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Analysis of resource allocation in the production of market eggs. Campbell, Robert Harold 1960-12-31

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AN ANALYSIS OF RESOURCE ALLOCATION IN THE PRODUCTION OF MARKET EGGS by ROBERT HAROLD CAMPBELL B.S.A., University of B r i t i s h Columbia, 1943 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE OF AGRICULTURE i n the Department of A g r i c u l t u r a l Economics We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF SCIENCE IN AGRICULTURE  Members of the Department of A g r i c u l t u r a l Economics THE UNIVERSITY OF BRITISH COLUMBIA October, I960  In p r e s e n t i n g  this thesis in partial fulfilment of  the r e q u i r e m e n t s f o r an advanced degree a t the o f B r i t i s h Columbia, I agree t h a t the i t freely  L i b r a r y s h a l l make  a v a i l a b l e f o r r e f e r e n c e and s t u d y .  agree t h a t p e r m i s s i o n f o r e x t e n s i v e  University  I further  copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood  t h a t copying o r p u b l i c a t i o n o f t h i s t h e s i s f o r gain  s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  Department o f  jfi^A^<^~ZKAA-^QJ  /&c.<nwy*sCc,a,  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada. Date  4^<^ U> I Ho  financial  permission.  ii  ABSTRACT  Farmers are confronted continually with the necessity of r e v i s i n g and reorganizing t h e i r production plans i n order to maximize the net returns from the available resources* This need arises from the dynamics of price and y i e l d f l u c t u ations, which can only be estimated within,a range.  I f future  changes i n prices and y i e l d s could be predicted with absolute certainty, a single plan could be formulated which would specify the resource combination at each point i n time, f o r each change i n techniques, and f o r each price situation* The present study involves an investigation of the r e sources employed by commercial market egg producers i n the Lower Fraser Valley and Vancouver Island areas during the period of 1949 t o 1951 to determine (1) the deviation of the actual resource combinations  employed during each year from  the t h e o r e t i c a l l y optimum combination required f o r maximum net returns and (2) the effectiveness of a l t e r a t i o n s to the r e source combination made by producers i n attempting to adjust t h e i r operations to variations i n the input-output price r e lationships* The production function method of analysis was used because i t recognized the basic functional relationships i n the production process and provided a quantitative a n a l y t i c a l technique founded on general economic p r i n c i p l e s *  The analysis  iii was based on input- output data compiled from detailed records of 66,  57 and 45 commercial market egg enterprises f o r the r e -  spective years 1949,  195© and 1951  ending on September 3 0 .  For  the purpose of t h i s analysis, the numerous i n d i v i d u a l resources employed i n the production of market eggs were aggregated into the categories of (1) ing f l o c k , (3)  land, buildings and equipment, (2)  labor, (4)  feed, and (5)  Cobb-Douglas production function was  lay-  other cash expenses.  A  derived f o r each year by  the least-squares method of f i t t i n g a l i n e a r multiple regression equation*  The marginal value products of the resource cate-  gories, with a l l inputs f i x e d at t h e i r geometric means, were estimated by p a r t i a l d i f f e r e n t i a t i o n of the production function with respect to each input v a r i a b l e . As indicated by the c o e f f i c i e n t of multiple determination, about 95 per cent of the variance i n t o t a l output income) from the market egg enterprises during each year explained by the f i v e input categories.  (gross was  According to the t-test,  c o e f f i c i e n t s of the following input categories were s t a t i s t i c a l l y d i f f e r e n t from zero at the f i v e per cent s i g n i f i c a n c e l e v e l : laying f l o c k and feed i n 1949; penses i n 1950;  feed and other cash  and laying f l o c k and feed i n 1951*  f i c i e n t s had a value l e s s than 1.0,  ex-  A l l coef-  indicating diminishing  marginal returns to a l l input categories.  Returns to scale, as  measured by the sum of the c o e f f i c i e n t s , were constant f o r each year. In each year, the marginal value products were l a r g e r f o r the input categories of laying f l o c k and feed than f o r the  iv other inputs.  In view of t h i s persistent inequality, i t was  apparent (1) that the t h e o r e t i c a l l y optimum combination of r e sources f o r these egg enterprises was not attained i n any of the three years and (2) that the adjustments i n resource inputs from year to year did hot constitute a major improvement i n the resource combination* The marginal value products of the various resources revealed the (average) results of the decisions taken by pro- » ducers i n using the resources at t h e i r disposal f o r the production pf market eggs*  The f a i l u r e to achieve the most profit*?  able combination of these resources was attributed to r e strictions-imposed by (1) production techniques and practices that prevented quick and precise adjustments to the input of certain resources, (2). i n f l e x i b i l i t y and i n d i v i s i b i l i t y of r e sources, and (3) imperfect knowledge of output and prices i n the future*  Some of these r e s t r i c t i o n s may preclude the  p o s s i b i l i t y of e f f e c t i v e improvement i n resource use i n the short run*  V  TABLE OF CONTENTS Page LIST OF TABLES  vi  LIST OF FIGURES  viii  ACKNOWLEDGEMENT.  ix  INTRODUCTION  1  Statement of the Problem . . . . . . . . . . . . .  2  Method of Analysis  3  THE ANALYTICAL MODEL  10  Characteristics of the Cobb-Douglas Production Function . . . . . Some Applications of the Cobb-Douglas Production Function i n Analysis of Resource Productivity on Farms •  14 16  LIMITATIONS OF PRODUCTION FUNCTION ANALYSIS  23  ANALYSIS OF EMPIRICAL DATA  28  Source of the Data . Method of Analysis The Results and Their S t a t i s t i c a l R e l i a b i l i t y INTERPRETATION OF THE RESULTS APPENDIX I  •  28 31  . . 32 39  PHYSICAL AND FINANCIAL ORGANIZATION OF THE  - MARKET EGG ENTERPRISE APPENDIX I I THE FEED-EGG PRICE RELATIONSHIP APPENDIX. I l l  THEORETICAL CONCEPTS  APPENDIX IV AGGREGATION OF TOTAL OUTPUT AND THE INPUT CATEGORIES IN THE PRODUCTION FUNCTION APPENDIX V COMPUTATION OF REGRESSION COEFFICIENTS AND TESTS OF STATISTICAL SIGNIFICANCE BIBLIOGRAPHY  56 . 77 83 123 126 130  vi  LIST OF TABLES Table 1. 2. 3.  Page Measures of R e l i a b i l i t y of the Production Function. 33 Regression Coefficients, Standard Errors, Values of t , and P r o b a b i l i t i e s . .  35  Geometric Means and Marginal Value Products of Input Categories . . . . . . . . . . . . . . . .  40  4*  Some Averages f o r Market Egg -Enterprises, Lower Fraser Valley and Vancouver Island,. 1949-51 . • . . 65  5.  Average Inventory Values f o r Market Egg Enterprises, Lower Fraser Valley and Vancouver Island, 1949-51 . .  6  0  ~. 71  Average Receipts f o r Market Egg Enterprises, Lower Fraser Valley and Vancouver Island, 1949-51 . 72  7«  Average Expenses f o r Market Egg Enterprises, Lower Fraser Valley and Vancouver Island, 1 9 4 9 - 5 1 7 3  8*  Average Returns f o r Market „Egg Enterprises, Lower Fraser Valley and Vancouver Island, 1949-51 . 74  9*  Egg and Feed Prices at Vancouver, October, ,1948 to September, 1951  78  10.  Feed-Egg Price Ratios, Based on Vancouver -Prices, October, 1948 to September, 1951 . . . . . 81  11.  Relationship of Resource Input t o Total, Average and Marginal Products  12.  Optimum Level of Applying a Variable Factor to Fixed Factors . . . . . . .  13. 14. 15.  *  Marginal Cost of a Factor and Marginal Value Product Relationship Between Input of Two Variable Factors and Output of jProduct . ... . . . . . . Diminishing Rate ,of Factor Substitution with Output Fixed at 100 -Units  85 94 100 . .-. 103 104  vii LIST OF TABLES — Table 16.  Continued  Page Minimization of Costs under a Diminishing Marginal Rate of Factor Substitution • • • • • . • 113  viii  LIST OF FIGURES Figure 1. Relationship of Input of a Single Variable Resource to Total, Average and Marginal Products  Page • .  2,  Factor/Product  Price Ratios • . . .  3,  Equation of the Factor/Product Price Ratio and the Marginal Physical Product f o r Maximum P r o f i t s . .,  4.  Isoquants or Iso-Product  5»  Ridge Lines and I s o c l i n e Indicating Equal Marginal Rates of Substitution at Different Levels of Output . . .  87 96  Curves  96 . 105  • 108  6.  Iso-cost Lines f o r Constant Factor Prices . . . . .  115  7.  Iso-cost Lines f o r Different Factor Prices  115  8.  Least-cost Combination of Factor Inputs as Indicated by Tangency of Iso-cost Lines and Iso-product Curves  9.  P r o f i t Maximization  and the Expansion Path  ....  115 ....  119  ix  ACKNOWLEDGEMENT  The author wishes to express sincere appreciation to Dr. Walton J . Anderson, Chairman of the Department of A g r i c u l t u r a l Economics, f o r h i s assistance and suggestions i n the development and writing of t h i s t h e s i s .  He also wishes to  acknowledge the guidance and c r i t i c i s m received from the Graduate Committee members, Dean Blythe A. Eagles,  Professor  Jacob Biely, Dr. Nora E. Neilson, Professor T. I. Matuszewski and Dr. Joseph J . Richter. The author i s also indebted t o Dr. J . F. Booth, Director of the Economics Division, Canada Department of Agriculture, f o r permission t o use the data on market egg enterprises which was collected-by the B r i t i s h Columbia Regional O f f i c e of the Economics D i v i s i o n .  . ,~ ,  AN ANALYSIS OF RESOURCE ALLOCATION IN THE PRODUCTION OF MARKET EGGS  INTRODUCTION  As managers, farmers are concerned with combining the limited resources at t h e i r disposal so as to maximize net r e turns or p r o f i t s .  Although some farmers may forego t h i s ob-  j e c t i v e i n favor of more l e i s u r e or f o r reasons of other ideals or b e l i e f s , the question of optimum a l l o c a t i o n of r e sources must be related to the economic end of maximizing profits.  I f a greater value of product can be obtained from  the same resources, or fewer resources can be used f o r the same value of product, then p o s s i b i l i t i e s exist f o r an increased net return through adjustments i n the combination of resources* The optimum use of given resources i s attained only when the net product i s at a maximum, and no re-arrangement of the r e sources w i l l r e s u l t i n an output which y i e l d s a greater net value* There are several main obstacles to achieving an o p t i mum  resource combination*  I n e f f i c i e n t use of resources  may  occur as a result (1) of imperfect knowledge of the physical input-outputrelationships or (2) of uncertainty as to the course of future prices of resources and products.  Also, a  2  reluctance to abandon f a m i l i a r methods of production,  inflexi-  b i l i t y i n the quantity and use of some resources, and l i m i t e d c a p i t a l a l l contribute to resource combinations which are not optimum.  Statement of the Problem The main categories of resources used f o r market egg production include land, buildings, equipment, laying birds, feed, labor and a group of miscellaneous  items.  In the aggre-  gate, c e r t a i n changes occurred from year to year i n both the quantity of resources employed and the quantity of eggs produced during the period from 1949 to 1951? the input of feed and layers declined s l i g h t l y from 1949 to 1950, and then increased i n 1951 to a l e v e l above that of 1949; labor input decreased  sub-  s t a n t i a l l y from 1949 to 1950, and increased by a small amount i n 1951.  At the same time, changes i n feed and egg prices were  such that the feed-egg p r i c e r a t i o was least favorable i n 1950 and most favorable i n 1951© Therefore, i t would seem that producers responded to the narrowed margin between feed and egg prices i n 1950 with a small reduction i n the input of some r e sources, p a r t i c u l a r l y those which could be e a s i l y and quickly adjusted.  On the other hand, encouraged by the improved feed-  egg price r e l a t i o n s h i p of 1951, they attempted to take advantage of the situation by s u b s t a n t i a l l y increasing the inputs of most of these same resources.  As a consequence of the adjustments i n  resource combination, t o t a l production of eggs f e l l  slightly  from 1949 to 1950, but rose i n 1951 well above the 1949  3 output*^" Two c l o s e l y related aspects of the problem of resource combination i n market egg production were investigated i n the following analysis*  E s s e n t i a l l y , t h i s required estimation of  the marginal value productivities of certain groups of r e sources employed i n market egg enterprises during each of the three years*  These estimates of value products made i t possi-  ble to observe any departure of the actual resource combinations employed during each year from the t h e o r e t i c a l l y o p t i mum combination required f o r maximum p r o f i t *  This could be  achieved by comparing the marginal value products with the r e spective marginal costs (or prices) of resources*  Secondly,  the effectiveness of a l t e r a t i o n s to the resource combination made by producers i n attempting to adjust t h e i r operations to variations i n the feed-egg price relationship can be appraised through the changes i n the marginal value product/marginal cost r a t i o s which occurred from year to year.  2  Method of Analysis Estimates of the marginalvalue productivity of the r e source categories were derived by the production function ^See Appendix I and II f o r a description of the physical and f i n a n c i a l organization of the market egg enterprises, and f o r d e t a i l s of other data used i n the following analysis* 2  ~  See Appendix III f o r a summary of the t h e o r e t i c a l concepts relevant to the problem of economic e f f i c i e n c y of r e source use i n the short run for- a single enterprise*  4 method of analyzing input-output data f o r farms.  This tech-  nique recognizes the basic functional relationships that underl i e the production process.  I t incorporates  these functional  relationships based on general economic p r i n c i p l e s into a quantitative method of analysis.  For t h i s reason, the pro-  duction function method o f f e r s c e r t a i n advantages over the more conventional method of tabular analysis as a technique f o r measuring resource productivity.1 The tabular method of analysis (also c a l l e d the method of d i r e c t comparison) o r d i n a r i l y depends on the grouping and c r o s s - c l a s s i f i c a t i o n of data and the c a l c u l a t i o n of averages to reveal relationships between various " e f f i c i e n c y f a c t o r s " and a "measure of returns" such as management return, labor i n 2 come, or other " r e s i d u a l " p r o f i t f i g u r e .  Management return  or a s i m i l a r measure i s often used to indicate the of resource a l l o c a t i o n on farms. residual return-implies  effectiveness  The method of c a l c u l a t i n g t h i s  that-the current market p r i c e of each  resource i s equal to i t s marginal value productivity.  This  equality could be expected to occur under long-run stable F o r a comparison of these methods of analysis, see E a r l 0. Heady, Glen L. Johnson, and Lowell S. Hardin (eds.), Resource Productivity. Returns to Scale, and Farm S i z e (Ames: Iowa State College Press, 1956J,-pp.-151-159* 2 For a discussion and i l l u s t r a t i o n of t h i s method of analysis, see G. W. Forster, Farm_ Organization^and Management (rev. ed.; New York: Prentice-Hall, Inc., 1946). pp. 97-112. For d e f i n i t i o n and c a l c u l a t i o n of many of the e f f i c i e n c y factors and measures of returns, see John D. Black et a l . . Farm Management, (New York:The Macmillan Co., 1949), pp* 4 8 9 - W ; G. W. Forst er, Farm Organization and Management, (rev, ed.; New York: Prentice-Hall, Inc., 1946), pp. 167-193; and John A Hopkins and E a r l 0. Heady, Farm Records and Accounting. (4th ed.; Ames: Iowa State College Press, 1955), pp. 163-203• x  r  f  5  competitive conditions, but not necessarily i n the short-run. When resources are under-priced r e l a t i v e to t h e i r actual prod u c t i v i t y , the return to the r e s i d u a l f a c t o r represents an amount which i s not due to management alone, but also includes a portion that i s due to the productivity of other resources whose productivity i s thereby underestimated.  Thus., i f manage-  ment i s set up as the r e s i d u a l claimant on income, resources may appear to be used more e f f i c i e n t l y on large farms than on small farms when, i n f a c t , a larger ^ r e s i d u a l " return to management could be caused e n t i r e l y by the greater quantity of resources, and not by any difference i n production practices or the kind of resources employed.  I f resources are assigned  prices greater than t h e i r true productivity, equally misleading conclusions on resource e f f i c i e n c y could be drawn from the under-estimated  return to management.  Thus, the productivity  of any one factor, when calculated by the residual method^ i s i n c o r r e c t l y estimated to the extent that the market price assigned to other resources deviates from the true marginal value productivity of these resources. The imputation of returns to factors of production by the residual method implies that (1)  the market price of each  resource i s equal to i t s marginal value product; (2)  the t o t a l  physical or value product can be divided into shares so that (a) each f a c t o r receives a reward equal to i t s marginal prod u c t i v i t y , and (b) the rewards so computed exactly exhaust thet o t a l physical or value product.  