c u l a t e d , have a l r e a d y been p r e s e n t e d i n T a b l e I I .  Column 1 p r e s e n t s  i n d i c e s o f a c t u a l output which were c a l c u l a t e d from a g g r e g a t i n g t h e d e f l a t e d d o l l a r v a l u e s o f each t y p e o f o u t p u t , and b y e x p r e s s i n g t h e d e f l a t e d aggregate o f d o l l a r v a l u e s i n terms o f a r e l a t i v e i n which t h e v a l u e as a t 1926 was s e t a t 100.  This quantity index f o l l o w s reasonably  c l o s e l y the p u b l i s h e d Index o f P h y s i c a l Volume o f A g r i c u l t u r a l P r o d u c t i o n . The i n d e x c a l c u l a t e d i n t h i s study i s , l e s s t h a n t h e p u b l i s h e d s e r i e s i n 1953,  1954, and 1958,  5 percentage  t h e c a l c u l a t e d i n d e x i s r e s p e c t i v e l y 6, 10, and  points higher.  The i n d i c e s o f c a p i t a l , c u r r e n t i n p u t s , and l a b o u r i n p u t r e s p e c t i v e l y a r e p r e s e n t e d i n Columns 2, 3, and 4» The  c a l c u l a t e d p r e d i c t e d output  (hence  composite  input i n t h i s  study, Z2.) from each p r o d u c t i o n f u n c t i o n i s p r e s e n t e d i n Table IV, Column 2.  The d i f f e r e n c e between t h e marked v a r i a b i l i t y o f output and  the l e s s marked v a r i a b i l i t y o f t h e c a l c u l a t e d j o i n t i n p u t i s n o t i c e a b l e .  AO.  iii though the effect of changes i n technology i s to alter output-input ratios an exogeneous variable such as r a i n f a l l may markedly affect the ratio i n any single year.  Consequently, since the  choice of a production function i s based on rational considerations, and since the possible effects of the exogeneous variables enter into the decision-making process of the entrepreneur, although i t may be reasonable to assume that their effects are randomly distributed i n the long run, the effects of changes i n technology are best studied by observing whether there has been any pattern i n output-input relationships, and what changes have occurred i n the pattern. These output-input relationships showing the calculated annual values of the average as well as the marginal productivity of each of the three independent variables used i n each of the production functions that had been determined, are presented i n Table 17,and i n Tables IX, and X, Appendix A.  Table IV, however, shows figures  representing the average product of composite and particular inputs. Output has increased beyond i t s 1926 level.  Under conditions  of diminishing returns and constant technology, when output i s increasing average and marginal products are inverse functions of the quantity of the particular resource i n use.  That being the case since  the quantity of labour i n use had declined over the period of the analysis, i n these circumstances i t follows that i t s average and marginal productivities would show a positive change. If technology i s changing, an increase i n the quantity of any input need not result i n a decline i n i t s average or marginal productivities, and changes i n the marginal productivities need not be  41. p r o p o r t i o n a l t o changes i n the average p r o d u c t i v i t i e s . t e c h n o l o g i c a l i n n o v a t i o n s w i l l i n c r e a s e the m a r g i n a l  Labour s a v i n g  productivity  o f l a b o u r more than the m a r g i n a l p r o d u c t i v i t y o f o t h e r i n p u t s ; and i n n o v a t i o n s which are '"very l a b o u r s a v i n g " w i l l be accompanied a r e d u c t i o n o f the q u a n t i t y o f l a b o u r i n use. saving" innovations w i l l  The  These " v e r y l a b o u r  c o n t r i b u t e s i g n i f i c a n t l y t o i n c r e a s e s i n the  average p r o d u c t i v i t y o f l a b o u r . f a c t o r s may  by  The  average p r o d u c t i v i t y o f o t h e r  a l s o be i n c r e a s e d . e f f e c t s o f the t e c h n o l o g i c a l i n n o v a t i o n s which had  been  adopted by the a g r i c u l t u r a l i n d u s t r y can be seen i n Table IV.  Those  p e r i o d s i n which the o u t p u t - i n p u t r a t i o s had been d e c l i n i n g show the f a c t o r u s i n g nature o f the i n n o v a t i o n s which were adopted. s a v i n g nature o f i n n o v a t i o n s may  be observed  The  from t h e r e l a t i v e  factor changes  i n the average and the m a r g i n a l p r o d u c t i v i t i e s o f f a c t o r s , i n t h a t these w i l l be  raised.  The lowered t o 1937  o u t p u t - i n p u t r a t i o s o f a l l f a c t o r s f o r the  p e r i o d are due p r i m a r i l y t o the low l e v e l o f o u t p u t .  1929 Column 1  shows the h i g h v a r i a b i l i t y o f output, whereas Column 2 shows t h a t composite i n p u t ha3 v a r i e d between v e r y narrow l i m i t s . as a whole i s examined, Table IV shows t h a t output o f 50.6  is  shot-red a n e t change  p e r cent, whereas composite i n p u t showed one  g i v i n g an i n c r e a s e o f 33.3  When the p e r i o d  o f 12.9  per  p e r cent i n t h e o u t p u t - i n p u t r a t i o s .  cent It  a l s o i n t e r e s t i n g t o note t h a t the peak y e a r s d i f f e r f o r each o f  t h e s e t h r e e s e r i e s r e p r e s e n t e d i n Columns 1, 2, and 3: the r e s u l t s o b t a i n e d f o r the y e a r 1942  however, i f  are r e g a r d e d as abnormal i t can  be observed from these columns t h a t the g r e a t e r p r o p o r t i o n o f the i n c r e a s e i n p r o d u c t i v i t y has been a c h i e v e d subsequent t o the y e a r  1950.  TABLE IV INDICES} OUTPUT, COMPOSITE INPUT, COMPOSITE AND PARTICULAR OUTPUT-INPUT RATIOS, CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1) Y  (2)  S V  Composite Input  (3)  (4)  I/K V  100.0 102.4 104.5  70.50 92.34 81.77 83.49 90.96  68.1 87.0 78.0  68.9  73.4  96.3 88.2  94.1  79.3 88.5  90.6 98.8  87.76 78.31 91.17 116.88 115.16  85.0  92.6  79.6 92.3 127.7 126.3  85.1 99.2 121.4 119.3  80.5 74.2 86.6 109.8 109.5  110.77 163.43 116.17 130.17 101.96  116.2 162.1 110.6 134.5 104.8  101.8 139.4 93.3 108.0 80.7  112.3 176.1 128.7 138.3 110.2  112.6  79.9  112.8 121.7 136.6 134.3 133.4  100.0 107.2 112.6 89.4 96.0  1931 1932 1933 1934 1935  77.9 100.0 88.8 91.0 99.6  110.5 108.3 108.6  1936 1937 1938 1939 1940  92.3 85.2 102.2  108.9  1941 1942 1943 1944 1945  112.1 161.8 113.5 137.2 109.2  101.2  1946 1947 1948 1949 1950  116.7 118.7 130.8 125.8 119.7  111.0 110.0 110.0 111.6 114.7  105.14 107.91 118.91 112.72  1951 1952  113.0  135.66  111.9 114.3  143.07  1953 1954 1955  153.3 160.1 163.4 129.3 149.6  1956 1957 1958  167.3 140.1 150.6  129.5 127.6  109.7  109.0 109.5  108.8 112.1 110.8 110.8  99.0 97.7 105.4 107.1  116.4 116.2  114.8 113.4  112.9  H  100.00 103.28 106.73 82.17 87.51  1926 1927 1928 1929 1930  105.5 108.8  v  OutputCapital Ratio  Output  103.8  2  OutputCurrentInput Ratio  (6)  OutputInput Ratio  Year  100.0  (5)  80.9 86.0  100.0 98.5 97.8 74.8 79.1  OutputLabour Ratio 100.0  105.9 111.0 87.0 93.7  80.6 82.1 87.8  114.7  76.9  128.1 122.5 113.5  81.4 75.6 66.0 80.4 82.5 80.0 62.6 70.6  188.1  142.96 111.08 128.74  142.6 147.3 149.6 116.9 135.0  145.73 123.54 133.39  150.2 126.2 130.5  75.6 65.6 70.2  248.6 212.3 244.1  104.36  207.9 217.3 170.1 211.0  43. The "very labour saving" nature of technological innovations may be observed from the results recorded in Column 6 of Table IV. Since 1946 the average productivity of labour has shown marked increases, the index of average product having moved from 112.8 in 1946 to 244*1 in 1958, a net increase over the thirteen year period of 131.3 percentage points, and at an average annual increase of 10.1 per cent of i t s 1926 level.  When the period as a whole was examined the average  productivity of labour showed a net increase of 144*1 per cent.  This  long-period increase in contrast to that just presented for the 1946 to 58 period provides an average annual increase of approximately 4.37 per cent of the 1926 level. The data in Column 6 which has just been examined- may be contrasted with those results shown in Columns 4 and 5.  