The i m p l i c i t assumption i n  the residual procedure i s that the exact return to each f a c t o r  6 can be imputed, and that neither an excess nor a d e f i c i t of the t o t a l product w i l l remain a f t e r imputation of returns to a l l factors*  However, the returns to a l l factors computed i n t h i s  manner amount to the t o t a l product under only one condition: the e l a s t i c i t y of production must equal 1.0.  With respect to  a single-factor production function, t h i s condition exists when the production function i s l i n e a r and homogeneous throughout a l l ranges,- that i s , a straight l i n e input-output curve.  It is  also attained on a production function characterized by d i minishing marginal resource productivity at the point where the marginal product equals the average product of the resource. Thus, i f the e l a s t i c i t y of production i s greater than 1.0, t o t a l returns to a l l factors (when imputed according to the marginal product of each factor) exceed the t o t a l product.  On  the other hand, i f the e l a s t i c i t y i s less than 1.0, the shares imputed to resources amount to l e s s than the t o t a l product. Consequently, imputation of f a c t o r returns by the residual procedure does not exactly d i s t r i b u t e a t o t a l product among the resources with which i t was produced, except when the e l a s t i c i t y of production f o r each f a c t o r i s equal to 1.0. The residual method gives the actual marginal value productivity of only one f a c t o r of production when market prices coincide with the marginal value products of other f a c t o r s , and when the e l a s t i c i t y of production i s 1.0 f o r a l l factors»  I f the production function i s not l i n e a r  throughout  a relevant range of resource use, or when farmers -have not attained a resource combination denoted by the l i n e a r portion  7 of a production function, then the e l a s t i c i t y of production w i l l d i f f e r from 1.0 and f a c t o r returns imputed on the basis of the marginal product of each f a c t o r w i l l not add exactly to the t o t a l product.  However, there i s no reason f o r a l l o c a t i n g  the residual surplus or d e f i c i t of the t o t a l product to land or any other single resource.^ The assumption,  i n the tabular method of analysis, of  a l i n e a r relationship between input of resources and output of product also implies a constant r e t u n r to a l l units of input. This means that using an additional unit of a resource always increases the t o t a l product by some constant amount regardless of the previous l e v e l of input.  Such an assumption i s i m p l i c i t  i n recommendations that advocate the maximum physical output per unit of input.  S i m i l a r l y , recommendations that larger  p r o f i t s are possible through continuous increases i n output per unit of input presume a constant marginal product, i n which case there would be no point beyond which increased physical production might lead to decreased p r o f i t s .  A l i n e a r pro-  duction function, however, cannot be accepted as an inputoutput model except i n s p e c i a l s i t u a t i o n s .  I t may provide a  s u f f i c i e n t explanation f o r greater p r o f i t s when output i s i n creased i n the short run.  I t seldom applies, however, to the  input-output relationship f o r a f i x e d technical unit such as an acre or an animal. Many production processes f o r the farm as a d i v i s i b l e E a r l 0. Heady, Economies of A g r i c u l t u r a l Production and Resource Use. (New York: Prentice-Hall, Inc., 1952), pp. 402-414.  8 producing unit involve a l i n e a r input-output r e l a t i o n s h i p . This relationship, of course, does not apply to a single animal or acre as a technical unit which i s i n d i v i s i b l e .  Yet  the t o t a l animals and acres that form part of a farm of f i x e d size, or of a farm with a f i x e d set of buildings and equipment, can be considered as d i v i s i b l e inputs.  In t h i s sense, a l i n e a r  relationship normally exists between the input of animals or land and the output of product.  When technical units (animals  and acres) as w e l l as other resources that enter d i r e c t l y into the production process (feed, seed, f e r t i l i z e r , etc.) are varied i n a fixed proportion, the input-output r a t i o f o r the farm i s l i k e l y to remain f a i r l y constant u n t i l f i x e d resources (operator and family labor, buildings and equipment) are f u l l y utilized.  For example, each additional acre of land used f o r  a crop requires an equal input of seed, f e r t i l i z e r , machinery and labor, and can be considered to add an equal increment to output.  S i m i l a r l y , f o r a farm with a f i x e d acreage and f i x e d  services i n the form of labor, buildings and equipment, the input-output relationship i s l i n e a r over a c e r t a i n range as both feed and livestock numbers are varied from zero to the capacity of the l i m i t i n g f a c t o r .  However, as soon as the stock  of services represented by the f i x e d resources becomes f u l l y engaged i n the production process, any further increase i n the composite input of variable factors may lead to a decline i n the additional output of product.  1  ^For a discussion of the short-run farm production function, see E a r l 0. Heady. Economics of A g r i c u l t u r a l Production and Resource Use. (New York: Prentice-Hall, Inc., 1952),  pp. 78-83.  9  The production function method of analysis i s based on concepts that allow a relaxation of these r e s t r i c t i o n s imposed by the tabular method.  Thus, i t i s capable of providing  esti-  mates of resource productivity that are more r e a l i s t i c f o r an investigation of economic e f f i c i e n c y i n resource use*  Howeverj  t h i s does not imply that the tabular method should be rejected completely as a technique i n farm management a n a l y s i s .  On  the  contrary, i t i s p a r t i c u l a r l y useful f o r summarizing f a c t u a l data i n studies that are primarily h i s t o r i c a l and descriptive i n nature rather than a n a l y t i c a l or p r e d i c t i v e .  This method  can also be applied e f f e c t i v e l y when emphasis i s given to determining and examining the c h a r a c t e r i s t i c s of d i f f e r e n t sizes aridtypes of farms, the variables associated with farm p r o f i t s , and average input-output  r a t i o s such as crop y i e l d per acre,  milk production per cow and feed requirements per animal.  In  addition, preliminary and supplementary analyses of farm inputoutput data by the tabular method are often e s s e n t i a l to the application of other techniques such as a c t i v i t y analysis*  10  THE ANALYTICAL MODEL  The terra ^production function" i s used to describe  the  input-output relationship since any observed relationship between variables corresponds to a functional relationship between the variables©  For example, the output of product i s de-  termined by the quantity of input such as seed, labor, land other resource services.  and  As i l l u s t r a t e d i n Appendix I I I , a  single-variable production function can be shown as a two  -  column tahle with the f a c t o r inputs and the resultant t o t a l output of product l i s t e d i n separate columns. may  be used as a geometrical presentation  Also, a graph  of a production func-  t i o n with the f a c t o r input measured on the horizontal x-axis and the product output measured on the v e r t i c a l y-axis. addition, a production function may  In  be expressed as an alge-  braic equation of the form Y = f(X), which indicates that a functional relationship i s assumed to exist between a single product Y and a single variable f a c t o r X,  In the usual s i t u a t i o n where production of a commodity  requires several resources, a production function i s expressed more accurately i n the form Y — f (Xj_,X2,X^ ) © Here, Y refers to a single product and X^, s p e c i f i c factors of production.  X2, and X3 r e f e r to  11 A production function i n t h i s general form indicates a l l factors that contribute to the output of products,  This  symbolic representation does not specify any quantitative r e lationships between variables*  These are expressed only by  writing the production function i n an algebraic form such as T = a + bX^,  Y=  or  axfyf.  The l e t t e r s a, b and c denote constants*  The values of these  constants specify the quantitative relationship between the output of product and the inputs of resources, or the amount by which the product Y changes as the inputs of f a c t o r X^ or are varied* Input-output relationships or production functions can be expressed by many d i f f e r e n t types of equations*  However, a  p a r t i c u l a r relationship i s not described with equal accuracy by a l l equations and, conversely, any one equation i s not adequate to express a l l relationships*  Each type of equation i s capable  of accurately representing only certain types of relationships* Several d i f f e r e n t equations might be f i t t e d to the same set of data, but considerable v a r i a t i o n would occur i n the accuracy with which each equation described the true relationship*  The  equation of a straight l i n e f i t t e d to data involving a l i n e a r relationship w i l l accurately express the true relationship shown by the data*  Any attempt to represent t h i s relationship  by any other equation would only r e s u l t i n a distorted and often misleading expression of the true relationship*  The true nature  of a relationship i s revealed only within the l i m i t a t i o n s of the  12  p a r t i c u l a r equation that i s used.  Consequently, the choice of  an equation to represent the relationship between two variables must depend on a l o g i c a l analysis of the  or more  relationship  as well as the a b i l i t y of any given equation to express the empirical  relationship.  Homogeneity of quality i n the factors of production and i n the product i s necessary f o r an input-output relationship to have any s i g n i f i c a n c e .  S i m i l a r l y , the input-output relationship  cannot be defined i f v a r i a t i o n i n the quality of product occurs with d i f f e r e n t l e v e l s of input.  The production function  also  relates to a s p e c i f i c time period and to a certain technique of production since the input-output relationship changes with the method of production. Several types of mathematical functions comprised of various combinations of squared, cubed, cross-product, square root, exponential, and r e c i p r o c a l terms have been used to e s t i mate the relationship between t o t a l output of product and or more inputs.  two  Each function imposes d e f i n i t e r e s t r i c t i o n s  on the relationships that can be expressed because the mathematical c h a r a c t e r i s t i c s of each function contain certain p l i c i t assumptions about the nature of the  im-  relationships.  Consequently, the p a r t i c u l a r function should be selected f o r i t s a b i l i t y to represent adequately the t h e o r e t i c a l model which describes the general form of the input-output r e l a t i o n s h i p . The selection of a function to s a t i s f y t h i s requirement becomes increasingly d i f f i c u l t with the complex relationships introduced by several resource categories and,  as a r e s u l t , some degree of  13  compromise i s often a p r a c t i c a l necessity* The function selected to represent the input-output r e lationships i n the production of market eggs was of the general form y = aX lX 2....x n. b  1  b  h  2  n  Commonly known as the Cobb-Douglas production function, i t was f i r s t used by Cobb and Douglas to estimate the proportions of t o t a l product attributable to labor and c a p i t a l i n manufacturing industries,  1  I t was also employed by Douglas and h i s associates  i n l a t e r studies that involved a similar analysis f o r various regions and time periods.  2  A function of t h i s general form was  amonggthose used by Nicholls i n an analysis of labor product i v i t y i n a meat packing p l a n t ^ and has been applied extensivel y i n the analysis of resource productivity on farms when the main objective was estimation of marginal value productivities of inputs f o r a sample of farms. •"•See Charles W. Cobb and Paul H, Douglas. "A Theory of Production?. The American_Economlc_Review. XVIII (March. 1928), pp, 139-165; and Paul H, Douglas. The Theory of Wages. (New York: The Macmillan Company, 1934). For example, see M a r j o r i e L . Handsaker and Paul H, Douglas, "The Theory of Marginal Productivity Tested by Data for Manufacturing i n V i c t o r i a . " The Quarterly Journal of Economics. L I I (1937-1938).. pp. 1-36 and 215-254; M. Bronfenbrenner and Paul H, Douglas, "Gross-sectional Studies i n the Cobb-Douglas Function." The Journal of P o l i t i c a l Economy. XLVII (December, 1939), pp. 761-785; and Grace T. Gunn and Paul H, Douglas, "The Production Function f o r American Manufacturing i n 1914," The Journal of P o l i t i c a l Economy, L (August, 1942), pp. 595-602. 2  3w. H. Nicholls, Labor Productivity Functions i n Meat Packing. (Chicago: University of Chicago Press, 1948J.  14 Characteristics of the Cobb-Douglas Production  Function  The Cobb-Douglas function possesses several desirable properties f o r the analysis of the productivity of  resources*  Compared with other functions, estimation of fewer constants  or  regression c o e f f i c i e n t s i s required f o r the same number of variables*  I t also permits either increasing or  decreasing  marginal productivity of each input variable with fewer terms (and regression c o e f f i c i e n t s ) than are required by other types of functions*  This reduces the loss i n degrees of freedom and  saves time i n computation*  Also, a s t a t i s t i c a l t e s t of s i g -  nificance can be r e a d i l y applied to each regression c o e f f i c i e n t * Since the Cobh-Douglas function i s l i n e a r i n the logarithms, i t can be f i t t e d by the l e a s t squares method of l i n e a r multiple regression*  After the parameters of the function have been de-  rived, i t i s . r e l a t i v e l y easy to compute marginal p r o d u c t i v i t i e s of the resource inputs from the p a r t i a l - d e r i v a t i v e of the function i n respect to each resource* The regression c o e f f i c i e n t s d i r e c t l y provide  the  e l a s t i c i t y of production of the respective factors-which i s the percentage change i n output that would-result  from a  one  per cent increase i n input of that f a c t o r with a l l other factors held constant.  I f an e l a s t i c i t y of production  (re-  gression c o e f f i c i e n t ) i s l e s s than one and greater than zero, the l e v e l of f a c t o r input f a l l s within the r a t i o n a l area of production*  Under t h i s condition,-additional inputs of the  f a c t o r r e s u l t i n a decreasing marginal product.  15  The sum of the e l a s t i c i t i e s (regression c o e f f i c i e n t s ) indicates the returns to scale associated with the resource combination represented by the production function.  A sum of  e l a s t i c i t i e s equal to one indicates constant returns to scale since a one per cent increase i n a l l f a c t o r inputs would add the same percentage increase to the output of product; a sum equal to less than one indicates decreasing returns to scale, and a sum greater than one shows increasing returns. There are other mathematical properties inherent i n the Cobb-Douglas function which may present c e r t a i n l i m i t a t i o n s to an adequate expression of factor-product and f a c t o r - f a c t o r r e lationships.  This function imposes a constant e l a s t i c i t y of  production f o r each f a c t o r over a l l ranges of input.  In other  words, i t implies that the proportional change i n output of product remains constant f o r any given proportional change i n the input of a f a c t o r , regardless of the l e v e l of f a c t o r input. The Cobb-Douglas function also imposes constant e l a s t i c i t i e s of s u b s t i t u t i o n f o r a l l l e v e l s and combinations of f a c t o r inputs.  This assumes that the slope of successive i s o -  product curves i s the same at the points of i n t e r s e c t i o n with a given scale l i n e , or that the rate of f a c t o r substitution remains constant at a l l l e v e l s of output f o r a f i x e d proportion of f a c t o r inputs.  Under t h i s condition, the i s o c l i n e s and  scale l i n e s are straight l i n e s , and the proportion of d i f f e r e n t resources i n the least cost combination does not vary with l e v e l of output. The Cobb-Douglas function expresses  either constant,  16 increasing, or decreasing marginal productivity, but not a combination of these conditions. Consequently  i t would not be  an appropriate function f o r expressing a factor-product r e l a t i o n s h i p covering the range of increasing and decreasing marginal returns* Iso-product contours under the Cobb-Douglas function become asymptotic to the input axes*  The contours never i n t e r -  sect the axes, suggesting that the product can never be produces with one resource alone*  This implies that complementar-  i t y of resources, or very nearly so, occurs i n the extreme ranges of f a c t o r combination, but that substitution of resources i s possible throughout the c e n t r a l portion of the iso-product contour* A high degree of c o r r e l a t i o n between input variables may d i s t o r t any estimates of resource productivity and, i n some cases, may prevent the determination of true productivities* For p r a c t i c a l purposes, i t may be necessary t o assume that j o i n t factors, or perfect complementarity  of f a c t o r s , are  present and that independent p r o d u c t i v i t i e s do no exist*  Under  t h i s assumption, the complementary factors would be treated as a single composite input*  Some Applications of the Cobb-Douglas Production Function i n Analysis of Resource Productivity on Farms Production functions, as a means of expressing the functional relationship between resource inputs and product output, have been used f o r two main purposes*  F i r s t , they have  17 been used to compute physical input-output r a t i o s f o r technical units of production such as quantity of f e r t i l i z e r applied per acre of crop, quantity of feed fed per animal, and of feeds i n a r a t i o n .  combinations  Second, they have been used as a diag-  nostic t o o l to estimate the productivity of general categories of resources to provide an indication of the efficiency with which resources are employed on farms. Use of the Cobb-Douglas function has been somewhat limited i n studies of the physical input-output relationships i n the application of variable resources to a fixed technical unit.  In many cases, some other equation was more appropriate,  both l o g i c a l l y and s t a t i s t i c a l l y , f o r defining these physical relationships, p a r t i c u l a r l y when only one or two variable resources were being examined. However, the Cobb-Douglas function has not been entirely disregarded i n analyses of t h i s aspect of resource u t i l i z a t i o n .  In an exploratory study based on data  from an experiment designed f o r a different purpose, Heady used a Cobb-Douglas function in^deriving a t o t a l product function f o r milk with forage and grain as variable inputs. An isoquant (iso-product) equation also was obtained, from which marginal rates of substitution of forage f o r grain were estimated,  1  Another publication contains the results of a feeding experiment purposely designed f o r investigation of the input-output relationship i n pork production with corn and a protein supplement as variable feed inputs, A Cobb-Douglas function was.one of two ^Earl 0, Heady, "A Production Function and Marginal Rates of Substitution i n the U t i l i z a t i o n of Feed Resources by Dairy Cows" Journal of Farm Economics.XXXIII (November,1951),pp.485498. ~  18 types of equations f i t t e d to several groups of data*  Functions  were derived also f o r estimating marginal physical products, corn-protein combinations  that produce a given gain i n weight  (iso-product curve), and marginal rates of corn/protein substitution.  1  Many studies of resource productivity relationships f o r the farm as a unit, involving at least four or f i v e categories of resources, have r e l i e d on the Cobb-Douglas production function.  Tintner and Brownlee were among the f i r s t to apply  t h i s method of analysis.  Using business records of 468 Iowa  farms f o r 1939, they estimated- the marginal value p r o d u c t i v i t i e s and production e l a s t i c i t i e s f o r s i x classes of resources on f i v e farm types (dairy, hog, beef feeder, crop and general). product was measured by gross income i n d o l l a r s .  Total  The categories  of resource inputs included land ( i n acres), labor ( i n months), farm improvements ( i n d o l l a r s ) , l i q u i d assets ( i n d o l l a r s ) , working assets.(in d o l l a r s ) and cash operating expenses ( i n dollars)•  2  In a subsequent study by Heady, production functions were derived from a random sample of Iowa farms f o r the year 1939.  The o r i g i n a l data was collected by the survey method.  The t o t a l value of products r e s u l t i n g from the year s operations 1  E a r l 0. Heady, Roger G. Woodworth, Damon Catron, and Gordon C.Ashton, "An Experiment t o Derive Productivity and Substitution Coefficients i n Pork Output," Journal of Farm Economics. XXXV (August, 1953), PP. 341-354. 1  Gerhard Tintner and 0. H. Brownlee, "Production Functions Derived from Farm Records," Journal of Farm Economics. XXVI (August, 1944), pp. 566-571. 2  19 was used as-the measure of t o t a l output.  Inputs were c l a s s i f i e d  as r e a l estat e (inventory value of land and buildings), labor (in months), machinery and equipment (value of machinery and cash expenses f o r repairs, f u e l and o i l ) , livestock (value of livestock, livestock expenses and value of feed fed to l i v e s t o c k ) and cash operating expenses ( f e r t i l i z e r , twine, custom work, etc,)*  Five groups of farms were defined according to l o c a t i o n  within the state i n order to examine the returns to s p e c i f i c resources used on land i n various productivity ratings, and to compare the returns f o r areas with d i f f e r e n t combinations land, labor and other resources,  of  A grouping was made also  according-to type of farm (crop, hog, dual purpose and dairy, general, and s p e c i a l ) .  F i n a l l y , the farms i n the sample were  c l a s s i f i e d as large or small on the basis of t o t a l c a p i t a l * This grouping was made to test a hypothesis, of a range of i n creasing as w e l l as decreasing returns to s c a l e ,  1  The main objectives of a study by Heady and Shaw were to measure the marginal value productivity of resources used i n d i f f e r e n t farming regions, and to predict the effect of d i f f e r ent quantities of resources on the value of product produced* Random samples of farms were selected i n 1951 f o r the Piedmont area of Alabama, North Central Iowa, Southern Iowa, and the dry-land wheat area of Montana*  These areas d i f f e r e d con-  siderably i n the kinds and quantities of resources employed on farms and i n the t o t a l amount of output per, farm.  Separate  "hsarl 0 « Heady, "Production Functions from a Random Sample of Farms " Journal of Farm Economics. XXVIII (November,  1946), pp, .96*9-1004".  !  20 production  functions f o r livestock and crops were computed f o r  each region t o enable a comparison of resource productivity i n primary (crop) production and secondary (livestock) production. The resource inputs f o r crops were c l a s s i f i e d as cropland ( i n acres), labor on crops ( i n months) and a l l c a p i t a l services used i n crop production  (seed, f e r t i l i z e r , t r a c t o r f u e l , r e -  pairs, depreciation on machinery, etc.)•  The resource cate-  gories f o r livestock consisted of labor used on l i v e s t o c k ( i n months) and a l l c a p i t a l inputs f o r livestock (value of grain, hay,  pasture and other feeds, purchase value of feeder  stock,  depreciation and repairs f o r livestock buildings and equipment, etc.).  1  An approach to the problem of deriving an independent production function f o r each enterprise on d i v e r s i f i e d farms was reported by Beringer.  A  single function derived from data  f o r farms with several enterprises was considered  unsatisfactory  because such a function i s u n l i k e l y to be a true expression of the inputsoutput  relationships f o r any one enterprise.  I t was  reasoned that enterprise functions f o r multiple enterprise farms are independent of each other, and usually d i f f e r from the corresponding functions derived f o r specialized single enterp r i s e farms.  Data was obtained from detailed cost accounts f o r  27 dairy-hog farms i n north-western I l l i n o i s .  Separate pro-  duction functions f o r the dairy, hog and crop enterprises, and a composite production function f o r the farm were derived from "^Earl 0. Heady and Russell Shaw, Resource Returns and Productivity C o e f f i c i e n t s i n Selected Farming Areas." Journal of Farm Economics. XXXVI (May, 1954), pp. 243-257.  21 the data.  Input categories f o r both l i v e s t o c k enterprise  functions included labor ( i n hours), feed ( i n d o l l a r s ) , cash expenses ( i n d o l l a r s ) , machinery investment ( i n d o l l a r s ) , l i v e stock investment ( i n d o l l a r s ) , and housing ( i n animal u n i t s ) . Only four resource c l a s s i f i c a t i o n s were used f o r the crop enterp r i s e function: labor ( i n hours), land ( i n acres), cash expenses (in d o l l a r s ) and machinery investment ( i n d o l l a r s ) *  Feed was  excluded as an input variable i n the composite function f o r the farm.  Marginal value p r o d u c t i v i t i e s were estimated f o r the  various input categories used i n the four production functions. The p o s s i b i l i t y of obtaining more meaningful productivity estimates from the enterprise functions was  examined by com-  paring the enterprise functions with the composite farm function.^" Changes i n the combination of resources employed on  146  commercial farms i n north-central I l l i n o i s between the periods of 1936-39 and 1950-53 were studied by Swanson. function was  A production  derived f o r each period from data contained i n  account books kept on these farms.  Resource inputs were c l a s s i -  f i e d as land investment, buildings and s o i l improvements, l i v e stock investment, labor, power and machinery, and purchased feed. I t was assumed that a reasonably  e f f i c i e n t combination of r e -  sources had been attained on these farms during the years to 1939.  1936  The production e l a s t i c i t y necessary i n the 1950-53  period to provide the marginal value productivity that prevailed ^Christoph Beringer, "Estimating Enterprise Production Functions from Input-Output Data on Multiple Enterprise Farms", Journal of Farm Economics. XXXVTII (November, 1956),pp. 923-930.  22  i n 1936-39 was calculated f o r each class of resources.  These  adjusted production e l a s t i c i t i e s were compared with the actual e l a s t i c i t i e s f o r 1950-53 t o specify any s i g n i f i c a n t differences i n the resource combinations employed during the two periods* Reference could be made t o many other studies of r e source productivity f o r the farm unit*  Those c i t e d above were  selected as i l l u s t r a t i o n s of the problems to which the CobbDouglas production function has been applied as a method of analysis* ^ E a r l R* Swanson, "Resource Adjustments on 146 Commercial Corn-belt Farms, 1936-1953", Journal of Farm Economics. XXXIX (May, 1957), pp. 502-5037  23  LIMITATIONS OF PRODUCTION FUNCTION ANALYSIS  The production function method of analyzing  farm;.input-  out put data i s subject to c e r t a i n l i m i t a t i o n s which originate mainly i n the aggregation  of numerous resources into a few i n -  H  put categories©  Basic c h a r a c t e r i s t i c s of the data prevent the  selection of a small number of independent input categories so that each retains a completely  separate, d i s t i n c t and additive  relationship to the dependent output v a r i a b l e .  I f the input  variables are not independent, the derived c o e f f i c i e n t s w i l l not be an accurate expression of the functional relationships between resource input and product-output.  This d i f f i c u l t y  may  be p a r t l y overcome by combining the i n d i v i d u a l inputs into categories that are neither good substitutes not good complements f o r each other. The input variables are not completely substitutable and d i v i s i b l e .  Many resources used i n a g r i c u l t u r a l production  can be replaced by others to only a l i m i t e d degree, or are available only i n discontinuous and i n d i v i s i b l e u n i t s .  Conse-  quently, something short of perfect s u b s t i t u t a b i l i t y and d i v i s i b i l i t y i s attained by grouping resources i n t o a small number of input categories. Management i s not included as a f a c t o r a f f e c t i n g output because a quantitative measurement of t h i s input i s most d i f f i cult.  Thus, i t s omission from the analysis must introduce a  24 bias into estimates of the effects of other inputs that are measured and taken into  account*  The production function derived from a group of farms does not indicate the relationships that exist within an i n d i vidual farm.  The aggregation of resource inputs necessary to  make the function manageable tends to obscure the d i v e r s i t y i n quality of resources and i n techniques of production that i s normally found on a group of farms.  Unless the farms i n the  sample are homogeneous with respect t o methods of production, quality of resources used and kind of products produced, the estimated relationships w i l l not be d e s c r i p t i v e of any single farm.  They are more l i k e l y to represent a "hybrid" of several  d i f f e r e n t functions.  Differences i n resource q u a l i t i e s may be  reconciled to some extent by expressing inputs i n terms of t h e i r d o l l a r values, but differences i n production techniques are not necessarily r e f l e c t e d by input values.  Some a d d i t i o n a l homo-  geneity i s introduced by grouping and s t r a t i f i c a t i o n of farms according to one or more f a c t o r s or c h a r a c t e r i s t i c s .  However,  the results of a production function analysis are not widely applicable to predicting the outcome of operations on i n d i v i d u a l farms. Selection of the input categories and a l l o c a t i o n of i n d i v i d u a l items to the appropriate category are among the more s p e c i f i c l i m i t a t i o n s to a p p l i c a t i o n of the production function method of a n a l y s i s . Although many i n d i v i d u a l items must be aggregated i n some manner, only a small number of input categories can be used i n order to minimize the amount of mathe-  25 matical computation and the loss of degrees of freedom.  A l l of  the important economic f a c t o r s that contribute to the output of product, and that are also subject to quantitative measurement, are grouped into categories which, i d e a l l y , are f u n c t i o n a l l y independent of each other*  These categories then become the  input variables i n the equation chosen to describe the inputoutput relationships* I f the input variables are not functiona l l y independent, the r e s u l t w i l l be a large proportion of unexplained v a r i a b i l i t y i n the dependent variable, i n t h i s case, the t o t a l output of product*  The value of the regression coef-  f i c i e n t s may be biased upwards i f j o i n t relationships exist with other factors that were not considered*  Some form of pre-  liminary analysis t o determine the relationships between proposed input categories would serve as a guide to s e l e c t i n g categories that conform as near as possible t o the requirements f o r independence* In addition to the problems of i d e n t i f i c a t i o n and separation of the input categories, there are a number of important problems of measurement associated with a production function analysis.  The most s a t i s f a c t o r y method of measuring  production function variables i s i n terms of physical units that express a standard quantity and q u a l i t y of each factor* However, t h i s i s a p r a c t i c a l i m p o s s i b i l i t y f o r categories such as equipment and r e a l estate due t o the d i f f i c u l t y of reducing resource inputs of inherently d i f f e r e n t sizes and q u a l i t i e s t o a common physical unit*  In many cases, the only a l t e r n a t i v e  i s t o measure these inputs i n d o l l a r values, which r e s t r i c t s  26  a p p l i c a t i o n of the r e s u l t s of the analysis to a s p e c i f i c costprice s i t u a t i o n . With resource inputs and product output measured i n terms of current prices, projection of the r e s u l t s i s l i m i t e d to situations that provide s i m i l a r factor-product price r e l a t i o n s h i p s .  On the other hand, i f inputs and output  are valued at long-time normal prices, the input-output relationships revealed by the analysis may wider range of conditions.  be extended over a  This, i n turn, involves the se-  l e c t i o n of an appropriate period on which the long-time prices may  be based. Production functions can be derived from data that are  expressed i n either physical or value u n i t s .  A l l quantities of  input and output i n the production function f o r a group of farms could be measured i n d o l l a r value.  Ordinarily, however, inputs  such as land and labor are measured i n physical units, and output and other input categories are measured i n d o l l a r s .  Even  though the product output and a l l resource inputs are measured i n d o l l a r s , the t e c h n i c a l relationships are the same as i f a l l data were expressed i n physical u n i t s ; the value function i s only a t r a n s l a t i o n of the physical  production  production  function. These l i m i t a t i o n s indicate the necessity f o r caution i n using the production function method of analysis and i n i n terpreting the r e s u l t s obtained.  A production function analysis  of farm business data i s most useful as a diagnostic device f o r defining problems that require further investigation with more s p e c i f i c techniques.  