The fact that  output had increased at a faster rate than that of the increase in the quantity of capital in use, while i t was at the same time increasing at a slower rate than the quantity of current inputs in use, may be deduced from the increasing average productivity of capital and the declining average productivity of current inputs. For the period as a whole the net increase of 30.5 per cent in the average productivity of capital may be contrasted with the net decrease of 29.8 per cent in the average productivity of current inputs. Additional comparisons may be made between the increase of 7.9 percentage points since 1946 in the average productivity of capital with the decline of 9.7 percentage points in the average productivity of current inputs for the same period. These changes when viewed with those that have already been observed for labour point to the heavy reliance of  44. agricultural industry on short term investment which i s measured i n this study as current inputs. A very instructive contrast i s also provided by examining the close relationship displayed here i n the changes of the over-all productivity (Column 3) and those of capital i n the two forms capital stock, and current input; i.e., long term capital, and short term investment with depreciation. This relationship i s seen i n the fact that over-all productivity as measured here showed a net increase of 33.3 per cent; and this may be compared with a closely similar net increase of 30.5 per cent i n the average productivity of capital, and the similar amount but negative change of 29.8 per cent i n the average productivity of current inputs. Measuring Technological Change When Land i s Excluded In this section the analytical procedure w i l l be similar to that used previously i n this study.  The modification which w i l l be  introduced i s that capital as measured here w i l l be the figure derived from aggregating i n constant 1935-39 dollars the value of machinery and livestock.  Since the value buildings and other improvements to  land are included i n the reported value of land, when this data for land was removed from the value of capital used i n the previous section, that of buildings and other improvements, unfortunately, was also removed. Changes i n technology are instrumental i n causing variations i n the quantity and quality of machinery and livestock which are combined with a given quantity of land.  Variations of capital i n the  form of machinery and livestock are therefore sensitive to changes i n technology.  £5.  Mth o f c a p i t a l was increased.  the v a l u e o f l a n d and b u i l d i n g s removed the r e l a t i v e  share  d i m i n i s h e d and t h a t o f the o t h e r i n p u t s a c c o r d i n g l y  As the q u a n t i t y o f l i v e s t o c k and machinery i n c r e a s e s , o t h e r  t h i n g s b e i n g e q u a l , the share o f c a p i t a l i n c r e a s e s .  However, under the  assumptions o f the model used i n t h i s a n a l y s i s t h i s cannot be the  case  u n l e s s the i n c r e a s e i n the q u a n t i t y o f c a p i t a l i s a c h i e v e d under c o n d i t i o n s o f c o n s t a n t , o r i n c r e a s i n g m a r g i n a l p r o d u c t i v i t y ; so t h a t  an  i n c r e a s e i n the q u a n t i t y o f c a p i t a l does n o t a u t o m a t i c a l l y l e a d t o an i n c r e a s e i n i t s share. Each t a b l e which i s p r e s e n t e d i n t h i s s e c t i o n compares w i t h a s i m i l a r one i n the s e c t i o n p r e v i o u s l y p r e s e n t e d .  Table V, g i v e s the  s h a r e s which were c a l c u l a t e d n e t o f l a n d , and compares w i t h Table I . I n t h i s t a b l e i t can be o b s e r v e d t h a t the share o f as a t 1958 it  was  a p p r o x i m a t e l y the same as i t s share as a t 1926,  had v a r i e d o y e r t h e p e r i o d , h a v i n g f i r s t i n c r e a s e d and  d e c r e a s e d t o l o w e r than i t s 1926  may  subsequently level.  a share s i m i l a r t o what i t had i n  be compared w i t h the l o w e r t h a n 1926  t o t a l c a p i t a l s t o c k as a t 1958,  although  l e v e l before i t returned to t h i s  T h i s phenomenon o f h a v i n g i n 1958 1926  capital  l e v e l o f the share o f  i n o r d e r t o observe one o f the  effects  o f the change i n t h e method o f measurement. The r e l a t i v e  share o f l a b o u r i n 1926  a l t h o u g h b e i n g 15 p e r -  centage p o i n t s h i g h e r than i t s share which was  c a l c u l a t e d i n Table I ,  d e c l i n e d by 1958  t o w i t h i n 6 percentage p o i n t s o f i t s share i n t o t a l  i n p u t s i n c l u s i v e o f l a n d (as shown i n Table I ) .  T h i s p r o v i d e s an  i n d i c a t i o n o f the s u b s t a n t i a l i n c r e a s e i n the p r o d u c t i v i t y and o f the non l a b o u r i n p u t s .  importance  46. The relative share of current non-labour inputs shows an increase i n Table V above i t s 1926 levels. Since the relative shares are also the coefficients of the elasticity of productivity, with the exclusion of land the elasticity of production of labour had declined over the years.  This has been  especially so since 1946. The elasticity coefficients (and hence also the shares) of a l l factors had been continually changing over the period of the analysis; and these changing coefficients reflect the changing emphasis which changes in. technology exert on factor inputs. Output Input Relationships Net of Land Since capital i s the only variable which i s measured differently i n this section the average productivities of labour inputs and current inputs w i l l be identical with those recorded earlier. Table VI, except for Column 1, presents data which have not been put forward earlier i n this thesis.  Column 2 records the calculated  quantities of composite input net of land and i s analogous to a similar column which has been presented earlier i n Table IV.  Columns 3  and 5 of Table VT, also compare with Columns 3 and 4 respectively of Table IV.  The remaining column of Table VI (Column 5), i s analogous  to Column 2 of Table II. On analyzing each column of Table VI i n turn, the following comparisons may be made with the data previously studied. Column 1 which records observed output i s unchanged from the data examined earlier since i t i s the identical series.  The net change  i n composite inputs can be observed i n Column 2, and this for the entire period as a whole was approximately two percentage points higher i n the  TABLE V FACTOR SHARES, NET OF LAND, CANADIAN PRIMARY AGRICULTURAL SECTOR, 1926-58 Excluding Land ~  (Ci)  (%)  (LIT"  Year  Capital  Current Inputs  1926 1927 1928 1929 1930  .085 .082 .090 .092 .090  .285 .287 .298 .307 .328  .630 .631 .612 .601 .582  1931 1932 1933 1934 1935  .093 .102 .102 .094 .092  .347 .380 .372 .367 .351  .560 .518 .526 .529 .557  1936 1937 1938 1939 1940  .084 .078 .073 .074 .068  .335 .326 .325 .324 .299  .581 .596 .602 .602 .633  1941 1942 1943 1945  .063 .064 .067 .059 .056  .305 .292 .266 .255 .251  .632 .644 .667 .686 .693  1946 1947 1948 1949 1950  .052 .055 .056 .063 .069  .254 .271 .289 .310 .346  .694 .674 .655 .627 .585  1951 1952 1953 1954 1955  .081 .078 .076 .075 .077  .364 .380 .396 .405 .425  .555 .542 .528 .520 .498  1956 1957 1958  .076 .076 .083  .436 .427 .441  .488 .497 .476  1944  Labour  48.  new  s e r i e s p r e s e n t e d here t h a n t h a t which was  inputs i n c l u s i v e of land.  o b s e r v e d f o r composite  There i s here a l a r g e r d i f f e r e n c e  c a l c u l a t e d i n d i c e s o f composite i n p u t s f o r the y e a r s 1950 those d i f f e r e n c e s  o f the  per  cent above i t s 1926  r e c o r d e d i n T a b l e IV. o f composite i n p u t , p r o d u c t i v i t y are  the  estate  l e v e l s as compared w i t h the  i n t h i s case  12.9  per  cent  buildings.  excluded  This i s p a r t i c u l a r l y true of  the  change i n o v e r - a l l p r o d u c t i v i t y here o f 31.4 o f 33.4  which was  per  observed e a r l i e r .  much more s i g n i f i c a n t change i n the  quantity  o f non  real  c a p i t a l t h a n t h a t o f t o t a l c a p i t a l becomes e v i d e n t when Column 4  net i n c r e a s e  of 4 2 . 9  the l a t t e r one  per  o f 15.4  cent o v e r i t s 1926  per  measures o f c a p i t a l i n p u t of c a p i t a l accordingly; i n c l u s i v e o f l a n d was  land  net  s l i g h t l y higher l e v e l s  o f Table V I i s compared w i t h Column 2 o f Table I I .  the  The  s l i g h t l y narrower f o r t h i s s e r i e s which has  A net  from  output-input r a t i o s i n d i c a t i n g o v e r - a l l  cent, compares w i t h one The  however, was  As a consequence o f the  the v a l u e o f l a n d and 1950-56 p e r i o d .  entire period,  the  t o 1956  d a t a which were p r e s e n t e d e a r l i e r .  change i n j o i n t i n p u t f o r the 14  in  cent.  The  I n the  average  average p r o d u c t i v i t y o f c a p i t a l s t o c k  c a p i t a l i s e v i d e n t from the f a c t t h a t  p r o d u c t i v i t y o f c a p i t a l net o f l a n d may  change i n the method o f measuring the  s i n c e 1946  In f a c t ,  those o f  the  non  average  be r e g a r d e d as f l u c t u a t i n g around  d a t a from t h i s s e c t i o n o f the  changes are not  productivity  h i g h e r t h a n t h a t o f c a p i t a l net o f l a n d .  