The Cobb-Douglas function provides  27 measurements of resource e f f i c i e n c y based on the performance of a group of farms*  I t i s only a guide to s p e c i f i c resource  use on the individual farm*  28  ANALYSIS OF THE EMPIRICAL DATA  Source of the Data Empirical data used i n t h i s thesis were obtained from records of poultry e n t e r p r i s e s which tend to f a l l i n t o one of 1  the following types: (1) Specialized f u l l - t i m e poultry farms on which income from other farm products and non-farm income,-: were small; (2) part-time farms usually operated by persons i n semi-retirement or who had a f u l l - t i m e occupation other than farming, with most of the farm income supplied by a small to medium s i z e poultry f l o c k , but with non-farm income often exceeding farm income; (3) f u l l - t i m e farms with poultry as a major or minor enterprise combined with one or more other enterprises such as small f r u i t s or dairy*  The data were obtained  almost e n t i r e l y from the specialized poultry farms*  A few of  the part-time farms were included and a l l enterprises of l e s s > than 200 laying birds were excluded* Detailed information on the poultry enterprise was collected by the account book method f o r a twelve-month period s t a r t i n g at October 1*  Enumerators completed the beginning i n -  ventory record and instructed the farm operator on the entries required i n the account book.  Supplementary forms were supplied  ^"These poultry enterprise records were obtained i n the Lower Fraser Valley and Vancouver Island areas of B r i t i s h Columbia by the Economics Division, Canada Department of A g r i culture, and cover the three-year period of October 1, 1948 to September 30, 1951.  29 as an a i d to keeping a d a i l y record of such items as egg production, c u l l i n g and mortality, and producers were asked to r e t a i n egg sales statements, feed b i l l s and other s i m i l a r records of receipts and expenses f o r the poultry enterprise. Most farms were v i s i t e d twice during the year to check the account books or to a s s i s t i n making the entries.  At the end  of the year a f i n a l c a l l was made to complete the ending inventory and to c o l l e c t the completed account book. The inventories included values f o r each item under land, buildings, equipment, f l o c k , feed and supplies, along with the description and quantity of these items.  Current  accounts included: (1)  Records of d a i l y egg production, mortality and c u l l i n g f o r hens and p u l l e t s ;  (2)  Amounts sold and cash receipts from market eggs, hatching eggs, fowl, fryers,and b r o i l e r s ;  (3)  The quantity and cost of each kind of feed fed to layers and young stock;  (4)  ^  Other expenses e n t i r e l y chargeable to the poultry enterprise such as l i t t e r , chicks and other poultry purchased, hired labor, brooder f u e l , disinfectant, repairs to poultry buildings and equipment;  (5)  Amounts charged to the poultry enterprise f o r e l e c t r i c i t y , insurance, r e a l estate taxes, and operating costs of car, truck and tractor, as estimated from the t o t a l farm expense f o r each item;  (6)  Labor time i n hours, as estimated by each producer,  30 divided between caring f o r the laying f l o c k and r a i s i n g young, birdso A t o t a l of 299 completed account books, each covering a period of 12 months, was obtained during t h i s study*  Some pro-  ducers co-operated throughout the three-year period of the studjj others participated f o r only one or two years*  Consequently,  the information collected i n each year pertained t o a somewhat different^ group of poultry enterprises* Income from the sale of market eggs was the major source of revenue f o r more than one half of the enterprises*  For the  remainder, market eggs were i n most cases the main product, supplemented by the sale of hatching eggs and/or poultry meat (fryers and b r o i l e r s ) on a seasonal basis*  C u l l layers sold as  fowl were a source of income common to a l l enterprises*  Thus,  i t was possible t o define four d i s t i n c t types of poultry enterprise based on the combination of products*  These were desig-  nated as: (1)  Specialized market egg;  (2)  Combination market and hatching egg;  (3) Combination market egg and poultry meat; (4)  Combination market egg, hatching egg and poultry meat* A l l data used i n t h i s section were taken from records  f o r the specialized market egg enterprises* T h i s group was selected with the objective of obtaining some degree of homogeneity i n the general characteristics of enterprise organi_ aation, production methods and kind of product*  I t includes  a t o t a l of 168 records comprised of 66, 57 and 45 records f o r  31 the respective years 1949, 1950; and 1951 ending on September 30.  Method of Analysis Total output and the various input categories selected f o r analysis of the data by the production function were designated as f o l l o w s :  1  t o t a l output measured i n d o l l a r s ; Xg, annual input of r e a l estate and equipment measured i n dollars; X3, laying f l o c k input measured i n layer years; X^, labor input measured i n hours; X5, feed input measured i n d o l l a r s ; X£, other cash inputs measured i n d o l l a r s . Output i s a function of the f i v e input categories which include the t o t a l resources used f o r the market enterprise. Accordingly, the production function can be expressed i n the general form of x  l  =  f  ( 2 > 3» 4> 5» x  x  x  x  x  6^  In the logarithmic form of the Cobb-Douglas function, the inputoutput r e l a t i o n s h i p i s s p e c i f i e d as: logX-j^ = log a -f b l o g X 2  2  + 0 3 ^ X 3 + b^logX^ + b 5 l o g X  5  + b^logXge Values f o r t o t a l output and f o r each of the input categories, calculated f o r each enterprise from data contained i n the enterp r i s e records, were converted to logarithms to allow estimation ^-See Appendix IV f o r d e t a i l s of the items aggregated i n t o t a l output and i n the input categories.  of the function i n t h i s forme  The Cobb-Douglas production  function f o r each year was derived from the respective sets of logarithmic values by the least-squares method of f i t t i n g a l i n e a r multiple regression  equation,  1  The Results and Their S t a t i s t i c a l R e l i a b i l i t y The following production functions were derived: Year 1949 logX  x  • logO.4250 - 0.0106logX +0.26001ogX3 - 0.08291ogX^ 2  + 0.79191olX5 + 0,04421ogX . 6  Year 1950 logX-L = logO.4792 - 0 . 0 5 8 7 ^ X 2 + 0 . - 1 5 1 4 ^ X 3 -4-0.01301ogX  4  + 0,65141ogX + 0.23231ogX . 5  6  Year 1951 logX  1  = logO.4847 - 0.0206logX +0.24641ogX3 -f 0.01021ogX^ 2  + 0.73 751ogX -f 0,02821ogX , 5  6  S t a t i s t i c a l measures r e l a t i n g t o the r e l i a b i l i t y of the production functions are given i n Table 1. The standard error of estimate indicates the discrepancy between estimates of t o t a l output based on the production function and the actual t o t a l outputs contained i n the sample. It i s a measure of the range of error that could be expected i n estimates of t o t a l output.  The s t a t i s t i c a l meaning of t h i s  measure i s that the t o t a l output estimated from the production •^•Computation of the regression c o e f f i c i e n t s , and the t e s t s f o r r e l i a b i l i t y of the regression c o e f f i c i e n t s and the production function are outlined i n Appendix V.  33  function would probably deviate from the actual t o t a l output by l e s s than one standard error of estimate i n 6 8 per cent of the cases and by less than two standard errors i n 9 5 per cent of the cases.  TABLE 1 MEASURES OF RELIABILITY OF THE PRODUCTION FUNCTION  Adjusted standard error of estimate (log value) Range of two standard errors f o r an estimated t o t a l output of #1,000: From To Range of two standard errors f o r an estimated t o t a l output of |10,000: From To Adjusted c o e f f i c i e n t of multiple determination Adjusted c o e f f i c i e n t of multiple correlation Standard error of c o e f f i c i e n t of multiple c o r r e l a t i o n Significance of c o e f f i c i e n t of multiple c o r r e l a t i o n (t-value) a  (P  =  1949  1950  1951  0.0550  0.0754  0.0608  776 1,288  1,415  756 1,323  707  7,762 12,882  14,151  7,558 13,231  0.9526  0.9381  0.9463  0.9760  0.9686  0.9728  0.0057  0.0079  0.0076  36.201&  7,066  29.227  A  27.937  A  S i g n i f i c a n t at one per cent l e v e l of p r o b a b i l i t y  0.01).  Since the standard error of estimate i s expressed as a logarithm, i t must be applied to the logarithmic value of an estimated t o t a l output.  The range of error when converted from  logarithms to natural numbers does not remain constant and the confidence i n t e r v a l s are not symmetric, but varies d i r e c t l y and proportionally with the s i z e of the estimated output.  For t h i s  reason, the range of two standard errors of estimate f o r t o t a l  34 outputs of $1,000 and $10,000 are given i n Table 1.  Since the  output of nearly a l l enterprises was between $1,000 and $10,000, these ranges indicate the approximate l i m i t s within which both the estimated and the actual outputs could be expected to f a l l * Although the range of error i n estimates appears large, i t would be expected that 95 per cent of the actual outputs are within these l i m i t s * As indicated by the c o e f f i c i e n t s of multiple determination, approximately 95 per cent of the variance i n t o t a l output (gross income) of the market egg enterprises i s explained by the input categories of r e a l estate and equipment, laying flock, labor, feed, and other cash expenses*  Inputs other than  these apparently had l i t t l e effect on t o t a l output* The c o e f f i c i e n t s of multiple c o r r e l a t i o n show that a high degree of association exists between t o t a l output and the c o l l e c t i v e input categories*  (Values as high as 0.97 are some-  what exceptional, since a value of 1.0 f o r the c o r r e l a t i o n coeff i c i e n t indicates perfect c o r r e l a t i o n ) .  A l l of the multiple  correlation c o e f f i c i e n t s are s t a t i s t i c a l l y s i g n i f i c a n t at the one per cent l e v e l of probability* The regression c o e f f i c i e n t s of the production functions derived f o r each year, along with the standard errors and t values, are l i s t e d i n Table 2.  A regression c o e f f i c i e n t i n the  Cobb-Douglas function i s the production e l a s t i c i t y of the r e spective resource category*  I t indicates the percentage change  i n t o t a l output that i s associated with a one per cent increase i n the input of a resource, with the input of a l l other r e -  35 TABLE 2 REGRESSION COEFFICIENTS, STANDARD ERRORS, VALUES OF t , AND PROBABILITIES 1949  1950  1951  -0.0106 0.2600 -0.0829 0.7919 0.0442  -0.0587 0.1514 0.0130 0.6514 0.2323  -0.0206 0.2464 0.0102 0.7375 0.0282  Sum of e l a s t i c i t i e s  1*0026  0.9894  1.0017  Standard error of regression coefficients: Real estate and equipment Laying f l o c k Labor Feed Other cash expenses  0.0367 0.1134 0.0573 0.1461 0.0386  0.0600 0.1773 0.0708 0.233 0 0.0570  0.0498 0.1469 0.0564 0.1891 0.0606  Values of t : Real estate and equipment Laying f l o c k Labor Feed Other cash expenses  0.289 2.293 1.446 5.412 1.145  0.978 0.854 0.184 2.796 4.075  0.413 1.677 0.181 3.901 0.465  Probabilities:* Real estate and equipment Laying f l o c k Labor Feed -Other cash expenses  0.387 0.014 0.081 b 0.130  0.168 0.199 0.427 0.004 b  0.341 0.051 0.429 b 0.323  Regression c o e f f i c i e n t s (production elasticities): Real estate and equipment ( X ) Laying f l o c k (Xo) Labor (X. ) Feed (XcT Other cash expenses (X5) 2  P r o b a b i l i t y that an equal or greater value of the observed regression c o e f f i c i e n t could have occurred because of sampling v a r i a t i o n . D  Less than 0.0005.  sources held constant.  For example, the production  elasticity  (regression c o e f f i c i e n t ) of the laying f l o c k input i n 1949 i s 0.2600.  This means that a one per cent increase i n the input  36 of laying f l o c k alone produced an increase of 0.26  per cent  i n t o t a l output. The magnitude of the production e l a s t i c i t y also reveals the nature of marginal returns to the production factor,  Di-  minishing marginal returns exist f o r the resource categories with an e l a s t i c i t y of production that i s p o s i t i v e and less than unity.  Total output increases, but at a decreasing rate, as  additional inputs of any one of these resource categories are combined with f i x e d quantities of a l l other resources.  Negative  marginal returns are indicated f o r the resource categories with a negative e l a s t i c i t y of production.  Precisely interpreted,  t h i s means that further increases i n the input of any one of these resource categories causes a decline i n t o t a l output. Such conditions, however, appear inconsistent with the l e v e l s of resource use and production that are usually found on farms. Normally, the input of any one resource would not be extended to the point where additional applications caused a reduction i n the t o t a l product.  Since none of the negative e l a s t i c i t i e s  d i f f e r s i g n i f i c a n t l y from zero (at the f i v e per cent l e v e l of p r o b a b i l i t y ) , i t i s more r e a l i s t i c to assume that the marginal return i s zero, and that the t o t a l output i s unaffected by i n creasing the input of these resource categories. Returns to scale, as indicated by the sum of e l a s t i c i t i e s , are constant f o r a l l p r a c t i c a l purposes.  Constant  returns to scale exist when a proportionally equal increase i n a l l resources i s accompanied by the same proportional increase i n product.  For example, a ten per cent increase i n the input  37 of a l l resource categories would enlarge the t o t a l output of product also by ten per cent. The standard error of a regression c o e f f i c i e n t indicates the r e l i a b i l i t y of the regression c o e f f i c i e n t as a measure of the functional r e l a t i o n s h i p between an input category and the output of product.  The regression c o e f f i c i e n t s are only the  best estimates of the input-output relationships i n market egg production as derived from a sample of enterprises and, therefore, are l i k e l y to deviate from the true parameters due to chance v a r i a t i o n i n the sample.  The standard error of a r e -  gression c o e f f i c i e n t provides a measure of the probable range of the difference between the estimated and the true inputoutput r e l a t i o n s h i p , A regression c o e f f i c i e n t and i t s standard error are interpreted as follows:  The chances are 68 out of  100 ( i . e . , P = 0.68) that the true regression c o e f f i c i e n t f a l l s within the range of one standard error on either side of the estimated regression c o e f f i c i e n t .  For example, the p r o b a b i l i t y  i s 0.68 that the true regression c o e f f i c i e n t of the laying f l o c k input i n 1949 f a l l s between 0.26 plus and minus 0.11, or between 0.37 and 0.15.  S i m i l a r l y , the p r o b a b i l i t y i s 0.95  that the true regression c o e f f i c i e n t f a l l s between 0.26 plus and minus two standard errors, or between 0.48 and 0.04. Stated i n terms of the input-output r e l a t i o n s h i p f o r 1949, an addition of one per cent to the l a y i n g f l o c k input would i n crease the t o t a l output by 0.15 t o 0.37 per cent i n two out of three cases, and by 0.04 and 0.48 per cent i n 19 out of 20 cases.  3*  A regression coefficient was appraised f o r significance according to the probability that i t differed from zero due to sampling variation, as determined by the t - t e s t .  The proba-  b i l i t i e s ( i n Table 2) indicate that the regression coefficients f o r laying flock and feed i n 1949, f o r feed and other cash expenses i n 1950, and f o r laying flock-and feed i n 1951 d i f f e r s i g n i f i c a n t l y from zero at the f i v e per cent l e v e l of s i g n i f i cance. Except f o r the labor input i n 1949, the coefficients f o r a l l other input categories are non-significant at the ten per cent l e v e l of significance.  39  INTERPRETATION OF THE RESULTS  The average l e v e l s of input f o r the various resource categories, as measured by the geometric mean, are shown i n Table 3.  The estimated marginal value products ( i n the same  table) r e l a t e s p e c i f i c a l l y to these input l e v e l s because a marginal product derived from the Cobb-Douglas function varies with the quantity (input l e v e l ) of resources.  The marginal  value products are the returns which, on the average, could be expected from the addition of one more unit of the respective resource categories. For example, increasing the laying f l o c k input by one layer year i n 1949 would have added $2.25 i n output of product, with other inputs held constant at the l e v e l of the geometric means.  S i m i l a r l y , an additional d o l l a r spent  on feed i n 1949 would have returned $1.33 i n output of product. The marginal value products i n the second part of Table 3 are expressed as dollars per unit of input used i n deriving the production function.  The laying f l o c k and labor inputs are  measured i n layer years and hours, respectively, while the other inputs are measured i n d o l l a r s .  In the t h i r d section of the  table, a l l marginal productivities are expressed as dollars per d o l l a r of input.  In t h i s form, a marginal value product i n d i -  cates the addition to t o t a l output of product obtained from i n creasing the input of a p a r t i c u l a r resource category by one d o l l a r , when a l l inputs are at the l e v e l of the geometric means.  40 Furthermore,  i t i s equivalent to the r a t i o of the marginal  value product to the f a c t o r price* TABLE 3 GEOMETRIC MEANS AND MARGINAL VALUE PRODUCTS OF INPUT CATEGORIES  Geometric means: Total output (|) Real estate and equipment ($) Laying f l o c k (layer years) Labor (hours) Feed (I) Other cash expenses ($) Marginal value products per unit of i n p u t : Real estate and equipment ($) Laying f l o c k (#) Labor ($) Feed ($) Other cash expenses (#) Marginal value products per d o l l a r of input: Real estate and equipment ($) Laying f l o c k ( $ ) Labor ( $ ) Feed (#) - Other cash expenses ($>)  1949  1950  1951  4,022  3,274 278 418 1,486 2,231  5,431 321 491 1,542 2,740 326  -0.13 2.25 -0.17 1.33 0.62  -0.69 1.19 :o;o3 0.96 2.96  -0.35 2.73 0.04 1.46 0.47  -0.13 1.09 -0.33 1.33 0.62  -0.69 0.55 0.06 0.96 2.96  -0.35 1.18 0.07 1.46 0.47  316 464 1,909 2,396 285  257  a  D  c  Estimated at geometric means of t o t a l output and input categories. a  Based on the average value of a p u l l e t layer: #2.07, $2.18 and $2.32 f o r the respective years. b  c  Based on the average hourly wage paid to hired labor:  $0.52, $0.49 and #0.59 f o r the respective years.  In view of the i n e q u a l i t y of the marginal value products per d o l l a r of input, the t h e o r e t i c a l l y optimum combination of resources was not attained f o r these market egg enterprises i n any of the three years.  In general, considerably higher returns  41 are indicated f o r inputs of laying flock and feed than f o r the other resource categories. Subject t o any p r a c t i c a l l i m i t a t i o n s imposed by technical conditions of production and physical characteristics of the resources employed, additional inputs of laying flock and feed would have been most effective i n i n creasing p r o f i t s (or decreasing losses) i n 1949 and 1951.  An  adjustment of t h i s nature would have been inappropriate i n 1950 f o r two reasons; the marginal value products of the laying flock and feed inputs were exceeded (1) by t h e i r marginal costs and (2) by the marginal value product of other cash expenses. I t i s equally apparent that adjustments i n the resource inputs from year t o year, made i n response t o variations i n the factor-product price relationships, did not constitute a major improvement i n resource a l l o c a t i o n .  I f these changes i n the  quantity of inputs had resulted i n a closer approximation to the optimum resource combination, the inequality of the marginal value products would have been reduced i n successive years. However, there i s l i t t l e evidence to support t h i s proposition. For example, the marginal value products of the r e a l estate and equipment input and the laying f l o c k input d i f f e r by #1.22 i n 1949, by #1.24 i n 1950, and by $1.53 i n 1951.  Likewise, the  difference i n the marginal value products of laying flock and labor i s #1.42 i n 1949, #0.49 i n 1950, and $1.25 i n 1951.  Com-  paring other pairs of marginal value products i n t h i s manner reveals a similar erratic fluctuation i n t h e i r differences. At t h i s point, i t i s possible to demonstrate that e s t i mates of resource productivity derived by the production function  42 and the r e s i d u a l methods of analyzing farm input-output  data  may lead to quite d i f f e r e n t conclusions about the r e l a t i v e e f f i c i e n c y of resource combinations.  In applying the r e s i d u a l  method of analysis, labor return or some s i m i l a r measure computed as a r e s i d u a l quantity serves as an i n d i c a t o r of eff i c i e n c y i n resource use*  The average labor return f o r the  market egg enterprises was $1,191 i n 1949, $617 i n 1950, and $2,296 i n 1951 (Appendix I, Table 8).  Accordingly, i t would  be concluded that the economic e f f i c i e n c y of the resource combinations employed during these three years was lowest i n 1950 and highest i n 1951.  This d i s t i n c t f l u c t u a t i o n i n e f f i c i e n c y  of resource use implied by the v a r i a t i o n i n labor return i s contrary t o the generally i n e f f i c i e n t resource combinations employed each year that i s indicated by the continued inequality i n the marginal value products per d o l l a r of input* A further deficiency of the measures of r e s i d u a l r e turns i s that they provide only a general index of p r o f i t s or resource e f f i c i e n c y and do not point out how the resource combination could be a l t e r e d to gain a larger net income*  Removal  of t h i s l i m i t a t i o n has been attempted by using the average r e turns per unit of resource input, such as the return per hour of labor, f o r comparison with a pre-determined standard of performance*  These measures, however, retained a l l the inherent  defects of the r e s i d u a l method, and, as a r e s u l t , could be misleading as indicators of the adjustments i n inputs needed to increase net income.  For example, the average return per hour  of labor computed by the r e s i d u a l method was $0.55 i n 1949,  43 #0.26 i n 1950, and #1.26 i n 1951 (Appendix I, Table 8).  Follow-  ing the procedure of the residual method, any departure from the most p r o f i t a b l e input of labor could be determined by comparing t h i s return with the average cost of hired labor of #0.52, #0.49 and $0.59 i n the respective years.  On t h i s basis, the labor i n -  put would appear to be near the optimum i n 1949, 1950,  and r e s t r i c t e d i n 1951.  excessive i n  On the other hand, the marginal  value product of labor (Table 3) indicates that an excessive amount of labor, r e l a t i v e to other inputs, was employed i n a l l years.  Assuming that the cost of unpaid labor was the same as  the wage paid to hired labor, a smaller input of labor would have increased the net income during each year. Within the l i m i t a t i o n s of the production function method of analysis, the marginal value products of the various  resource  categories reveal the (average) r e s u l t s of the decisions made by producers i n combining the resources at t h e i r disposal f o r the production of market eggs.  There are a number of r e s t r i c t i o n s  associated with production techniques and practices, r i g i d i t y and i n d i v i s i b i l i t y of resources, and imperfect knowledge of production and prices i n the future that p a r t i a l l y explain the f a i l u r e of producers to achieve the optimum or most p r o f i t a b l e combination of resources.  Some of these r e s t r i c t i o n s also may  reduce and even prevent the p o s s i b i l i t y of e f f e c t i v e l y improving the a l l o c a t i o n of resources within a short period of time. The physical i n d i v i s i b i l i t y of the buildings required f o r the poultry enterprise precluded a prompt adjustment i n the input of housing services.  A laying house, once i t was b u i l t ,  44 became a f i x e d quantity which could not be expanded and contracted to exactly meet the f l u c t u a t i o n s i n housing requirements a r i s i n g from variations i n the s i z e of laying f l o c k within the production period*  The maximum capacity was established within  a narrow range by the f l o o r area of the building*  Overcrowding  f o r any extended period of time was almost c e r t a i n t o create problems i n sanitation, control of disease and other factors related t o maintainence of the p h y s i o l o g i c a l condition of the layers*  Consequently, the construction of new buildings was  the only e f f e c t i v e means of obtaining a d d i t i o n a l housing*  A  current need, however, could not be met i n t h i s way due to the time required f o r planning and erection of a building*  Further-  more, the stock of housing services supplied by a building was not depleted during a s i n g l e production period, but was extended into the future over the l i f e span of the building*  For t h i s  reason, a new laying house would not l i k e l y be constructed unless the c a p i t a l outlay could be recovered from the a n t i c i pated increase i n income from a d d i t i o n a l housing services i n the following years*  Income from the market egg enterprise,  p a r t i c u l a r l y i n 1949 and 1950, was not conducive to optimistic expectations f o r the future, and undoubtedly deterred most producers from extending the f a c i l i t i e s f o r housing layers* Aside from the depressed prospects f o r future income, many producers probably had l i t t l e or no i n c l i n a t i o n toward any physical expansion of the enterprise*  For some producers, the  production of market eggs was undertaken on a small scale to supplement t h e i r income from other sources, and was not necess a r i l y e s s e n t i a l to t h e i r l i v e l i h o o d *  In other cases, pro-  45  dueers i n the older age groups were often p h y s i c a l l y unable to do the work required  i n the operation of a larger  enterprise*  The lack of f l e x i b i l i t y i n the laying house capacity and the current practices i n laying f l o c k replacement cont r i b u t e d t o u n d e r - u t i l i z a t i o n of the laying houses f o r most of the year*  The number of layers reached a maximum usually i n  September and October when p u l l e t s raised f o r f l o c k replacement had been placed i n the laying houses*  Since additions to the  laying f l o c k were seldom made during the production period, c u l l i n g and mortality caused a continual decline i n the number of layers.  As a r e s u l t , the number of layers was inadequate  f o r complete u t i l i z a t i o n of the existing housing f a c i l i t i e s except during the f i r s t two to three months of the production period*  In e f f e c t , the practice of adding replacements to the  laying f l o c k only once a year created the need f o r housing f a c i l i t i e s i n excess of that a c t u a l l y required*  Evidence of  t h i s condition i s provided i n Table 4 (Appendix I) by the r a t i o of the number of layer years (as a measure of the actual s i z e of laying f l o c k f o r the year) to the f l o c k inventory at October 1  (as an approximation of the laying house capacity).  On t h i s  basis, laying houses were occupied at 7 7 , 76 and 83 per cent of t h e i r capacity f o r the respective  years.  Most of the equipment required f o r the laying f l o c k was subject to the same conditions that were responsible f o r underu t i l i z a t i o n of the existing housing services.  Installations  such as feeder, water system and water troughs formed an i n t e g r a l part of a laying house.  Although t h i s equipment was l e s s  46 durable than the building, i t d i d not require annual replacement but, with occasional minor repairs, remained serviceable over a period of several years. The generally accepted practice among producers of rearing p u l l e t s f o r replacement of the laying f l o c k necessitated specialized buildings and equipment that were unemployed f o r several months during the year.  For the t y p i c a l producer who  purchased a l l h i s chicks i n a single l o t , t h i s was a seasonal a c t i v i t y which extended over a s i x month period beginning i n l a t e February or early March.  Under normal weather conditions,  the brooder houses and brooding equipment were used f o r about two months, and seldom f o r more than three months.  These  buildings and equipment then remained i d l e f o r the rest of the year, with the occasional exception of a brooder house that served also as a shelter f o r young p u l l e t s on range.  Shelters,  feeders, water troughs and other range equipment were essential f o r three to four months while the growing p u l l e t s were kept on range, but were not used f o r any other purpose during the year. Apart from the small area occupied by the laying houses, land was needed only as range f o r young p u l l e t s .  Although t h i s  land was quite necessary under the prevailing practices i n r a i s i n g p u l l e t s , i t also was generally unused f o r as much as nine months of the year.  In addition, the amount of range land  was frequently excessive i n r e l a t i o n to the number of p u l l e t s raised.  Many producers were not compelled to l i m i t the range  area to actual requirements because a l t e r n a t i v e and competitive uses f o r the land d i d not exist on these single enterprise farms.  47 This applied p a r t i c u l a r l y to producers with small f l o c k s and to those owning several acres of land suitable f o r poultry range. These conditions, undoubtedly, were l a r g e l y responsible f o r the low marginal value product of the r e a l estate and equipment input i n each of the years.  For a l l p r a c t i c a l consider-  ations, the land, buildings and equipment associated with the market egg enterprise constituted a f i x e d quantity of input that could not be quickly modified.  At the same time, the  current production practices were such that the services supp l i e d by these resources were either under-employed or unused f o r several months during the year.  Also, most of the annual  costs incurred i n providing these resources  ( i . e . , depreciation,  i n t e r e s t on investment, taxes and insurance) were unaffected by using the services l e s s i n t e n s i v e l y . As a r e s u l t , the amounts of land, buildings and equipment necessary to meet a maximum requirement during part of the year were i n excess of that actua l l y needed at other times.  In effect, the under-utilized and  unused r e a l estate and equipment represents an excessive a p p l i cation of these resources r e l a t i v e to the input of other r e sources.  However, the inherent i n f l e x i b i l i t y of these resources  combined with the usual production practices offered l i t t l e opportunity to avoid t h i s condition of waste and i n e f f i c i e n c y i n resource use. In contrast t o the r i g i d i t y of input of buildings and equipment, the inputs of a l l other resources were much more flexible.  The greater f l e x i b i l i t y of these inputs originated  p r i m a r i l y i n one or both of the following conditions:  (1)  48  d i v i s i b i l i t y of the resource into small units which enabled more refined adjustment i n the l e v e l of input at any time, and (2) complete consumption of the resource i n the production process within a single production period.  As a r e s u l t , the  inputs of these resources could be controlled more e f f e c t i v e l y by the market egg producer, and adjustments could be r e a d i l y made i n the l e v e l of input which, i n h i s judgement, were appropriate t o changes i n the input-output  price relationship.  For a l l but a very few producers who purchased layers during the year, the maximum input of laying f l o c k was established by the number of layers housed at the beginning of the production period, that i s , the p u l l e t s raised f o r f l o c k r e placement plus any layers retained i n the f l o c k f o r t h e i r second year of production.  However, changes i n the i n i t i a l s i z e of  laying f l o c k could be made from year to year, within the capacity of the l a y i n g houses, by either increasing or decreasing the number of p u l l e t s and/or hens.  The i n i t i a l f l o c k inventory  1  indicates that producers accomplished t h i s adjustment mainly by varying the number of hens. In effect, the number of p u l l e t s had been determined i n advance by the number of chicks that were purchased f i v e to s i x months previously.  The depressed prices f o r eggs during Febru-  2  ary and March,  when the decision was made regarding  chick  purchases, d i d not encourage producers to increase t h e i r l a y i n g •'•See Table 4, Appendix I . 2  See Table 9, Appendix I I .  49 f l o c k f o r the coming year.  At the same time, expectations of  higher prices f o r eggs during the year ahead may have deterred any plans f o r reduction of the laying f l o c k .  Confronted with  these alternatives, producers apparently chose to compromise by neither increasing nor decreasing the number of pullets i n the laying f l o c k at October 1 i n both 1949 and 1950. The higher annual production of eggs by a p u l l e t , as compared with a hen, influenced the majority of producers to follow the practice of completely replacing the laying f l o c k each year.  Despite t h i s advantage of the a l l - p u l l e t f l o c k , some  producers preferred to keep some layers through at least part of a second period of production.  These layers were not usually  selected u n t i l the onset of the moulting period i n August and September.  Apparently, the current price of eggs was not a  major consideration of producers i n deciding on the number of layers to be kept f o r a second year.  Although egg prices had  advanced sharply i n August and September of 1949, the number of hens i n the laying f l o c k s at October 1 had been reduced from the previous year.  In contrast to 1949, egg prices during  August and September of 1950 had remained r e l a t i v e l y stable at a lower l e v e l , but laying flocks contained a larger number of hens.  Presumably, producers r e l i e d to a greater extent on  t h e i r expectations of egg prices f o r the year ahead, which proved to be correct f o r both years, and also on current and anticipated production costs, p a r t i c u l a r l y as affected by the price of feed. Within the l i m i t imposed by the i n i t i a l s i z e of laying  50 f l o c k , producers possessed a large measure of control over the laying f l o c k input f o r the year as a whole.  Except f o r the  i n e v i t a b l e decrease caused by mortality, the s i z e of laying f l o c k could be reduced e a s i l y and quickly at any time by c u l l i n g any number of layers that s t i l l remained i n the f l o c k .  The  annual mortality of layers r e l a t i v e to the i n i t i a l number of layers was approximately the same f o r each year, varying only from 11 to 12 per cent f o r hens and from 14 to 16 per cent f o r pullets.  Therefore, assuming a random d i s t r i b u t i o n of mortality  within each year, f l u c t u a t i o n s from year to year i n the net s i z e (input) of laying f l o c k , measured i n layer y e a r s , can be 1  attributed almost e n t i r e l y to the effects of c u l l i n g . Producers reduced the laying f l o c k input s l i g h t l y from 1949 to 1950, but expanded i t s u b s t a n t i a l l y i n 1951.  