s l i g h t l y the i n d e x o f the  in  d i f f e r e n c e s i n the l e v e l s o f t h e s e  c l o s e r e l a t i o n s h i p between the l e v e l s o f output and  The  the  l e v e l s i s r e c o r d e d , and  a f f e c t e d the measure o f the  i n t h a t the  former  analysis, indicate that  quantity  the  of capital affects  amount o f c a p i t a l i n use.  g r e a t enough t o s e r i o u s l y a f f e c t the  The  resulting  over-all  productivity  1.  TABLE V I INDICES; OUTPUT, COMPOSITE INPUT, COMPOSITE AND PARTICULAR OUTPUT-INPUT RATIOS, NET OF LAND, CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1)  (2)  (VT  (I)  Tear  Output  1926 1927 1928 1929 1930  100.0 107.2 112.6 89.4 96.0  1931 1932 1933 1934 1935  77.9 100.0 88.8 91.0 99.6  1936 1937 1938 1939 1940  92.3 85.2 102.2 129.5 127.6  1941 1942 1943 1944 1945  (3)  (4) )  Composite Input  Output-Input Ratio  100.0  100.00 103.08 105.93  104.0 106.3 108.6 109.0 109.0 105.7 106.3 105.4 108.2  71.47  111.4  98.0 105.9  69.9 99.2 78.6 92.9 94.1  105.4 103.4 99.2 106.6 107.2  87.6 82.4 103.0 121.5 119.0  94.3 99.4 114.1 115.1 118.6  118.9  102.64 106.08 116.18 110.25 101.53  120.1  97.2  123.6  96.0 109.0 99.6 86.4  131.70 138.98 138.83 108.36  145.4  94.16  83.15 86.34  92.05 84.99  113.02  112.1 161.8 113.5 137.2 109.2  101.8  110.12 163.60 113.73 128.71  1946 1947 1948 1949 1950  116.7 118.7 130.8 125.8 119.7  113.7 111.9 111.9  1951 1952 1953 1954 1955  153.3 160.1 163.4 129.3 149.6  116.4 115.2 117.7 119.7  124.98  1956 1957 1958  167.3  119.8 115.4 114.6  121.40  140.1 150.6  117.9  119.3  Output-Capital Ratio  88.07  82.32  114.30  114.1  Capital  100.0 98.1 100.3 78.6 87.8  112.9  106.6 108.2  (Oj.)  100.0 109.3 112.3 113.8 109.3  108.6 108.9 111.5 113.3  98.9 99.8  (5)  78.07 91.66  100.92  139.68 131.41  110.9 113.0  118.3 126.3 138.6  150.0 150.2 151.4 152.5 145.3 140.6 142.9  126.8  99.5 119.2  92.1  105.4 106.7 108.8 85.4 98.1 115.1 99.6 105.4  50  measurement.  However, t h e changes i n the average p r o d u c t i v i t y o f c a p i t a l  when l a n d i s e x c l u d e d a r e d i f f e r e n t from those changes o b s e r v e d by t h e o t h e r method.  An  Evaluation  o f t h e Two Methods Used  T a b l e s IV and V I i n d i c a t e t h a t  so f a r , t h e p r i n c i p a l  d i f f e r e n c e between t h e two methods o f measuring t h e q u a n t i t y i s t h a t when c a p i t a l i s measured e x c l u s i v e smaller  o f land the r e s u l t i s a  change i n the average p r o d u c t i v i t y o f non r e a l e s t a t e  than that o f t o t a l c a p i t a l .  of capital  capital  The n e t change i n o v e r - a l l p r o d u c t i v i t y  between 1926 and 1958 was v e r y s i m i l a r i n both c i r c u m s t a n c e s a l t h o u g h the  d a t a from b o t h methods p r o v i d e d i f f e r e n t e s t i m a t e s o v e r t h e 1950  t o 1956 p e r i o d . A change i n t h e p r o d u c t i o n f u n c t i o n has been the c r i t e r i o n which t h i s a n a l y s i s has r e g a r d e d as b e i n g i n d i c a t i v e o f t e c h n o l o g i c a l change. evident  The e f f e c t s o f t h e changes i n t h e p r o d u c t i o n f u n c t i o n a r e n o t i n t h e o b s e r v e d changes i n t h e average p r o d u c t o f each f a c t o r ,  because t h e r e s u l t s would have been t h e same whether t h e p r o d u c t i o n f u n c t i o n had remained s t a t i o n a r y o r n o t .  The p r i n c i p a l e f f e c t o f t h e  d i f f e r e n c e i n t h e methods o f measurement, may be o b s e r v e d by comparing the  former r e s u l t s w i t h t h o s e which were o b t a i n e d when the m a r g i n a l  p r o d u c t i v i t y o f f a c t o r s was c a l c u l a t e d . by t h e r e s u l t s p r e s e n t e d i n Table V I I . be made from t h e r e s u l t s r e p o r t e d  T h i s comparison i s f a c i l i t a t e d An analogous comparison may a l s o  i n T a b l e X, Appendix A.  Table V I I r e c o r d s the c a l c u l a t e d i n d i c e s which show how much change o c c u r r e d i n t h e p r o d u c t i v i t y o f the m a r g i n a l u n i t s as t e c h n o l o g y changed.  These i n d i c e s may be compared w i t h those which showed the  51  change i n the average productivity of each factor. Over-all productivity has been already presented, and from the calculations made the conclusion has been drawn that the inclusion or the exclusion of land did not significantly affect the measure of the extent of the change i n over-all productivity.  Table VII also indicates the changes  which have been observed i n the marginal productivity of factor inputs when land was included i n total capital, and also when i t was excluded. Within each method Golumns 1 and 4 respectively indicate that the change i n the marginal productivity of capital has been less than that of other inputs.  The change i n that of labour was the greatest;  and this i s bourne out i n Columns 3 and 6« This result, i s different from that observed earlier, i n that i t was current inputs and not capital which had shown the smallest increase i n average productivity; and i n fact, this change was a decline rather than the observed increase i n marginal productivity which i s recorded here. Betx/een method comparisons, show that the net change i n the marginal productivity of capital stock net of land was not as great as that for total capital stock.  The marginal physical productivity of  labour, and current inputs, was higher when capital included land; and this result i s similar to that observed for the average productivity. The net change for current inputs was 24.3 per cent over i t s 1926 level i n the one case, and 8.6 per cent i n the other case when capital was measured net of land.  ii/hen total capital was considered, the net change  i n the marginal productivity of labour was 110.8 per cent above i t s 1926 level; inhereas the net change of i t s marginal product when land and buildings were removed was 85.6 per cent above i t s 1926 level. The comparisons made from the method of measurement which deletes the value  52.  o f l a n d and  b u i l d i n g s from c a p i t a l s t o c k , i n d i c a t e a more t h a n  favourable  adjustment p r o c e s s i n the a g r i c u l t u r a l s e c t o r i n so f a r as the use c a p i t a l i s being  considered.  Column 1 shows t h a t the new  p o s i t i o n s t o which the farm s e c t o r had moved, had  equilibrium  been a t t a i n e d w i t h  l e s s e r s a c r i f i c e i n the p r o d u c t i v i t y o f a d d i t i o n a l u n i t s o f  capital  t h a n those s a c r i f i c e s o f p r o d u c t i v i t y as the output expands t h a t suggested by Column 4* the  be  drawn as r e g a r d s the p r o d u c t i v i t y o f the  a v a i l a b l e stock o f The  conclusions  additions to  1929  t o 1938  v a r i a t i o n s which are o b s e r v a b l e i n each column o f  t o exogeneous v a r i a b l e s .  I t i s noticeable  t e c h n o l o g y o v e r the p e r i o d were l a b o u r u s i n g . s a v i n g t e c h n o l o g i c a l changes o f the 1946  On  t o both  t h a t i n the  p e r i o d the m a r g i n a l p r o d u c t i v i t y o f l a b o u r was  t h a t o f the o t h e r i n p u t s , and t h u s i n d i c a t e s t h a t the  labour  the  resources.  T a b l e V I I p o i n t t o the e f f e c t s o f changes which have been due t e c h n o l o g y and  are  These v a r y i n g r e s u l t s t h e r e f o r e i n d i c a t e t h a t  c h o i c e o f the method o f measuring c a p i t a l does a f f e c t the  which may  of  l o w e r than  changes i n  the o t h e r hand, the  t o 1958  period  are  r e v e a l e d i n the s u b s t a n t i a l changes t h a t the m a r g i n a l p r o d u c t i v i t y o f l a b o u r has made from i t s 1926 The  level.  e f f e c t s o f t e c h n o l o g i c a l change may  r e l a t i o n s h i p s between the  c a l c u l a t e d changes i n the  o f c u r r e n t i n p u t s o v e r the p e r i o d 1946  t o 1958,  changes o f i t s m a r g i n a l p r o d u c t i v i t y o v e r the  and  a l s o be o b s e r v e d i n the average p r o d u c t i v i t y the  calculated  same p e r i o d .  The  when measured i n c l u s i v e o f l a n d , showed a n e t d e c l i n e o f 9.7 p o i n t s o v e r the p e r i o d , h a v i n g gone from an i n d e x o f 79.9 whereas the o t h e r  (marginal  one  percentage  t o one  o f 70.2j  p r o d u c t i v i t y ) showed a n e t i n c r e a s e o f  percentage p o i n t s , by h a v i n g gone from an i n d e x o f 84.3  t o one  4-0  o f 124.3.  