Although  t h i s adjustment was p a r t l y the r e s u l t of f l u c t u a t i o n i n the i n i t i a l number of layers, i t was achieved also by varying the length of time that layers were retained i n the f l o c k .  For the  f l o c k as a whole, a layer was kept f o r an average of 282 days i n 1949, 276 days i n 1950 and 302 days i n 1951.  However, an  appreciable difference existed between hens and p u l l e t s i n t h i s respect.  A hen was kept f o r an average of 190, 193 and 255  days  i n the respective years, or approximately nine weeks longer i n 1951 than i n either of the two previous years.  In comparison,  a p u l l e t was retained f o r a longer and more nearly equal period; 308 days i n 1949, 298 days i n 1950 and 318 days i n 1951.  Thus,  producers reduced the laying f l o c k input f o r 1950 mainly by See Table ~4, Appendix I»»  51 c u l l i n g p u l l e t s at an e a r l i e r date than i n 1949*  On the other  hand, they expanded the f l o c k input f o r 1951 by delaying the c u l l i n g of both hens and p u l l e t s to a l a t e r date.  Most of t h i s  increase over the 1950 input was gained from the longer period that hens were retained i n the f l o c k , which amounted t o 65 days as compared with 20 days f o r p u l l e t s .  Furthermore, the i n i t i a l  f l o c k inventory f o r 1951 contained more hens but the same number of p u l l e t s . Appraised on the basis of the marginal value product per d o l l a r of input, the laying f l o c k input was close to the optimum i n 1949 although a larger input would have produced a small increase i n p r o f i t s .  Producers, i n t h e i r anxiety over  the unfavorable feed-egg price relationship that existed from December through J u l y , may have been premature i n t h e i r de1  cisions on c u l l i n g , and so reduced the f l o c k input more than was necessary.  They decreased the f l o c k input f o r 1950 i n  response to a further decline i n the feed-egg price r a t i o , but the marginal value product indicates that t h i s reduction should have been much larger. As previously stated, the smaller input of laying f l o c k f o r 1950 resulted mainly from increased dulling of p u l l e t s .  Considering that a hen produced 30 per cent fewer  eggs than a p u l l e t , increased c u l l i n g of hens would have been 2  more appropriate i n adjusting the f l o c k input.  Moreover, i t i s  doubtful that any s i g n i f i c a n t economic benefit was derived from retaining hens i n the laying f l o c k during a year when egg prices •'•See Table 10, Appendix I I . 2  See Table 4, Appendix I .  52 were so depressed.  Producers expanded the f l o c k input f o r  1951  to take advantage of the v a s t l y improved egg prices that prev a i l e d from January through September, but s t i l l f e l l short of a t t a i n i n g the most p r o f i t a b l e input. productive period to 255  Extension of the average  days f o r hens and 318  days f o r p u l l e t s  indicates that producers delayed c u l l i n g as long as possible i n order to obtain the maximum use of the available  layers.  Consequently, l i m i t a t i o n s imposed by the i n i t i a l s i z e of laying f l o c k prevented any further addition to the f l o c k input f o r 1951.  This r e s t r i c t i o n would not have existed except f o r the  i n a b i l i t y of producers to predict the sharp advance i n egg prices during 1951.  Otherwise, i t i s probable that they would  have raised a larger number of p u l l e t s during the previous year. Total feed input f o r the market egg  enterprise  was  divided between the laying f l o c k and the young p u l l e t s raised f o r f l o c k replacement, with the larger proportion (at least per cent) going to the laying f l o c k .  80  Young p u l l e t s consumed  approximately the same quantity of feed each year because the number of p u l l e t s raised, as shown by the laying f l o c k inventory at October 1, did not vary.  Consequently, changes i n the  feed requirements of the laying f l o c k were mainly responsible f o r variations i n the quantity of feed used by the Feed f o r the laying f l o c k amounted to 626, and  cost $2,270, $2,317 and $2,542 i n 1949,  spectively.  enterprise.  619 and 660 1950  cwt.,  and 1951  re-  Since the cost of t h i s feed accounted f o r 65 to  70 per cent of a l l cash costs f o r the enterprise, there  was  considerable incentive f o r producers to exercise a l l possible  53 control over the feed input* Total feed input f o r the laying f l o c k could be comp l e t e l y controlled through the number of layers kept during the year and the amount of feed fed per layer* bility  However, the p o s s i -  of adverse effects on egg production deterred producers  from varying the l e v e l of feeding except within r e l a t i v e l y narrow l i m i t s *  Some evidence of t h i s r e s t r i c t i o n i s provided  by the small f l u c t u a t i o n s i n the annual consumption of feed by layers which, expressed  i n pounds of feed per layer year, i n -  creased from 110 pounds i n 1949 to 113 pounds i n 1950 and decreased to 106 pounds i n 1951*  As a r e s u l t , producers were  forced t o r e l y almost e n t i r e l y on adjustments i n the s i z e of laying f l o c k f o r regulation of the feed input*  Thus, the  conditions that influenced the decisions of producers i n regard to the f l o c k input (that i s , the i n i t i a l number of layers and the c u l l i n g of layers during the year) were equally pertinent to the feed input.  In f a c t , c u l l i n g was done p r i m a r i l y to  maintain a minimum input of feed r e l a t i v e t o the output of eggs, and only i n c i d e n t a l l y to reduce the number of layers*  In  a t t a i n i n g t h i s objective, the removal of unproductive layers from the f l o c k was most e s s e n t i a l because they consumed nearly as much feed as layers i n f u l l  production*  Producers were under l i t t l e or no r e s t r a i n t i n making adjustments to the labor input*  Labor f o r the market egg enter-  p r i s e was provided almost e n t i r e l y by the producers and t h e i r f a m i l i e s , so that an adequate supply was r e a d i l y a v a i l a b l e at a l l times*  In addition, there were inherent i n f l e x i b i l i t i e s i n  54 the labor input which impeded a precise a l t e r a t i o n i n the amount of labor used i n conformity to variations i n the labor requirement of the enterprise.  Although producers possessed v i r t u a l l y  unrestricted control over the labor input, i t s p e r s i s t e n t l y low marginal value product can be attributed mainly to the use of an excessive amount of t h i s resource r e l a t i v e t o other  resources  employed i n the market egg enterprise. Several circumstances contributed to t h i s seemingly extravagant use of labor f o r the poultry enterprise.  Foremost  among these was the. absence of any strong inducement f o r most producers to make a deliberate e f f o r t toward minimizing the labor input.  Since labor was supplied mainly by the producers  and t h e i r f a m i l i e s , the small cash outlay f o r labor had no moderating influence on the t o t a l amount of labor that was used. In addition, there was generally no other enterprise on these farms to provide competition f o r the use of t h i s unpaid labor. As a r e s u l t , many producers were able to accomplish the necessary work at a l e i s u r e l y pace.  Most small and medium s i z e  enterprises were only a part-time a c t i v i t y i n which labor eff i c i e n c y received no p a r t i c u l a r emphasis.  Furthermore, many of  these enterprises were operated by persons i n older age groups whose physical capacity f o r work was l e s s than that of younger and more a c t i v e persons., Only an incomplete and somewhat s u p e r f i c i a l  explanation  can be given f o r variations i n the marginal value product of other cash expenses because of the several heterogeneous and unrelated items that comprise t h i s input category.  However, at  55 l e a s t 50 per cent of these cash expenses was incurred i n each year as the cost of purchased chicks.  Also, the marginal value  product of these cash expenses fluctuated i n the opposite d i r e c t i o n to changes i n the l e v e l of egg p r i c e s .  Although t h i s  r e l a t i o n s h i p could be e n t i r e l y coincidental, i t does suggest the p o s s i b i l i t y that the practice of r a i s i n g p u l l e t s f o r layer replacements provided producers with the largest return i n 1950 when egg prices were low, and conversely, with the smallest return i n 1951 when egg prices were high.  56  APPENDIX I PHYSICAL AND FINANCIAL ORGANIZATION OF THE MARKET EGG ENTERPRISE  The following i s a description of some of the characteri s t i c s of the land, buildings, equipment, laying f l o c k and production practices associated with the market egg enterprises. Except f o r building s i t e s , the land requirements of the poultry enterprise were l a r g e l y l i m i t e d to range f o r young p u l l e t s during the summer months*  Almost without  exception,  layers were confined t o the laying house throughout the year* Generally, the land used f o r poultry had been cleared and seeded at some time with a mixture of grass and clover*  However,  native wild grasses and weeds often predominated as a r e s u l t of inadequate maintenance of the o r i g i n a l seeding*  The amount of  land used f o r poultry range was determined more by the t o t a l acreage i n the farm unit than by the number of young birds raised*  On small parcels of l e s s than three acres, young  p u l l e t s usually had access to a l l land that was not required f o r the dwelling and other r e s i d e n t i a l purposes, regardless of the number of young birds raised*  On l a r g e r farm units, the  amount of land a v a i l a b l e f o r poultry was less r e s t r i c t e d which, i n some cases, induced an excessive use of land f o r t h i s purpose*  Only the land a c t u a l l y used f o r poultry during the  year was recorded  i n the inventory*  This excluded any ad-  d i t i o n a l land that would be used i n following years i f r o t a t i o n  57 of the poultry range was practised to control contamination of the s o i l by diseases and parasites. Land values varied from 150 to #500 per acre.  In general, the larger enterprises were  located on the more expensive land.  However, value of the land  appeared to be related mainly to the size of parcel, the presence or p o s s i b i l i t y of other a g r i c u l t u r a l uses, and whether the land was used primarily f o r a g r i c u l t u r a l or r e s i d e n t i a l purposes and, as a consequence, provided l i t t l e i n d i c a t i o n of the s u i t a b i l i t y of the land f o r poultry production. Poultry buildings included laying houses, brooder houses and any part of other buildings that was used f o r egg and feed storage.  Occasionally, a vacant pen i n the laying  house was used as a brooder house.  Brooder houses frequently  served also as shelters f o r young p u l l e t s on range. Most laying houses were one-storey, wooden frame buildings on a foundation of concrete blocks, cedar blocks or poured concrete.  Wooden f l o o r i n g was most common, although  concrete f l o o r s were used i n a few cases.  Open screened windows  f o r l i g h t i n g and v e n t i l a t i o n of the building extended along one side of the laying house.  A room f o r feed storage was usually  incorporated i n the laying house.  Storage space f o r eggs was  generally provided i n the basement or other cool area i n the operator's dwelling, and seldom i n a separate building s p e c i a l l y constructed f o r t h i s purpose.  In most laying houses, manure  under the perches was c o l l e c t e d on a board platform raised above the f l o o r l e v e l , and was removed at least twice a week and often daily.  A l e s s common arrangement f o r manure c o l l e c t i o n con-  58 s i s t e d of a p i t under the perches which was cleaned only once or twice during the year.  Individual laying nests were pro-  vided i n many laying houses, although the larger community nest accommodating several layers at the same time was favored by some producers.  Lights were i n s t a l l e d i n nearly a l l laying  houses and, i n a few instances, were controlled by means of an automatic  time-switch.  T y p i c a l l y , a laying house contained from two to four laying pens, although a few houses contained s i x or more pens. The average laying pen had a f l o o r area of 512 square feet, which i s approximately equal to dimensions of 20 x 25 f e e t . However, there was some v a r i a t i o n i n both the f l o o r area and the dimensions of laying pens.  The f l o o r area was between 350  and 449 square feet i n most cases, and was seldom larger than 750 square f e e t .  Many laying pens were 20 x 20 feet i n s i z e ,  but the dimensions ranged from 16 to 24 feet wide and from 20 to 40 feet long. Based on the operators  T  estimates of the normal capacity  of t h e i r laying pens, the average laying pen with 512  square  feet of area would accommodate 141 layers, providing 3«6 square feet of f l o o r per layer.  However, the number of layers that  could be placed i n a laying pen depended l a r g e l y on the s i z e of the pen.  Consequently, the estimated normal capacity ranged  from 100 to 149 layers f o r most laying pens and seldom exceeded 300 l a y e r s . The laying houses and the feed storage room f o r the average enterprise  contained 3,255 square feet of f l o o r area  59 with a normal capacity, again based on the operators' of 857 l a y e r s .  estimates,  The cost of replacing the laying houses was  estimated at $3,060, or $0.94 per square foot of f l o o r area. This was  the cost, as estimated by the operators,  of replacing  the existing buildings at the prices of materials and labor that prevailed during the period of the study.  I t included the cost  of nest, perches, dropping boards or p i t s , and e l e c t r i c a l wiring and f i x t u r e s , but excluded water and feed equipment. In most cases, brooder houses were single-wall frame construction with no i n s u l a t i o n except double-flooring, and were permanently located on some kind of foundation. usually was  Ventilation  provided by adjustable windows i n the front of the  building and v e n t i l a t o r s i n the roof, although louvered a i r outlets i n the gables or under the eaves were also used instead of roof v e n t i l a t o r s . The dimensions varied considerably, two-thirds  but  of the brooder houses were 10 to 14 feet wide and  to 18 feet long.  A f a i r l y standard  10  s i z e of brooder house,  measuring 12 x 14 feet, provided f l o o r space f o r approximately 400  ehicks. Brooder houses f o r the average enterprise contained  square feet of f l o o r area. $527, or $1.20  The estimated replacement cost  439 was  per square foot of f l o o r area.  Other building requirements of the poultry enterprise included a place f o r cleaning, packing and storing eggs which was  usually located i n part of the basement or a porch i n the  farm house.  Occasionally, part or a l l of a shed was  used f o r  storage of t o o l s , equipment, l i t t e r and other supplies.  The  60 replacement cost of these buildings, or the portions used f o r poultry, amounted t o #160. The main items of equipment i n the laying house were the water system and mash feeders.  Water under pressure was piped  to f l o a t - c o n t r o l l e d water troughs i n each laying pen or to a tap inside the laying house on two-thirds  of the farms.  On the r e -  mainder, water was carried i n p a i l s to each laying pen from a source outside the laying house.  The mash portion of the layer  r a t i o n usually was f e d from shallow troughs, mounted on low stands, which were f i l l e d at l e a s t once d a i l y .  Self-feeders  equipped with hoppers to contain mash f o r several days feeding were used on nearly 20 per cent of the farms.  Other laying  house equipment included a wheelbarrow, feed p a i l s or a feed cart, egg baskets, and hand t o o l s f o r cleaning the laying pens. The hover type of brooder heated by o i l or e l e c t r i c i t y , with a rated capacity of 500 chicks, was most popular.  Water fountains  and chick feeders completed the brooder house equipment. standard  A  set of equipment on the range consisted of shelters,  feeders, water fountains, and fencing.  Range shelters f o r young  stock were t y p i c a l l y low, open- side, movable structures with mesh wire under the perches.  Many of these shelters were 8 x 10  feet or 10 x 12 feet i n size, providing room f o r 120 and 210 young p u l l e t s , respectively.  Egg cleaning was done by hand with  an abrasive buffer i n most cases, although a c i r c u l a r cleaner powered by an e l e c t r i c motor was used on a few farms.  Egg cases  were supplied to the producers by the wholesale buyers. With the exception of the larger enterprises, most  61 laying f l o c k s were composed e n t i r e l y of one breed, New  Leghorn,  Hampshire and the Leghorn-New Hampshire cross were by f a r  the most prevalent breeds, accounting f o r nearly 90 per cent of a l l l a y e r s .  Leghorns predominated i n both the small and  large s i z e f l o c k s , while New  Hampshires out-numbered a l l other  breeds i n the medium s i z e f l o c k s .  The Leghorn-New Hampshire  cross was most prominent i n the smaller f l o c k s . Laying birds were divided into two classes according to age.  Layers i n t h e i r f i r s t year of production were classed as  p u l l e t s , and those that had completed one year of production were classed as hens,  1  For a l l farms, about 75 per cent of the  laying f l o c k was replaced annually, as indicated by the percentage of t o t a l layers at September 30 that were c l a s s i f i e d as pullets.  Complete replacement of the laying f l o c k was a common  practice among the smaller enterprises. However, many of the l a r g e r f l o c k s were only p a r t i a l l y replaced each year, and so contained hens as w e l l as p u l l e t s .  Some depletion of the laying  f l o c k resulted throughout the year from routine c u l l i n g and losses due to disease and other causes.  The main disposal of  layers normally occurred toward the end of the production year, usually i n August and September,  At that time, young p u l l e t s  s t a r t i n g to l a y were taken from the range and placed i n the laying houses. Nearly a l l p u l l e t s were raised from day-old chicks purchased from a commercial hatchery during the period of ^In t h i s study, layers over 18 months of age were classed as hens.  62 February 15 to A p r i l 15.  An average of 81 per cent of the  chicks reached the laying age of approximately f i v e and oneh a l f months.  A l l brooding and range losses, including mor-  t a l i t y , losses due to predatory animals, and unhealthy or poorl y developed birds that were destroyed, amounted to 16 per cent. The remaining three per cent included cockerels missed i n sexing and p u l l e t s culled on the range.  In a few cases, part of the  laying f l o c k replacements was obtained by purchasing ready-tol a y or laying p u l l e t s i n the l a t e summer and early f a l l , or by purchasing immature p u l l e t s and r a i s i n g them to laying age. A l l feed, with the exception of small quantities of oats grown on a few of the larger farms, and most supplies used by the poultry enterprise were purchased from feed and farm supplies companies located i n the larger towns.  Most poultry  producers had feed delivered as i t was required, usually once a week, and normally had only a small quantity on hand. Wheat and oats comprised most of the whole grain that was fed i n the layer ration, although barley and corn were i n cluded occasionally.  Poultry producers purchased the various  grains separately and then combined them i n the ration to meet the requirements of the laying f l o c k .  Poultry mashes, on the  other hand, were mixed by the feed manufacturers according to a standard formula.  Although most feed manufacturers would  prepare mash according to a s p e c i f i e d formula at some extra charge, nearly a l l producers fed the standard laying mash cont a i n i n g 19 per cent protein.  A few producers substituted a  breeders mash, containing s l i g h t l y less protein (18 per cent)  63 and a higher concentration of vitamins, f o r part or a l l of the standard laying mash.  In some cases, a vitamin supplement was  added to the r a t i o n during the winter months.  The general  practice, however, was to feed the standard laying mash as i t was prepared by the feed manufacturer. Several kinds of feed, p a r t i c u l a r l y mashes, were used i n r a i s i n g young p u l l e t s i n order to meet the changes i n nut r i t i o n a l requirements at various stages of growth.  Although  several methods and feed combinations were used, the most common practice can be described as follows: (1)  Chick starter-mash was fed f o r the f i r s t f i v e or s i x weeks, with chick grain introduced by mixing i t with the mash or placing i t i n separate feeders;  (2)  At f i v e to s i x weeks of age, the mash r a t i o n was gradually changed to a growing or developing mash of lower protein content;  (3)  At the same age or before, the feeding of oats and wheat was started.  Usually, t h i s grain was medium  s i z e or coarsely ground u n t i l the p u l l e t s could u t i l i z e whole grain. (4)  As the p u l l e t s neared laying age, the growing mash was replaced with laying mash. Labor f o r the laying f l o c k was required l a r g e l y f o r the  routine d a i l y chores such as feeding and watering, cleaning dropping boards, and c o l l e c t i n g , cleaning and packing eggs. The seasonal jobs included removal of manure from dropping p i t s , complete cleaning and d i s i n f e c t i n g of laying pens, and moving  64 young p u l l e t s from the range to laying houses.  Most of the  labor i n r a i s i n g young p u l l e t s was required f o r d a i l y feeding and watering, and other less frequent jobs such as relocating feeders, water troughs and shelters on the range.  Other jobs  done only once or twice a year included preparation of brooders and brooder houses f o r chicks, and thorough cleaning and d i s i n f e c t i n g of brooder houses, shelters and range equipment. The operator and h i s family supplied nearly a l l of the labor f o r the poultry enterprise.  Hired labor was employed  mainly on the larger enterprises, but usually f o r only one or two weeks to a s s i s t with seasonal work. The data presented i n Table 4 provide additional i n f o r mation on the market egg enterprises.  I t indicates some of the  changes that occurred from year to year during the period covered by the study. The average number of layers at October 1 ranged between 723 and 753 over the three year period.  This small v a r i -  ation was due e n t i r e l y to the number of hens i n the laying f l o c k , with the number of p u l l e t s remaining unchanged from year to year. The poultry producers were asked to value t h e i r laying birds according to the prices p r e v a i l i n g at the beginning of each survey year.  Thus, these values, especially f o r hens, re-  f l e c t changes i n the market price f o r fowl.  The consistent i n -  crease i n the value of p u l l e t s i s influenced p a r t l y by a continuous r i s e i n the major costs, p a r t i c u l a r l y feed costs, of raising pullets.  65 TABLE 4 SOME AVERAGES FOR MARKET EGG ENTERPRISES, LOWER FRASER VALLEY AND VANCOUVER ISLAND, 1949-51  1949 Flock inventory (no. of l a y e r s ) : * Hens Pullets Total Value-of layers ($ per b i r d ) : Hens Pullets Mortality (rio. of l a y e r s ) : Hens Pullets Total C u l l i n g (no. of l a y e r s ) : Hens Pullets Total Price received f o r c u l l s ($ per b i r d ) : Layer-years (no.): Hens Pullets Total Eggs l a i d per layer-year (no.): Hens Pullets Flock Price received f o r eggs d per doz.): Feed per layer-year ( l b s . ) : Grain Mash Total Feed per dozen eggs ( l b s . ) : Grain Mash Total Price of feed f o r layers ($ per cwt.): Grain Mash Total r a t i o n Feed-egg p r i c e r a t i o : Labor per layer-year (hrs.):  161 572 733 1.34 2.07  151 572 723  109  18 82 100  82 362 444  77 396 473  1.24  1951 182 571 753  1.28 2.18  18 91  1.49  2.32  21 34  105  146  301  447  1.19  1.63  84 483 567  80 467 547  127 497 624  140  147 207 193  143 211 193  209  199  45*5  41.9  54.3  51.6 53.7 110.3  52.8 60.4 113.2  43.4 57.4 105.8  3.13 3.56 6.69  3.26 3.72 6.93  3.00 3.55 6.55  3.27 3.94 3.63 12.5 3.28  3.29 4.14 3.74 11.2 2.77  3.39 4.24 3.35 14.2 2.43  At October 1, 1943, 1949 and 1950,  tf  1950  respectively.  66 Relative to the i n i t i a l s i z e of f l o c k , layer mortality was nearly the same f o r each year—15, 1949,  1950 and 1951, respectively.  14 and 14 per cent i n  The annual mortality f o r  hens was s l i g h t l y less than f o r p u l l e t s , ranging from 11 to 12 per cent f o r hens and from 14 to 16 per cent f o r p u l l e t s . More extensive c u l l i n g of the laying f l o c k was practiced i n 1950 than i n the other two year; 65 per cent of the t o t a l f l o c k was 1949 and 1951.  culled i n 1950 and about 60 per cent i n  C u l l i n g of hens increased from 51 per cent i n  the f i r s t two years to 80 per cent i n 1951*  C u l l i n g of p u l l e t s ,  on the other hand, was higher i n the f i r s t two years, r i s i n g from 63 per cent i n 1949 to 69 per cent i n 1950 and then f a l l i n g to  53 per cent i n 1951.  A considerably higher price was r e -  ceived f o r c u l l layers, when sold as fowl, i n 1951 than i n either of the two preceding years. C u l l i n g and mortality removed 70 to 80 per cent of the layers from the f l o c k at some time during each year.  Consequent-  l y the f l o c k inventory at the beginning of the survey year was inadequate f o r measurihg the s i z e of f l o c k f o r the year as a whole.  This d i f f i c u l t y was overcome by using the layer-year as  the standard unit of measurement.  In so doing, layers that  remained i n the f l o c k f o r less than the year were converted to f r a c t i o n s of l a y e r - y e a r s .  1  The t o t a l layer-years then provide  •^•A layer-year i s the equivalent of one layer i n the f l o c k f o r one year. For example, two layers i n the f l o c k f o r 150 and 215 days, respectively, are equal to one layer i n the f l o c k f o r 365 days, or one layer-year. Thus, the number of layer-years were calculated by aggregating the days that i n d i vidual layers were i n the f l o c k , and dividing the t o t a l by 365.  67 a measure of the net s i z e of laying f l o c k f o r the year. The net s i z e of laying f l o c k , measured i n decreased s l i g h t l y from 1949 s t a n t i a l l y i n 1951.  to 1950,  Variations  layer-years,  but increased sub-  i n the i n i t i a l f l o c k inventory,  as well as i n the average length of time each layer was i n the f l o c k , contributed hen was 255  1950  and 1951,  nine weeks longer i n 1951 There was  for  and  respectively, or approximately  than i n either of the previous years.  days i n 1949,  298 days i n 1950,  For the f l o c k as a whole., a layer was 282,  193  A  l e s s difference i n the length of time a p u l l e t was  tained; 308 1951.  to t h i s f l u c t u a t i o n i n f l o c k s i z e .  kept i n the laying f l o c k f o r an average of 190,  days i n 1949,  retained  276 and 302  days i n the respective  and 318  re-  days i n  kept i n the f l o c k years.  Apparently,  variations i n the i n i t i a l number of hens and i n the average length of time a hen was  retained  i n the laying f l o c k were the  main causes of the changes i n the net size, p a r t i c u l a r l y the large increase i n  1951.  The rate of production, as measured by the number of eggs per layer-year, and p u l l e t s .  remained reasonably constant f o r both hens  A hen produced approximately 30 per cent less  eggs than a p u l l e t i n a l l years.  Consequently, the  explanation  of the s l i g h t decline i n f l o c k rate of production l i e s i n the larger number of hens that were retained i n the f l o c k f o r a longer period. The average p r i c e received f o r eggs sold during the year declined moderately from 1949 sharply i n  1951.  to 1950,  and then rose quite  68 Feed input f o r the laying f l o c k increased by nearly three pounds per layer-year from 1949 to 1950, creased by more than seven pounds i n 1951.  and then de-  The feed inputs per  layer-year shown i n Table 4 are averages f o r the f l o c k , i n cluding both hens and p u l l e t s .  Since the 1951 f l o c k contained  a larger proportion of hens, adjustments i n the l e v e l of feeding consistent with the rate of egg production could have caused feed input f o r the f l o c k to decline from the previous years.  However, the quantity of feed per dozen eggs indicates  that the l e v e l of feeding was not i n constant proportion to the rate of egg production.  In view of t h i s , i t i s concluded that  the l e v e l of feeding was  s l i g h t l y higher i n 1950 than i n 1949,  but lower i n 1951 than either of the previous years. The proportion of grain and mash i n the layer r a t i o n was  p r a c t i c a l l y constant at 46 per cent grain and 54 per cent  mash.  However, there was a small but consistent s u b s t i t u t i o n  of mash f o r grain i n successive years, amounting to one pound per 100 pounds of r a t i o n during the three year period. The average p r i c e of grain i n the layer r a t i o n did not r i s e to any extent u n t i l 1951.  The p r i c e of mash f o r layers,  on the other hand, increased by 20 cents i n 1950 and 10 cents i n 1951.  A  s a r e s u l t , increases i n the p r i c e of feed f o r the  laying f l o c k averaged 11 cents per 100 pounds i n both 1950  and  1951. Total feed cost per layer-year amounted to $4.00, $4.24 and $4.07 i n 1949,  1950 and 1951,  respectively. This, of  course,reflects both the p r i c e of feed and the quantity of feed  69 used.  The larger quantity of feed purchased at a higher p r i c e  caused an increase i n feed costs per layer-year during 1950, However, the s t i l l higher p r i c e i n 1951 was more than compensated by a reduction i n the quantity of feed used, thereby causing a decrease i n feed costs per layer-year* Of greater importance i s the cost of feed required to produce a dozen eggs, since i t includes the effects of the l e v e l of egg production.  Feed inputs per dozen eggs cost 24,3, 26.1  and 25,2 cents during the respective years.  With e s s e n t i a l l y  no change i n the f l o c k rate of production from 1949 to 1950, the l a r g e r quantity of more expensive feed used i n 1950 carries through completely as higher feed costs per dozen eggs. A l though a dozen eggs was produced at a lower feed cost i n 1951, part of the gain r e a l i z e d from the reduction i n feed input was l o s t through the lower rate of egg production. The feed-egg p r i c e r a t i o indicates the pounds of layer r a t i o n that are equal i n value t o a dozen eggs."**  Variations i n  t h i s p r i c e r a t i o from year to year show the r e l a t i v e changes that occurred i n feed and egg p r i c e s . With an increase i n feed prices and a decrease i n egg prices from 1949 t o 1950, the feedegg p r i c e r a t i o declined, i n d i c a t i n g the increase i n feed prices r e l a t i v e to egg prices and also the smaller quantity of feed that could be purchased with a dozen eggs.  The feed-egg p r i c e  r a t i o i n 1951 was considerably higher than i n the two previous •••The feed-egg p r i c e r a t i o was calculated by dividing the average p r i c e received f o r a dozen eggs by the average p r i c e paid f o r a pound of the composite grain and mash r a t i o n f o r layers.  70 years.  Although feed and egg prices advanced during t h i s year,  the increase was proportionately greater f o r eggs.  As a  r e s u l t , a dozen eggs i n 1951 would purchase 26 per cent more feed than i n 1950, and 14 per cent more than i n 1949. The substantial reduction i n labor requirements of the laying f l o c k , as indicated by the hours of labor per l a y e r year, cannot be a t t r i b u t e d to the widespread adoption of any new labor-saving equipment and production techniques.  Severe  weather conditions during the winters of 1948-49 and 1949-50 probably added t o the d a i l y chore time required f o r care of the l a y i n g f l o c k and maintenance of the laying pens.  Seasonal  work such as cleaning the laying houses would not vary to any extent from year to year and, consequently, some small decline i n the hours of labor per layer-year might be expected i n 1951 as a r e s u l t of the l a r g e r laying f l o c k .  However, i t i s quite  probable that weather conditions and f l o c k s i z e provide only a p a r t i a l explanation of the consistent decline i n labor input f o r the l a y i n g f l o c k .  Due t o the d i f f i c u l t y of obtaining  accurate estimates of labor time, there i s also the p o s s i b i l i t y that the downward trend i n labor requirement could be the r e s u l t of bias i n the o r i g i n a l data. Changes i n the average investment i n the poultry enterprises during the three year period occurred mainly i n the value of buildings and f l o c k (Table 5)«  In general, the larger inven-  tory value i n 1951 was caused primarily by r i s i n g prices, since any physical expansion of either buildings or poultry f l o c k was only i n c i d e n t a l .  71 TABLE 5 AVERAGE INVENTORY VALUES FOR MARKET EGG ENTERPRISES, LOWER FRASER VALLEY AND VANCOUVER ISLAND, 1949-51  1949  1950  1951  $  Land Buildings Equipment Feed • Supplies Poultry f l o c k  #  #  743 2,479 333 51 14 1,406  752 2,546 374 45 14 1,392  755 2,814 369 34 8 1,735  Total  5,076  5,123  5,715  The complete s p e c i a l i z a t i o n of these enterprises i n market egg production i s i l l u s t r a t e d by the summary of receipts presented i n Table 6.  Eggs and c u l l layers sold as fowl, which  are j o i n t product of the market egg enterprise, provided at least 96 per cent of the cash receipts each year*  Egg sales  alone accounted f o r approximately 85 per cent of the cash r e ceipts i n each year*  Other cash receipts and the value of  poultry products consumed on the farm amounted to l e s s than  #250. Receipts from sale of market eggs, then, determined to a large extent the amount of income from the poultry enterprise* Egg receipts, of course, depended on the quantity of eggs sold and the market price*  The quantity sold decreased from 9,029  dozen i n 1949 to 8,835 dozen i n 1950.  Thus, the decline i n egg  receipts and also i n t o t a l cash receipts during 1950  was  caused more by lower prices than by curtailment of production. Egg output expanded moderately i n 1951 under the influence of  72 more favorable prices, with sales of eggs increasing to 9,770 dozen*  However, the higher p r i c e f o r eggs, rather than the i n -  crease i n production, was responsible f o r most of the gain i n receipts during 1951. TABLE 6 AVERAGE RECEIPTS FOR MARKET EGG ENTERPRISES, LOWER FRASER VALLEY AND VANCOUVER ISLAND, 1949-51 1949  1950  1951  #  $  $  4,108 542 28 53 79 10 11  3,702 544 14 44 50 8 15  5,354 709 21 15 44 12 5  4,831  4,377  6,160  46 19  38  Meat  23  65 26  Total  65  61  91  -112  -196  233  L  Cash receipts: Eggs Fowl Chicken Chicks and breeders Feed sack refunds Manure Co-op dividends Total Poultry products consumed on farm: Biggo  Change i n value of poultry f l o c k inventory:  The year-to-year f l u c t u a t i o n s i n expenses f o r the poultry enterprise (Table 7) were much smaller than i n r e c e i p t s . After remaining p r a c t i c a l l y unchanged from 1949 to 1950, expenses moved upward in'1951.  