TABLE VTI RELATIVES^ MARGINAL .PHYSICAL.AND VALUE PRODUCT OF FACTOR INPUTS, CANADIAN AGRICULTURE, 1926-58,1926 = IOO (1)  (2) EXCLUDING LAND  M.P. P. Capital (Ol)  M.P. P. Current Inputs  (71  M  (3)  INCLUDING LAND  M.P.P. Labour  M.P. P.  M.P.P. Current  Capital  M.P. P.  Inputs  Labour  (%)  (Ll)  (C )  (K )  (L )  2  2  M.V.P. C,K,L,  2  1926  100  100  100  100  100  100  1927 1928 1929 1930  94.6 106.2 85.1 92.9  99.2 102.2 80.6 91.0  106.1 106.9 883.0 86.5  100.3 106.1 81.7 86.5  99.9 102.8 81.3 84.8  106.5 108.0 83.0 92.5  99.4 99.7 81.2 80.8  83.9 128.4 115.1 116.7 121.7  65.2  71.3 97.2 86.9 84.4 89.1  82.8  64.0 74.8 65.1 68.9 77.8  64.3 71.4 69.4 82.6 85.1  108.8 97.3  74.2 70.2 82.7  77.0 74.5 89.4  86.2 93.2 98.2  114.6 123.1  104.4  126.7 205.2 157.4 175.5  99.6 139.8 109.7 123.6 100.7  146.8  108.4 103.1 128.5 120.3  1931 1932 1933 1934 1935  76.5 108.2 , 94.4 102.7 101.9  77.4 67.3 70.2 77.6  124.6 112.1 115.1 122.8  100  138.0 125.-2  109.6  77.0 66.2 70.3 95.0 84.3  122.6 78.4 82.7 60.7  108.9 142.8 87.1 96.6 71.1  112.7 180.0 136.3 150.6 121.2  74.1 97.9 64.0 71.3 53.1  1946 1947 1948 1949 1950  59.4 62.1 72.4 73.8 70.1  71.2 73.1 82.5 82.2 80.1  124.3  52.9 55.8 63.2 62.9 61.3  84.3 86.4 97.5 97.1 94.4  153.4 167.1 157.3  1951 1952 1953 1954 1955  100.5 97.9 97.3 75.3 88.8  102.7 110.0 111.2 88.9 105.3  165.7 178.9 182.1  83.8 85.0 88.8 69.0  120.6 129.0 129.5 103.7 121.8  193.5 209.1 211.0 162.7 191.8  141.8  1956 1957 1958  102.9 89.1 102.9  115.6 98.3 108.6  192.6 167.5 185.6  133.1 114.0  221.4 191.7 210.8  123.2  1936 1937 1938 1939 1940  86.6 75.6 111.6 105.7 95.2  1941 1942 1943 1944 1945  88.1  113.1  104.9  130.2 142.0 143.3  123.9  140.4 166.8  83.4 93.3 77.9 85.6  113.4 103.8 123.3 151.5 140.6 123.3 163.7 101.0 112.9 83.6  124.3  141.8  145.2  100.0  114.8 140.1 125.8 102.6 117.2  104.2 117.0  54. Column 7 records the changes i n the marginal value productivities of the factor inputs. These were calculated from inserting the current dollar values of each factor i n the production function.  It shows that the changes i n the physical product of each  factor have been i n most cases greater than the value change. Summary Tables I, and V, show that the relative shares of the factors have been changing.  Under the criterion used i n this analysis these  changes indicate the shifts which have taken place i n the production function.  Tables IV, and VI, indicate that the inclusion or the  exclusion of land does not substantially affect the calculated measure of joint productivity, i n that i n the one case a net change of 33.4 per cent above the 1926 level was recorded, and i n the other case one of 31.4 per cent.  Both methods of calculating capital show that the  greatest proportion of this increase (approximately 28.5 per cent above 1926) has been achieved since 1946. In view of the two abnormal economic periods (the Great Depression, and Tforld ¥ar II) which preceded 1946, i t i s unwise to draw any conclusions as regards the efficiency of operation of the agricultural industry as a whole between the years 1926 and 1945.  The  data must be regarded as indicating the adjustments which were effected under the conditions which these two periods imposed on the industry. The changes i n technology have had a positive effect on the productivity of factors used i n the agricultural sector. These changes have been accompanied by substantial increases (115 per cent) i n the use of current inputs (Table II)j and these inputs have'been chiefly associated with the expenses associated with farm mechanization, and  55.  a l s o w i t h use o f f e r t i l i z e r  (Table I I I ) .  Other changes have been n e t  i n c r e a s e i n the amount o f machinery and l i v e s t o c k o f a p p r o x i m a t e l y cent  above i t s 1926 l e v e l  43 p e r  (Table V I ) j and t h i s has been a s s o c i a t e d w i t h  a net d e c l i n e o f approximately  28 p e r cent i n the q u a n t i t y o f l a b o u r i n  use. The s h i f t s i n the p r o d u c t i o n f u n c t i o n s have been i n s t r u m e n t a l i n combining more r e s o u r c e s w i t h l a n d a t h i g h e r l e v e l s o f o v e r - a l l efficiency  (Table IV, Column 4$ and Table V I I , Columns 5 and 6 ) .  The  r e s u l t s o f the i n v e s t i g a t i o n have s u b s t a n t i a t e d the main h y p o t h e s i s o f t h i s t h e s i s ; i n t h a t t e c h n o l o g i c a l change has had a p o s i t i v e e f f e c t on the p r o d u c t i v i t y o f f a c t o r s used i n the a g r i c u l t u r a l s e c t o r o f the Canadian economy.  BIBLIOGRAPHY A.  A c k l e y , Gardner. Macroeconomic Company, 1961.  BOOKS  Theory.  New  York:  The M a c m i l l a n  American Economic A s s o c i a t i o n . Readings i n the Theory o f Income Distribution. E d i t o r s , F e l l n e r , W i l l i a m , and Haley, Bernard P. A r t i c l e s number 8, 9, 10, 20, and 21. P h i l a d e l p h i a : The B l a c k s t o n Company, 1951. . Readings i n P r i c e Theory. E d i t o r s , S t i g l e r , George J . , and B o u l d i n g , Kenneth E. A r t i c l e s number 9, 11, and 12. Baumol, W i l l i a m J.- Economic Dynamics. M a c m i l l a n Company, 1959.  C l i f f s , N.J.:  2nd E d i t i o n .  Nex* York:  Economic Theory and O p e r a t i o n s A n a l y s i s . P r e n t i c e - H a l l , Inc. 1961.  The  Englewood  Bohn^-Bawerk, Eagene von. P o s i t i v e Theory o f C a p i t a l . Translated with a P r e f a c e and A n a l y s i s by W i l l i a m Smart. New York: G.E. S t e c h e r t & Company, 1923. B o u l d i n g , Kenneth. Economic A n a l y s i s , t h i r d e d i t i o n . Harper & B r o t h e r s , 1955.  New  York:  Chamberlain, Edward H a s t i n g s . Towards a More G e n e r a l Theory o f V a l u e . New York: O x f o r d U n i v e r s i t y P r e s s , 1957. Clemmence, R i c h a r d V., and Doody, F r a n c i s S. The Schumpeterian Cambridge 42, Mass.: Addison Wesley P r e s s , I n c . , 1950.  System.  Conference on Research i n Income and Wealth. Input-Output A n a l y s i s ; An A p p r a i s a l . - S t u d i e s i n Income and Wealth, Volume E i g h t e e n . A r e p o r t o f t h e N a t i o n a l Bureau o f Economic Research, New York. P r i n c e t o n : P r i n c e t o n U n i v e r s i t y P r e s s , 1955. Croxton, F r e d r i c E., and Cowden, J . J . A p p l i e d G e n e r a l S t a t i s t i c s , 2nd e d i t i o n . New York: P r e n t i c e - H a l l , I n c . , 1955. Davidson, P a u l . T h e o r i e s o f Aggregate Income D i s t r i b u t i o n . Rutgers U n i v e r s i t y P r e s s , 1959. D a v i s , Hiram S. P r o d u c t i v i t y Accounting. P e n n s y l v a n i a P r e s s , 1955.  Philadelphia:  Douglas, P a u l H. The Theory o f Wages, New Company, 1934-  York:  Fellner, U l l i a m . Modern Economic Book Company, I n c . , I960.  Analysis.  New  New  Jersey:  University of  The M a c m i l l a n  York:  McGraw-Hill  57. Fossati, Eraldo. The Theory of General Static Equilibrium. Shackle. Oxford: Basil Blackwell, 1 9 5 7 . Friedman, Milton. Essays i n Positive Economics. University of Chicago Press, 1 9 5 3 .  BI., G.L.S.:  Chicago: The  Heady, Earl 0 . Economics of Agricultural Production and Resource Use. Euglewood C l i f f s , N.J.: Prentice-Hall, Inc., 1 9 5 2 . Henderson, James M., and Quandt, Richard E. Microeconomic Theory. New York: McGraw-Hill Book Company, Inc., 1 9 5 8 . Hicks, J.R.  The Theory of Wages. London: Macmillan & Co., Limited,  1932.  . Value and Capital, second edition. University Press, 1 9 3 9 . Higgins, Benjamin. Economic Development. Company, Inc., 1 9 5 9 .  London: Oxford  New York: 3ff.\W. Norton &  Hood, Win. C , and Scott, A.D. Output, Labour and Capital i n the Canadian Economy. Ottawa: Queen's Printer, 1 9 5 7 . Jevons, William S. The Theory of Political Economy. Third Edition. London: Macmillan & Co., Limited, 1 8 8 8 . Keynes, J.M. The General Theory of Employment Interest and Money. London: Macmillan & Co., Limited, 1 9 3 6 . Knight, Frank. Risk Uncertainty and Profit. M i f f l i n Company, 1 9 2 1 . Learner, Abba P.The Economics of Control. Company, 1 9 4 6 .  New York: Houghton New York:  The Macmillan  Leftwich, Richard. The Price System and Resource Allocation. Revised Edition. New York: Holt, Rinehart and Weston, I 9 6 0 . Leontief, Wassiley 1W., and others. Studies i n the Structure of the American Economy. New York: Oxford University Press, 1 9 5 3 . Marshall, Alfred. Principles of Economics. Macmillan & Co., Limited, 1 9 5 0 . . Economics of Industry. Macmillan & Co., Limited, 1 9 5 8 .  Eighth Edition. Third Edition.  Patinkin, Don. Money, Interest, and Prices. Peterson and Company, 1 9 5 6 .  London:  London:  Evaston, I l l i n o i s :  ROXJ  Ricardo, David. On The Principles of Political Economy and Taxation. Edited by P. Sraffa. Cambridge, England: Cambridge University Press, 1 9 5 2 .  58 Robinson, Joan. The Accumulation o f C a p i t a l . L i m i t e d , 1956.  London:  S a l t e r , ¥.E.G. P r o d u c t i v i t y and T e c h n i c a l Change. Cambridge U n i v e r s i t y P r e s s , I960.  Macmillan &  Cambridge,  Samuelson, P a u l A. F o u n d a t i o n s o f Economic A n a l y s i s . Harvard U n i v e r s i t y P r e s s , 1947.  England:  Cambridge,  S c h u l t z , T.W. The Economic O r g a n i z a t i o n o f A g r i c u l t u r e . McGraw-Hill Book Company, I n c . , 1953.  New  Co.,  Mass.:  York:  Schumpeter, Joseph A. The Theory o f Economic Development. Translated by Redvers Opie. New York: O x f o r d U n i v e r s i t y P r e s s , 1961. W a l r a a , Leon. Elements o f Economics, Pure. T r a n s l a t e d by 15.111 am London: George A l l e n and Unwin, L t d . , 1954* M i c k s e l l , Khut. Volume One.  L e c t u r e s on P o l i t i c a l London, 1934*  Economy.  Zeuthen, F.W. Economic Theory and Method. U n i v e r s i t y P r e s s , 1955.  B.  Jaffee.  T r a n s l a t e d by E. C l a s s e n .  Cambridge, Mass.:  Harvard  PERIODICALS  Abramovitz, Moses. "Resource and Output Trends i n t h e U n i t e d S t a t e s S i n c e 1870,° The American Economic Review, Papers and P r o c e e d i n g s , XLVI (May, 195677 5-23. Anderson, H.J. " " P r o d u c t i v i t y o f Labour i n Canadian A g r i c u l t u r e , " Canadian J o u r n a l o f Economics and P o l i t i c a l S c i e n c e , XXI (May, 228-36.  1955),  Buchman, Kenneth. "The A n a l y s i s o f Changes i n A g r i c u l t u r a l Supply: Problems and Approaches," J o u r n a l o f Farm Economics, X L I I , (August,  1960), 531-51. Champerowne, D.G. "The P r o d u c t i o n F u n c t i o n and the Theory o f C a p i t a l : A Comment," The Review o f Economic S t u d i e s , XXI (1953-54), 112-35. , w i t h Khan, R.F. "The P r o d u c t i o n F u n c t i o n and the Theory o f C a p i t a l , a Mathematical Addendum," The Review o f Economic S t u d i e s , XXIII (1955-56), 107-11. Domar, S.D. "On t h e Measurement o f T e c h n o l o g i c a l Change," J o u r n a l , LXXI, (December, 1961), 709-29. Gruen, F.H. " A g r i c u l t u r e and T e c h n i c a l Change," Economics, X L I I I , (November, 1961), 838-58.  The  Economic  The J o u r n a l o f Farm  59.  Hogan, Warren P. " T e c h n i c a l P r o g r e s s and P r o d u c t i o n F u n c t i o n s , " The Revievr o f Economics and S t a t i s t i c s , XL, (November, 1958), 407-11. Johnston, B.F., and M e l l o r , J.W. " A g r i c u l t u r e i n Economic Development^'" The American Economic Review, L I , (September, 1961), 566-93. K a l d o r , N. " A l t e r n a t i v e T h e o r i e s o f D i s t r i b u t i o n , " Economic S t u d i e s , X X I I I , (1955-56), 83-100.  The Review o f  K e n d r i c k , John ¥ . "Some T h e o r e t i c a l Aspects o f C a p i t a l Measurement," The" American Economic Review: Papers and P r o c e e d i n g s , L I , (May, 1961), 102-11. . " P r o d u c t i v i t y Trends: C a p i t a l and L a b o u r , " The Review o f Economics and S t a t i s t i c s , XXXVIII, (August, 1956), 248-57. Lok, S.H. An E n q u i r y I n t o t h e R e l a t i o n s h i p s Between Changes i n Overa l l P r o d u c t i v i t y and R e a l Net Return P e r Farm, and Between Changes i n T o t a l Output and R e a l Gross R e t u r n . Canadian A g r i c u l t u r e 1926-57, T e c h n i c a l P u b l i c a t i o n , Canada Department o f A g r i c u l t u r e , Economics Branch, (October, 1961). Mackenzie, M l l i a m . "The Impact o f T e c h n o l o g i c a l Change on t h e E f f i c i e n c y o f P r o d u c t i o n i n Canadian A g r i c u l t u r e , " Canadian J o u r n a l o f A g r i c u l t u r a l Economics, X, (1962), 41-53. P a s i n e t t i , L u i g i L . "On Concepts and Measures o f Changes i n P r o d u c t i v i t y , The Review o f Economics and S t a t i s t i c s , X L I , (August, 1959), 270-82. . " R e p l y , " The Review o f Economics and S t a t i s t i c s , X L I , (August, 1959), 285-86. Phelps Brown, E.H. ""The Meaning o f t h e F i t t e d Cobb-Douglas F u n c t i o n , " Q u a r t e r l y J o u r n a l o f Economics, LXXI,(November, 1957), 546-60. Robinson, Joan. "The P r o d u c t i o n F u n c t i o n and t h e Theory o f C a p i t a l , " The Review o f Economic S t u d i e s , XXI, (1953-54), 81-103. Ruttan, Vernon ® . "Research on t h e Economics o f T e c h n i c a l Change," J o u r n a l o f Farm Economics, X L I I , (November, I 9 6 0 ) , 735-54-. . "The C o n t r i b u t i o n o f T e c h n o l o g i c a l P r o g r e s s t o Farm Output: 1950-75," The Review o f Economics and S t a t i s t i c s , XXXVIII, (February, 1956), 61-69. Schmookler, Jacob. "The Changing E f f i c i e n c y o f t h e American Economy: 1869-1938, The Review o f Economics and S t a t i s t i c s , XXIV, (August, 1952), 214-31. 18  Solow, Robert M. " T e c h n i c a l Change and t h e Aggregate P r o d u c t i o n F u n c t i o n , The Review o f Economics and S t a t i s t i c s , XXXIX, (August, 1957), 312-20.  60  (November,  . "Reply" The Review o f Economics and S t a t i s t i c s , XL, 1958), 411-13.  . "The P r o d u c t i o n F u n c t i o n and t h e Theory o f C a p i t a l , " The Review o f Economic S t u d i e s , X X I I I , (1955-56), 101-08. . "On Concepts and Measures o f Changes i n P r o d u c t i v i t y : Comment," The Review o f Economics and S t a t i s t i c s , X L I , (August, 1959), 282-85. . "A S k e p t i c a l Note on t h e Constancy o f R e l a t i v e S h a r e s , " The American Economic Review, X L V I I I , (September, 1958), 618-31. U r q u h a r t , M.C. " C a p i t a l Accumulation, T e c h n i c a l Change, and Economic Growth," The Canadian J o u r n a l o f Economics and P o l i t i c a l S c i e n c e , 25,  (November, 1959), 411-30.  APPENDIX The theoretical model which has been used i n the analysis w i l l be presented i n this appendix.  The data derived from the calculations  which were made when capital was measured as an annual flow of interest payments, and also those which were made when a stationary function was used, w i l l be presented. These results may be compared with those presented i n the main body of the thesis. The Model Used The elements of the production function are: Y = The gross output of the farm sector. C =  Gross quantity of capital.  C - Annual input of capital. K  = Quantity of current non labour inputs, excluding feed and seed.  L  =  Quantity of labour input.  The measurement of the amount of change due to technology involves the comparing of the calculated measures of composite input (which i s equivalent to predicted output) from a linear and homogeneous production function of degree unity, with observed levels of output. This calculated measure of composite input may also be regarded as a geometric aggregate i n which the quantity of each item i n the aggregate i s weighted by i t s relative share. Over-all productivity was measured by dividing observed annual output by the computed measure of composite inputj and the average productivity of each factor input was obtained by dividing the index of observed output, by the index of each factor input, for each of the years 1926-1958.  62, Within the data the effects of weather and other such exogeneous variables are assumed to be randomly distributed over the time period i n such a manner as not to introduce any serious bias i n the results. Wars and depressions are regarded as being different from random events, and although their effects influence the data of the analysis there i s not much that can be done to mitigate their effects, beyond omitting the specific periods from the analysis. A family of isoquants may be derived from each production function. It i s further assumed that a smooth production surface characterizes each of the production functions which are used.  The production function may  be linear i f there are constant marginal rates of substitution, or curvelinear i f there are changing marginal rates of substitution. Changing marginal rates of substitution characterize the agricultural sector.  In order to discover the production function at any point i n  time given the values of Y, K, C, and L, l e t the function be of the form  Y = XQ  X  L  j  where X i s the quantity of input of the particular  factor, and where the sum of the exponents i s unity. Let the wage payments to factors exhaust total product. .*. P^Y  =  + \%g +  the factor, and P, the price.  ; where W, represents the vrages of  The wage share of the factor was obtained  from the followings %  ¥  p_  V  .  •  X  W  &  :  X h  y v  J are the relative shares of C, K, and L  respectively. As long as the V.M.P. (Value of the Marginal Product) i s less than the wage rate i n a system i n which there are several factors of production, ceteris bar!bus i t w i l l pay the producer to use additional units of each  63. factor up to the point where the following conditions hold true. V.M.Pj^  !1  (a)  V.M.P  X  =  3.  Xn  P  x  P  l P„  X  (b)  « - x« P  p  p  *2  (c)  1  *2  M.P.P M  =  X~  x  ^2  T  l  \ = M.P.Pxc  Now  •  Py j  where XQ i s the unit of the factor X ^  and Py i s the unit price of output.  This condition holds i n circumstances  of pure competition. The function  Y -  X Q Xg X£ describes a physical relation-  The M.P.Px„  iscV Y  ship.  Let the M.P.P. = 1  a physical relationship. Y  -2 Y  *C P  y  = o£  =  i s a value relationship.  T.V.P.  If factor inputs are measured i n terms of value relationships, that i s to say, i f the physical quantities of input and output are weighted by their respective prices i t i s possible to determine the exponents, and to regard the value ratios as representing the physical relationship  , since value i s a transpose of price and quantity. Y  The c r i t i c a l question becomes shifted to the conditions under which the  64. prices of the factor and the product are determined.  This analysis  assumes that the prevailing prices are equilibrium ones. In the production function which i s used i n this analysis, the exponent of each factor i s also equal to the elasticity of production as well as i t s relative share.  If the relative share of  each factor i s constant through time, as long as factors are paid at the value of their marginal product, there i s only one function. If the relative shares are changing i n the time series data, there are changes of the relative shares. Figure 1 illustrates the fact that when units of factors are paid as wages the value of their marginal product and when a CobbDouglas type function describes the production relationship, a change i n the relative shares of factors represents a change i n technology. Consider the agricultural economy as having a fixed stock of resources.  ( X^ ), which must be used to induce the services of the  other factors of production.  Let X2 be a measure of a l l these other  factors whose services may be exchanged with the stock at varying marginal rates of substitution.  Let the economic conditions be such  that larger quantities of X2 are only forthcoming at higher costs i n terms of X-j_. Under prevailing conditions the opportunity curve of the agricultural sector i s represented i n Figure 1 by the curve LV. The aggregate production function for the agricultural economy under the prevailing conditions i s represented by the isoquants 0^, §2* . . .  On • Under these conditions the optimum equilibrium  combination of X]_ and X£ i s represented by the combination Ox-^ of X-^ and O X 2 ° ^ ^ 2 *  ^  e  P  r i c e  °^ ^ 2 ^  n  terms of X]_ under these conditions  65.  figure  t  66. i s represented by the line P]/Pg  f  o  r  "the level of output ^ 5 .  Assume  that an innovation makes i t possible to u t i l i z e Xj_ but not Xg more fully.  With the shift to the new curve MV, under the old price ratio  the quantity of Xg i n use w i l l be reduced by OXg - Ox' g.  At the same  time the quantity of Xj_ xri.ll be increased by the amount Ox'-^ - Ox^. If the quantity of Xg i n use vrere kept at Xg the quantity of X-j_ would be increased by Ox^ The old price ratio of X tangential to S.  2  Ox^, a smaller increase than the above.  i n terms of X]_, however, would not be  A new price ratio  / Pg would be established. At  point S the marginal rate of transformation on the new curve i s greater than that at point T. Since at equilibrium the marginal cost of Xg i n terms of X-^ i s also equal to the marginal rate of transformation of X-^ into Xg , with neutral technological change, i f the shares are to remain constant the wages of Xg w i l l have to increase i n the same proportion that i t s marginal rate of transformation i s increased. T, i s an equilibrium position at the old price ratio.  Hith the  shift to the new transformation curve MV i f the price ratio remains constant a new equilibrium position xrould be established at R, A solution which requires tangency of the isoquants with the price line Bj. Pg, would involve a change i n their shape.  At the same time since  the quantity of X-j_, which would be kept for use, would be increased, and the amount of Xg, which i s bought, decreased.  The relative share  of X-j_, which i s kept by the sector, would be as a consequence increased, and the relative share of X under the old price ratio would decrease. 2  A non neutral technological change, therefore, involves a change i n factor shares.  Given that there are no discontinuities i n  67. the marginal productivity function, the converse may be proved.  2  Within the context of the above model i t can also be shown that a change i n technology which does not involve the shift of the curve LV may occur.  This happens when a shift i n the production function results  i n anew point of tangency of the isoquant whose point of tangency i s now at T.  Depending on the pressures causing the shift the new point of  tangency w i l l be to the l e f t or the right of point T.  For further discussion of the effects of technological change on the factor product relationships i n agriculture c f . F.H. Gruen "Agriculture and Technical Change," Journal of Farm Economics, Vol. XLIII, Number 4, Part I (November, 1961), pp. 838-58 and references. A discourse on the association of research and technological change i s presented by Vernon W . Ruttan i n the article "Research on the Economics of Technological Change i n American Agriculture," Journal of Farm Economics, Volume XLII, Number 4, (November, I960), pp. 735-54* Footnote references throughout this article provide a comprehensive guide to work i n the f i e l d of evaluation and measurement of technological change. Technological change viewed as a supply response i s discussed by Mark Nerlove, and Kenneth L. Buchman, "The Analysis of Changes i n Agricultural Supply: Problems and^Approaches," Journal of Farm Economics, Volume XLII, Number 3, (August, I960), pp. 531-51. This article provides an extensive bibliography on the subject of technological change.  COMPUTATION Output The value of each category of output obtained from the D.B.S. data, was deflated by i t s price index, 1935-39 = 100.  The total value  of output was determined by aggregating the deflated values. Since the price indices are supposed to remove the effects of price changes from the aggregate value series, the deflated series represents annual physical quantities weighted by 1935-39 prices.  The data were then  converted to index numbers, 1926 = 100, from vrhich the changes i n the quantity of output over the period could be observed. Specifically total output was obtained as follows: (Cash farm income + Changes i n (from livestock " inventory / (  Income i n kind _ f livestock  +  r o m  Feed and Seed ) expenses ) 1  Index number of farm price of livestock and livestock products.  ) )  (Cash income + Change i n Income i n kind ) (from crops inventory from crops ) +( ... •, • . ) ( Index of farm prices ) ( for crops. ) +  _  (Cash income from forest ( and maple products +  (  ••  / / (  +( ( (  Income i n kind from ) forest and maple products )  +  •  •  -  '  •,. i  •  Price index for lumber and lumber products. House rent  =  )  )  Index of building materials ) taxes and interest rates. )  Feed and seed were removed to avoid couble counting.  )  \ \  69 Inputs The value of the input factors G, K, and L, were changed from current dollar terms to constant dollars, and the indices of physical quantities were calculated i n the same manner as was output.  Here-under  are set out the members of each category and the deflator index which was used i n conjunction with each member before the aggregate constant dollar value was determined and then indexed i n terms of 1926 being made equal to 100. Capital  Co =  c; =  ( ( ( / /  Machinery value less depreciation „ „_ ,. Index of machinery prices  T  J  ) (Value of ) (livestock ) { \ /Index number of \ /farm prices of /livestock and ^livestock products  ( Land value  +  (Total current value ) '( of capital goods )  ( Index of land ( value per acre  ( Rate of interest on ) ( farm mortgages )  Index of interest rates. &L  =  C net of land 2  ( Value of capital goods ) ( net of land )  ( Rate of interest on ) ( farm mortgages )  Index of interest rates The other non capital inputs were the following: Cost of f e r t i l i z e r ) and lime ) K  =  (Machinery depreciation) (and repairs )  Index of f e r t i l i z e r ^) + ( (Price index of farm prices \ ( machinery  -) + )  Building de-) preciation ) and repairs ) Price index ) of building ) materials )  70.  _  ( Tractor truck auto] ( engine and combine] ( expenses  (  | Index of Gasoline ( o i l and grease  ( Index of ( taxes  ( Canadian labour force ) ( i n agriculture )  Miscellaneous expenses  Taxes  (-  Index of hardware prices  ( Monthly wage rate ) ( without board ) ,  Index of farm wage rates Capital was calculated i n two different ways because there are two schools of thought each with a reasonable set of arguments supporting the claim that land should or should not be l e f t out i n an analysis of this sort.  The f i r s t school i s represented by this quotation from  Marshall. . . . Uhen regarding capital from the social point of view i t i s best to put under separate heads those of the nation's resources which are made by man, and those which are not; and to separate the capital x-rtiieh i s the result of labour and saving from those things which nature has given freely. This plan i s well adopted for the main purposes of the economist. For indeed his chief concern with capital i n general, or social capital, i s when he i s considering the way i n which the three agents of production, land (i.e., natural agents) labour and capital, contribute to producing the national income . . . , and the way i n which this i s distributed among the three agents.4The argument used by the other school of thought i s well represented by the following quotation from Fossati. The productive power which land brings to agriculture i s therefore i t s e l f produced, i n the sense that f e r t i l i t y can be increased by man's labour and knowledge . . . . To ignore this to regard land as merely so much earth, denying i t s fundamental property, f e r t i l i t y . > 4 Alfred Marshall, Economics of Industry, (London: Macmillan, 1958 reprint) p. 4-7. Sraldo Fossati, The Theory of General Static Equilibrium edited by G.L.S. Shackle (Oxford: Basil ELackwell, 1957), p. 132.  71  I t i s true t h a t F o s s a t i was diminishing returns  r e f e r r i n g t o l a n d w i t h i n the  controversy,  context  of  a  but the f a c t t h a t a g r i c u l t u r a l l a n d i s  n o t r e q u i r e d merely f o r i t s s i t e v a l u e i s a p o w e r f u l argument i n s u p p o r t o f i n c l u d i n g l a n d as a c a p i t a l good. c a p i t a l i n use production  and not  process.  i n i f l a n d value  But  as Solow p o i n t e d  out^ i t i s  c a p i t a l on hand which i s i m p o r t a n t i n the  The  problem o f excess c a p a c i t y c o u l d e a s i l y  i s i n c l u d e d when the v a l u e  creep  of c a p i t a l i s being  determined. A problem i n v o l v e d i n the i n c l u s i o n o f l a n d l i e s i n the t h a t the v a l u e  fact  o f l a n d does n o t n e c e s s a r i l y r e f l e c t i t s p o t e n t i a l  a g r i c u l t u r a l p r o d u c t i v i t y but a l s o r e f l e c t s demand from the a g r i c u l t u r a l use  o f the  site.  non  Investment i n l a n d i s f r e q u e n t l y used  as a hedge a g a i n s t i n f l a t i o n , and i n f a c t , many c r e d i t i n s t i t u t i o n s t i e d t o the ovmership o f p r o p e r t y . o f a g r i c u l t u r a l l a n d may  not  The  r e s u l t i s t h a t the market  always r e p r e s e n t  are  value  the p r i c e t h a t a farmer  a c t i n g i n h i s c a p a c i t y as a farmer would be w i l l i n g t o pay f o r the site.  Despite  these c o n s i d e r a t i o n s ,  however, i t must be r e c o g n i z e d  t e c h n o l o g i c a l improvements are o f t e n d e s i g n e d t o e x t r a c t more c a p a c i t y from a g i v e n amount o f l a n d . l a n d whose p r i c e i s i n f l u e n c e d by non t h u s a t any  The  r e f l e c t s i t s p r o d u c t i v i t y i n a given  productive  proportion of a g r i c u l t u r a l  a g r i c u l t u r a l use  p o i n t i n time the t o t a l v a l u e  i s not  large;  of a l l a g r i c u l t u r a l land  state of technology.  I n t h i s a n a l y s i s c a l c u l a t i o n s were made i n which l a n d r e g a r d e d from the two  p o i n t s o f view p r e v i o u s l y e x p r e s s e d .  was  However, i t  must be n o t e d t h a t the i n c l u s i o n o f l a n d reduces the share g o i n g t o  Solow, " T e c h n i c a l Change" e t c . p.  that  314*  72  labour and current inputs, and increases the share of capital.  The  effect of i t s inclusion w i l l also depend upon the behavior of the nonland i n relation to land inputs.  Simultaneous decreases i n the relative  importance of land and increases i n non land capital inputs w i l l be masked i n a value aggregate.  Under these circumstances, the changes  i n the share of capital w i l l be less marked when the value of land i s included and as a consequence, since there w i l l be less variation i n the relative shares, changes i n technology w i l l be less apparent. The analysis done here has therefore made use of both approaches. Estimating Input and Output Relationships Several modifications of the input variables were used i n order to describe f u l l y the interaction i n the system.  The  modifications make use of the following variables and parameters. (l)  (2) (3)  =  G  2  :  ~1  o<  == =  2  ==  U)  :  (5)  ~*2  (6)  Capital stock  =  Depreciated value of buildings and machinery  =  Capital stock net of land  Capital stock including land Share of Share of C  2  Share of current inputs (K) when C ==  :  n  II  =  "  «  i  n  =  tl  tt  "  C =  labour  "  (L)  tt  c  n  tt  ti  tt  tl  :  =  :  c = :  °1 C  2  °L C  2  An analysis using the more traditional approach was also done. The shares were kept constant at 1926 levels and capital input was measured as the interest payments on capital stock inclusive land (Cg).  73. The use of a stationary production function facilitates prediction.  If non-neutral technological changes are occurring, the  production function i s changing as a result.  At the same time, i f  neutral changes are occurring the predictive accuracy of the stationary production function i s restricted. However, i f technology i s changing at some known rate reasonably accurate predictions may  be  made, and information as to the known or expected rate of change of technology, or regarding the expected frequency of i t s change together with the probable amount of change i f available would be invaluable. There i s as yet no means of acquiring such information as regards the expected future rate of changej and as the review of the literature presented i n this thesis has shown, there i s no consensus as regards the best method of measuring past changes. Under the criterion used by this analysis the data available show that the aggregate production function has been shifting, thus technological changes have been occurring.  As a result, those calculations using the stationary  production, which were made i n this analysis, are presented for purposes of making comparisons of the results with those results of other methods. A Mote on Some of the Price Indices Used Most of the price indices used were compiled by D.B.S.j however, the indices of Farm Price for Crops and also for livestock products for the years 1926-34 were computed by establishing a link relative between the respective Farm Price indices and the Wholesale Price indices for the years 1935 to 1958.  The link relative was then  used to convert the wholesale price index for 1926 to 1934 into Farm Price indices.  The deflator index used for taxes was also computed byestablishing a conversion ratio between the available Index of Tax and Interest rates and the Index of Interest Rates.  The annual indices of  taxes were then computed out of both series. Additional Results It i s instructive to examine the difference vrhich the use of some of the other methods of calculating composite inputs would have made to the results.  One method involves the use of a stationary  function, that i s to say, the relative shares were not allowed to vary from those values which they had i n 1926.  In this case the level of  composite input has been designated here as X^.. Another method made use the shifting production function, but capital i n this case was measured i n terms of an indexed series of the value of interest payments going to capital stock, and i n which the deflator index used was an index of interest rates.  The designation of  this type of capital index i s C', and the composite input which was calculated from this series i s designated X l . The weakness of this method has already been discussed i n the main body of this thesis. The results of these calculations are presented i n Tables VIII, IX, and X; and the effect of the various methods on the estimate of the change i i . ^ v e r - a l l productivity may best be examined, i n Table IX.  This  table shows that for the entire period, the estimate of the change i n the over-all productivity which was calculated from the use of the stationary function was similar to that which was calculated with the use of the shifting functions.  Over the period 1931 to 1946, however,  the estimated change i n over-all productivity was greater when the measurement was made with the use of the stationary function than the  7.5.  amount of change registered by the other methods.  During the years  1948 to 1954- inclusive, the greatest amount of change from the base period values was recorded by the function which measured capital as a stock inclusive of real estate. It therefore appears that the changes recorded by these three methods of measurement at times moved together with closely similar results, as characterized the 1926-30 period while at other times they changed i n pairs, or independently.  For example,  between the years 1936 and 194-5 the results which embody the use of and Cg were closely similar; whereas those embodying the use of Cg and Cg  were closely similar for the years 1955 to 1958 inclusive.  Under these circumstances i t must be concluded that these variations i n the calculated results of each method are to a large extent due to the characteristics of the changes which were taking place i n the particular periods. The choice of the method of measurement i s thus not immaterial; because i f the time series data of this analysis had terminated i n a different year the estimates of net over-all change produced by each method would be much more dissimilar.  The choice  of the method must therefore be determined by the economic logic which can be brought to bear on the particular circumstances:  and the  method of measurement chosen therefore w i l l depend upon the amount as well as on the type of changes which are occurring i n the sector. The data of Columns 3 and 4- of this table were derived from a model whose conceptual weakness has already been discussed; but since this method of measuring capital (as an annual flow of interest payments) has been used at different times by various writers, these columns are included here i n order that the results of the use of the shifting production function i n conjunction with a geometric aggregation  TABLE V I I I INDICES; OUTPUT-INPUT RATIOS, ADDITIONAL SELECTED METHODS, CANADSS AGRICULTURE, 1926-58; 1926 = IOO (1)  (2) (3) STATIONARY FUNCTION* 1  2j CompositeInput A  OutputInput Ratio  Year  Output  1926 1927 1928 1929 1930  100 107.2  104.5  112.6 89.4 96.0  107.2 108.7 109.2  105.04  1931 1932  77.9 100.0 88.8 91.0  102.0 100.1 96.5 96.7 98.2  76.37 99.90 92.02  1933 1934 1935  99.6  100  100 102.58 82. 24 87.91  94.11  101.42  97.7 97.9 98.1  104.18  97.3 99.1  133.09 128.76  91.9 94.8 102.6  121.98 175.11 119.73 133.72  104.7  104.3  1936 1937 1938 1939 1940  92.3 85.2 102.2 129.5 127.6  1941 1942 1943 1944 1945  112.1 161.8 113.5 137.2 109.2  1946 1947 1948 1949 1950  116.7 118.7 130.8 125.8 119.7  110.0 110.8  1951 1952 1953 1954 1955  153.3 160.1  119.9 116.9 118.0  1956 1957 1958  92.4  94.47 87.03  (4) (5)_ SHIFTING FUNCTION** ,  2i CompositeInput L  OutputInput Ratio  100 104.5 107.3 109.0 109.9  100.00 102.58  101.9 94.5 94.8 95.5 97.5  76.45 105.82 93.67 95.29 102.15  98.2  93.99 85.71 101.19 126.10  99.4 101.0 102.7 103.3 95.6 95.0 95.3 103.8 105.7  104.94 82.02 87.35  123.64 117.25  170.03 119.10 132.18 103.31  111.1 110.6 112.7 115.3 119.6  105.04 107.32  121.1 119.5 112.8  118.4 116.3  127.86 136.95 138.47 109.21 128.63  126.59 133.97 133.06 103.86 119.39  167.3  115.2  145.23  124.3  140.1  113.4 112.0  123.54  122.8  134.46  123.6  163.4 129.3 149.6  150.6  114.1 116.3 118.7  105.14 107.13 113.94 108.17 100.84  124.5 125.3  115.35 109.11 100.00  134.59 114.09 121.84  *  C a p i t a l was measured as an annual f l o w a c c r u i n g t o a l l c a p i t a l s t o c k i n c l u d i n g l a n d and s h a r e s were k e p t a t t h e 1926 l e v e l s .  **  The same as f o r the s t a t i o n a r y f u n c t i o n except t h a t the s h a r e s were v a r i e d as t h e d a t a d i c t a t e d .  TABLE IX SUMMARY INDICES, GROSS OUTPUT-INPUT RELATIONSHIPS; VARIOUS SELECTED METHODS CANADIAN AGRICULTURE, 1926-58;  1926 = 100  (1)  Year  (2)  U)  (5)  Index of Productivity when Index of Index of Index of Index of c = Cg and Productivity Productivity Productivity Productivity function when c = C^ when c = Cg when c = C[ when c = Cg Stationary 100 103.28  1926 1927 1928 1929 1930  100 103.08 105.93 82.32  88.07  106.73 82.17 87.51  1931 1932 1933 1934 1935  71.47  70.50  1936 1937 1938 1939 1940  (3)  92.33  94.61  81.77 83.49 90.96  83.15 86.34  92.05  84.76 78.31 91.17 -  84.99 78.09  100 103.38 106.03 81.87  100 102.58  100 102.58  104.94  105.04 82.24  88.24  82.02 87.35  72.67 97.79  76.45 105.82  76.37  86.30  93.67 95.29  92.02  88.09 94.23  102.15  93.99  87.91  99.02 94.11 101.42 94.47 87.03  91.66 114.30  116.88  113.02  115.16  86.59 79.26 92.57 116.98 113.83  1941 1942 1943 1944 1945  110.12 163.60 113.73 128.71  110.77  110.12  163.43 116.17 130.17  162.45 114.50  100.92  101.97  1946 1947 1948 1949 1950  102.64 106.08 116.18 110.25 101.53  105.14 107.91 118.18 112.72 104.36  1951 1952 1953 1954 1955  131.70 138.98 138.83 108.38  135.66 143.07 142.96 111.08  102.86  103.86  127.86 136.95 138.47 109.21  124.98  128.70  119.11  119.39  128.63  1956 1957 1958  139.65  145.73  132.78 115.02  134.59  145.23  114.09  131.41  123.54 133.39  123.14  121.84  123.54 134-46  121.40  .  85.71 101.19 126.10  104.18 133.09  123.64  128.76  117.25 170.03 119.10 132.18  121.98  99.7  103.31  104.3  101.39  105.04  105.14  107.32 115.35  107.13  127.15  104.40 112.85 106.61  97.7  109.11 100.00  124.13  126.59  137.19  132.09  133.97 133.06  175.11 119.73  133.72  113.94 108.17  100.84  TABLE X RELATIVE CHANGES, M . P . P . FACTOR INPUTS, CANADIAN AGRICULTURE, 1926-58; 1926 = IOO (1)  (2)  U)  (3)  SHIFTING FUNCTION M. P . P .  °2 1926 1927 1928 1929 1930  100 100.3 106.1 81.7 84.8  M T P T P T M T P T P T C  2  100 98.3  102.0  81.1 84.5  93.3 146.6  1933 1934 1935  71.3 97.2 86.9 84.4 89.1  1936 1937 1938 1939 1940  77.0 66.2 70.3 95.0 84.3  112.9 95.5 111.1 134.6 120.0  1941 1942 1943 1944 1945  74.1 97.9 64.0 71.3 53.1  99.8 123.7 73.8  1946 1947 1948 1949 1950  52.9 55.8 63.2 62.9 61.3  55.4 54.0  1951 1952 1953 1954 1955  83.8 85.0 88.0 69.0  1956 1957 1958  93.3 77.9 85.6  1931 1932  83.4  131.0 128.4 131.6  78.4  58.2  46.6 50.8  47.1  56.4  58.1 59.2 47.1 55.2 60.6  50.4 54.1  *2 100 99.9 102.8 81.3  92.5 82.8  124.6 112.1 115.1  122.8  113.4  103.8 123.3  151.5  140.6  123.3 163.7  101.0 112.9 83.6  (5)  (6) (7)  STATIONARY FUNCTION M.P.P. L  2  M.P.£ C  2  100 106.5 108.0 83.0 88.0  100 102.4  M.P.P.  *2  L  2  80.9 86.0  100 98.5 97.8 74.7 79.1  100 105.9 111.0 87.0 93.7  64.0 74.8 65.1 68.9 77.8  68.1 87.0 78.0 79.3 88.5  68.9 96.3 88.2 90.6 98.8  73.4 94.1 80.6 82.1 87.8  77.0 74.5 89.8  85.0 79.5 92.3 127.7 126.3  92.6 85.1 99.2 121.3 119.3  80.5 74.2 86.6 109.8 109.5  116.2 162.1 110.6 134.5 104.8  101.8 139.4 93.3 108.0 80.7  112.3 176.1 128.7 138.3 110.2  79.9 76.9 81.4 75.6 66.0  112.8 121.7 136.6 134.3 133.4 188.1 207.9 217.3 170.1 211.0 248.6 212.3  114.6 123.1 126.7 205.2 157.4 175.5 141.8  104.5  84.3 86.4 97.5 97.1 94.4  146.8 153.4 167.1 157.3  112.6  120.6 129.0 129.5 103.7 121.8  193.5 209.1 211.0 162.7 191.8  142.6 147.3 116.9 135.0  80.3 82.5 80.0 62.6 70.6  133.1  221.4 191.7 210.8  150.2 126.1 130.2  75.6 65.6 70.2  114.0 124.3  M.P.P.  145.2  114.7  128.0 122.5 113.5  149.6  244.1  of inputs may be compared with the results of those studies which make use of a different method. Since changes i n the marginal productivities are equivalent to changes i n the average productivities when there i s no change i n the shape of the production function, the data presented i n Columns 5, 6 and 7 of Table X, and which represent the indices from which may be observed changes i n the marginal productivity when the stationary function i s used, may also be regarded as equivalent to the changes i n the average productivity of the respective factors.  A comparison of  the changes from the base period, of Columns 1, 2, A with those of Columns 5, 6 and 7 respectively i s analogous to comparing the changes of the marginal productivities of the respective factors with the changes i n the average productivities.  Therefore these columns do not  only present the changes i n the respective marginal productivities with the use of the stationary function.  The inferences which were made i n  the body of the thesis with respect to the former comparison, (that i s , comparisons of the changes i n the average productivity of factors with those of their marginal productivities), are therefore applicable here.  

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