Cash expenses, l i k e cash receipts,  were dominated by a single item.  Feed purchases accounted f o r  about 86 per cent of the annual cash expenses.  A l l other items,  73  except f o r purchase o f c h i c k s , i n v o l v e d o n l y s m a l l cash o u t l a y s . Purchases  o f f e e d and c h i c k s r e q u i r e d a p p r o x i m a t e l y 9 2 p e r c e n t  o f t h e cash e x p e n d i t u r e s d u r i n g each y e a r . for  The non-cash  d e p r e c i a t i o n and i n t e r e s t amounted t o j u s t o v e r  charges in  $300  1951  whieh was s l i g h t l y h i g h e r t h a n i n p r e v i o u s y e a r s . TABLE 7 AVERAGE'EXPENSES FOR MARKET EGG ENTERPRISES, LOWER FRASER VALLEY AND VANCOUVER ISLAND, 1949-51  Cash expenses: Purchased f e e d Farm grown f e e d Purchased l i t t e r Farm grown l i t t e r C h i c k s and o t h e r s t o c k Hired labor Electricity Brooder f u e l M e d i c i n e and d i s i n f e c t a n t Taxes and i n s u r a n c e O p e r a t i o n o f c a r , t r u c k and tractor R e p a i r s t o equipment Repairs t o b u i l d i n g s S m a l l t o o l s purchased Other Total Depreciation: Buildings Equipment Total I n t e r e s t on i n v e s t m e n t : Land Buildings Equipment Total  1949  1950  1951  $  $  $  2,861 12 56 4 202  3,343 5 40 1 258 45  34  2,868 9 33 3 219 59 21 18 28 31  33 4 15 5 12  29 3 11 3 21  42 5 17 6 28  3,326  3,361  3,397  34 59  34 53  93 52  142  150  30 99 15  30 102 15  113  144  147  153  27  20 14 27  143  23  16 35 33  30  15  74 T o t a l s o f 626, 619 and 660 cwt. o f f e e d f o r l a y e r s were purchased a t c o s t s o f $2,270, $2,317 and $2,542 i n t h e r e s p e c t i v e -years.  D e s p i t e a s m a l l r e d u c t i o n i n q u a n t i t y purchased, f e e d  c o s t s f o r l a y e r s r o s e s l i g h t l y f r o m 1949 t o 1950 a s a r e s u l t o f the higher p r i c e s .  The l a r g e r e x p e n d i t u r e s  f o r l a y e r feed  d u r i n g 1951 was caused by a moderate i n c r e a s e i n q u a n t i t y p u r chased a s w e l l a s t h e c o n t i n u e d advance i n p r i c e s . The  c o s t o f f e e d used t o r a i s e p u l l e t s f o r r e p l a c e m e n t  o f t h e l a y i n g f l o c k d e c l i n e d f r o m $591 i n 1949 t o $551 i n 1950. S i n c e t h i s d e c r e a s e was n e a r l y equal t o t h e i n c r e a s e i n f e e d c o s t s f o r l a y e r s , t o t a l f e e d c o s t s f o r t h e e n t e r p r i s e remained a l m o s t unchanged f r o m 1949 t o 1950. W i t h f e e d c o s t s f o r young s t o c k r i s i n g t o $801 i n 1951, t h e a d d i t i o n a l c o s t o f f e e d f o r t h e e n t e r p r i s e was s h a r e d , a l m o s t e q u a l l y by l a y e r s and young stock. TABLE 8 AVERAGE RETURNS FOR MARKET EGG ENTERPRISES,® LOWER FRASER VALLEY AND VANCOUVER ISLAND, 1949-51 1949 Net cash income ($) F a m i l y l a b o r e a r n i n g s ($) L a b o r r e t u r n ($) R e t u r n on i n v e s t m e n t ($) R e t u r n p e r h o u r o f l a b o r ($) Rate o f r e t u r n on i n v e s t m e n t {%)  1,505 1 164 1,191  296  0.55 5.8  1950  1951  1,016 558 617 -55 0.26 -1.1  2,263 2,251 2,296 1,454 1.26 25.4  C a l c u l a t e d by the residual method. Some o f t h e s t a n d a r d measures o f n e t r e t u r n s a s d e r i v e d i n a n a l y z i n g f a r m b u s i n e s s d a t a by t h e r e s i d u a l method a r e  presented i n Table 8*  A l l of these measures indicate that net  income from market eggs dropped i n 1950 well below the 1949 l e v e l , but increased i n 1951 t o exceed the two preceding  years  by a considerable margin. The measures of net returns i n Table 8 were calculated as follows: Net cash i n c o m e — t o t a l  cash receipts minus t o t a l cash expenses.  Family labor earnings—net  cash income minus net decrease i n  t o t a l inventory value, or plus net increase i n t o t a l  inven-  tory value, plus value of poultry products consumed on farm, minus interest on c a p i t a l investment.  The net change  i n t o t a l inventory value included depreciation charges. The return imputed to c a p i t a l investment was calculated at four per cent of the t o t a l inventory  value.  Labor r e t u r n — f a m i l y labor earnings plus wages paid to hired labor. Return on investment—net cash income minus net decrease i n t o t a l inventory value, or plus net increase i n t o t a l  inven-  tory value, plus value of poultry products consumed on farm, minus value of operator and unpaid family labor.  The  net change i n t o t a l inventory value included depreciation charges.  The value of operator and unpaid family labor was  based on the average hourly wage paid to hired labor, that i s 52, 49 and 59 cents per hour i n 1949, 1950 and 1951 r e spectively.  Operator and family labor amounted to 2,118,  1,670 and 1,739 hours i n the respective  years.  Return per hour of l a b o r — l a b o r return divided by t o t a l hours  76 of labor, including operator, family and hired labor, e of return on investment—return percentage of the t o t a l inventory  on investment expressed i n value.  77  APPENDIX I I THE FEED-EGG PRICE RELATIONSHIP  The summaries of receipts and expenses (Tables 6 and 7) demonstrate that the net income from market egg production was determined mainly by egg receipts and feed costs.  In turn, egg  receipts depended on the price of eggs and the quantity of eggs sold, and feed costs depended on the price of feed and the quantity of feed purchased.  The producer had some control over  the quantities of eggs sold and feed purchased but, i n both cases, had to accept prices as they  occurred.  The quantity of feed required to produce a dozen eggs varied only s l i g h t l y from year to year (Table 4).  Consequently,  most of the differences i n net income, as determined by egg receipts and feed costs, can be traced t o variations i n egg prices and feed p r i c e s .  In order to show the nature of these  variations, the market prices f o r Grade "A" Medium eggs and f o r three kinds of feed at the mid-point of each month throughout the period of the study are l i s t e d i n Table 9»  The average  price received by producers f o r a l l grades and sizes of eggs was close to the market p r i c e f o r Grade "A" Medium during t h i s period and, as stated previously, the layer r a t i o n consisted mainly of wheat, oats and laying mash. Consistently low egg prices prevailed throughout the second year, p a r t i c u l a r l y from July to September when the  78 TABLE 9 EGG AND FEED PRICES AT VANCOUVER OCTOBER, 1948 TO SEPTEMBER, 195! Oct., 1948 to Sept.,1949 Grade "A" Medium eggs (fi per d o z . ) : October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  Oct., 1949 to Sept.,1950  Oct., 1 9 5 0 to Sept.,1951  a  51 53 41.5 41.5 40 40 38 40 41 47 54 55  No. 5 wheat ($ per cwt.): October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15 Feed oats ($ per cwt.): October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  51 51 38 31 36 36 36 37 39 46 48 48  48 48 57 40 40 47 51 56 57 65 59 53  b  3.45 3.45 3.55 3.55 3.55 3.55 3.55 3.55 3.55 3.55 3.45 3.45  3.45 3.50 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.45 3.30 3.30  3.30 3.15 3.05 3.15 3.25 3.35 3.35 3.40 3.45 3.65 3.65 3.65  2.80 2.70 2.85 2.65 2.65 2.55 2.70 2.70 2.70 2.70 2.75 2.60  2.60 2.80 2.75 2.75 2.75 2.90 3.20 3.45 3.55 3.40 3.05 2.95  2.95 2.95 3.20 3.40 3.45 3.55 3.55 3.45 3.30 3.05 2.95 2.95  D  79 TABLE 9 ~  Continued  Oct., 1948 to Sept.,1949 Laying mash ($ per cwt.): October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  Oct., 1950 to Sept.,1951  D  3.70 3.70 3.90 3.90 3.90 3.90 3.95 3.95 3.95 3.95 4.05 4.10  P r i c e to producer, from Egg and 1948 to 1950 (Ottawa: Marketing Service, Agriculture) and Poultry Products Market Mark eting S ervi c e, Canada Department of a  Oct., 1949 to Sept.,1950 4.10 4.25  4.10 3.95 3.95 3.95 4.05 4.15 4.25 4.25 4.25 4.25  4.25 4.15 4.15 4.15 4.15 4.15 4.25 4.25 4.25  4.25 4.10 4.10  Poultry Market Report; Canada Department of Report; 1951 (Ottawa: Agriculture)•  kprice picked up at Vancouver, from Markets B u l l e t i n ; ( V i c t o r i a : Markets Branch, B r i t i s h Columbia Department of Agriculture). season peak normally occurred. During the t h i r d year, however, egg prices advanced to a much higher l e v e l than i n the two preceding years, especially i n December and from March to August.  The change i n feed prices, on the other hand, was more  gradual and regular. the  The price of wheat dropped s l i g h t l y i n  second year but, a f t e r a further decline early i n the t h i r d  year, i t increased r a p i d l y above the f i r s t year's l e v e l .  Al-  though the oats price moved e r r a t i c a l l y , i t s trend was generally upward during the second and t h i r d years.  The price of laying  maeh increased slowly but p e r s i s t e n t l y throughout the f i r s t year, fluctuated within a narrow range at a moderately higher  80 l e v e l i n the second year, and remained generally steady but s t i l l somewhat higher f o r most of the t h i r d year, A more important aspect of the changes i n these prices i s the v a r i a t i o n i n feed prices r e l a t i v e to egg p r i c e s .  With  the quantity of feed required to produce a dozen eggs remaining nearly constant, net returns would increase as feed prices became lower i n r e l a t i o n to egg prices, and vice versa.  This  p r i c e relationship i s indicated by the feed-egg price r a t i o , which shows the pounds of feed equal i n value to a dozen eggs. Thus, as the feed price increases i n r e l a t i o n to the egg price, the feed-egg price r a t i o declines because l e s s feed can be purchased with the receipts from a dozen eggs.  Conversely,  when the feed price decreases r e l a t i v e to the egg price, the feed-egg price r a t i o increases. The feed-egg price r a t i o s f o r wheat, oats and laying mash (Table 10) show the price r e l a t i o n s h i p between eggs and an i n d i v i d u a l feed.  Since the layer r a t i o n was composed  mainly of these three feeds, a feed-egg p r i c e r a t i o was  calcu-  lated f o r a r a t i o n consisting of 31 per cent wheat, 15 per cent oats and 54 per cent laying mash.  As indicated by the  r a t i o of prices f o r the composite layer r a t i o n and eggs, the feed-egg price relationship which confronted producers of market eggs was least favorable during the second year, and most favorable during the t h i r d year of the study.  Compared  month by month with the f i r s t year, t h i s price r a t i o was  lower  throughout a l l of the second year, and was higher during the t h i r d year except i n October, November, January, February and  81 September,  However, i t was only i n October and November of the  t h i r d year that the price r a t i o dropped appreciable below the f i r s t year. (15.3  The maximum and minimum values of the price r a t i o  and 10.4 i n the f i r s t year, 13.9 and 8.6 i n the second  year, and 16.8 and 10.6 i n the t h i r d year) further emphasize the conditions with regard to feed and egg p r i c e s . TABLE 10 FEED-EGG PRICE RATIOS BASED ON VANCOUVER PRICES, OCTOBER, 1948 TO SEPTEMBER, 1951 a  Oct.,  1948 to Sept;,1949  Oct.,  1949 to Sept.,1950  Oct.,  1950  to Sept.,1951  No. 5 wheat: October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  14.8 15.4 11.7 11.7 11.3 11.3 10.7 11.3 11.5 13.2 15.7 15.9  14.8 14.6 11.0 9.0 10.4 10.4 10.4 10.7 11.3 13.3 14.5 14.5  14.5 15.2 18.7 12.7 12.3 14.0 15.2 16.5 16.5 17.8 16.2 14.5  Feed oats: October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  18.2 19.6 14.6 15.7 15.1 15.7 14.1 14.8 15.2 17.4 19.6 21.2  19.6 18.2 13.8 11.3 13.1 12.4 11.2 10.7 11.0 13.5 15.7 16.3  16.3 16.3 17.8 11.8 11.6 13.2 14.4 16.2 17.3 21.3 20.0 18.0  82 TABLE 10 —  Laying mash: October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15 Total layer r a t i o n : October 15 November 15 December 15 January 15 February 14 March 15 A p r i l 15 May 15 June 15 July 15 August 15 September 15  Continued  Oct., 1948 to Sept.,1949  Oct., 1949 to Sept.,1950  Oct., 1950 to Sept.,1951  13.8 14.3 10.6 10.6 10.3 10.3 9.6 10.1 10.4 11.9 13.3 13.4  12.4 12.0 9.3 7.a 9.1 9.1 8.9 8.9 9.2 10.8 11.3 11.3  11.3 11.6 13.7 9.6 9.6 11.3 12.0 13.2 13.4 15.3 14.4 12.9  14.6 15.3 11.4 11.5 11.1 11.1 10.4 11.0 11.3 12.9 14.7 15.0  13.9 13.4 10.3 8.6 9.9 9.9 9.6 9.7 10,0 11.9 12,7 12.8  12.8 13.1 15.5 10.7 10.6 12.3 13.2 14.5 14.8 16.8 15.6 14.0  0  Pounds of feed equal i n value to one dozen eggs, calculated from prices i n Table 94, Based on a r a t i o n containing 31 per cent wheat, 15 per cent oats, and 54 per cent laying mash. D  83  APPENDIX I I I THEORETICAL CONCEPTS  1  Two  sets of relationships are relevant to the formu-  l a t i o n of a t h e o r e t i c a l solution to the problem of economic e f f i c i e n c y of resource use i n the short r u n enterprise.  2  f o r a single  The f i r s t set i s the input-output r e l a t i o n s h i p  including the f a c t o r - f a c t o r or resource substitution r e l a t i o n ship.  These define the response of output i n physical terms  to changes i n f a c t o r combinations.  The second set i s the p r i c e  r a t i o s between factors and products which provide a c r i t e r i o n f o r specifying the combination of factors and the product output l e v e l that w i l l maximize p r o f i t s or minimize costs.  The Input-Output  Relationship  The input-output r e l a t i o n s h i p i s outlined here i n terms of the transformation of factors into product when one varies and a l l other factors remain constant.  factor  The problem i s  i F o r a detailed and f u l l y i l l u s t r a t e d presentation of the concepts outlined i n t h i s section, see E a r l 0. Heady. Economics of A g r i c u l t u r a l Production and Resource Use (New York: Prentice-Hall, Inc., 1952), pp. 21-199. t  A short-run condition of production exists when the quantities of some resources are f i x e d at any l e v e l , regardless of the number of f i x e d resources and the l e v e l at which each i s f i x e d . In the long-run condition, variations i n the input of a l l resources i s possible. 2  84 one of i n t e n s i t y of f a c t o r use, that i s , what amount of the variable f a c t o r w i l l give the optimum (most p r o f i t a b l e ) output. Usually,  one f a c t o r alone cannot be varied.  However, the  p r i n c i p l e applies equally when more than one f a c t o r i s varied i n proportion  to the f i x e d f a c t o r s .  The input-output r e l a t i o n s h i p between a single variable input, with the quantity of other resources held constant, and the output of a single product can take one of three general forms, namely, constant, decreasing or increasing  returns.  Constant returns occur when each additional unit of the variable f a c t o r applied to the f i x e d f a c t o r r e s u l t s i n equal additions to t o t a l output of product; the r a t i o of t o t a l output to t o t a l Input remains constant.  Decreasing returns to the  variable  f a c t o r occur when each a d d i t i o n a l unit of input adds less to t o t a l output than the previous u n i t . output/input r a t i o declines.  Under t h i s condition,  Increasing  the  returns to a single  f a c t o r exist when each successive unit of the variable resource adds more to the t o t a l product than the previous unit of  input.  When increasing productivity of a variable f a c t o r occurs, the output/input r a t i o  increases.  Many input-output relationships include two conditions  stated above.  Most common i s one that combines both  increasing returns and decreasing returns to the factor.  variable  The t h e o r e t i c a l model based on t h i s combination of re-  lationships i s as follows: increased  of the  I f the quantity  of one resource i s  by equal increments with th'e quantities of other re-  sources held constant, the increments to t o t a l product  may  85 increase at f i r s t but w i l l decrease a f t e r a certain point. This statement i s i l l u s t r a t e d i n Table 11 and Figure 1.  In-  creasing returns to the variable f a c t o r X exist f o r a l l increments of input up to and including the sixth u n i t .  Up to t h i s  l e v e l of input, the t o t a l product increases at an increasing rate, and the t o t a l product curve (Yp i n Figure 1) i s convex to the x-axis. of input.  Decreasing returns occur a f t e r the s i x t h unit  The t o t a l product continues to increase but by  successively smaller amounts, causing the t o t a l product curve to bend toward the x-axis of the graph. TABLE 11 RELATIONSHIP OF RESOURCE INPUT TO TOTAL, AVERAGE AND MARGINAL PRODUCTS (HYPOTHETICAL DATA) Input of Output of Output/Input Ratio Additional or Variable Factor Product or Average Product Marginal Product X Y Y/X AY/AT 0 2 4 6 8 10 12 14 16 18  0 2 8 18 26 32  36 38 36  30  1.00 2.00 3.00 3.25 3.20 3.00 2.71 2.25 1.67  1 3 5 4 3 2 1 -1 -3  The average and marginal products are basic quantitative measurements derived from t h i s general input-output model.  The  average product, or average productivity, i s the amount of product per unit of input of the v a r i a b l e f a c t o r .  I t can be  expressed by the r a t i o Y/X, where Y i s the t o t a l product and X  86 i s the t o t a l input of the variable f a c t o r .  When the input-  output r e l a t i o n s h i p i s l i n e a r , the average product remains constant.  I f the input-output relationship represents i n -  creasing returns, the average product increases as more of the v a r i a b l e f a c t o r i s employed.  Conversely, under the conditions  of decreasing returns, the average product of the variable f a c t o r decreases as more units are applied t o the f i x e d f a c t o r . The marginal product i s the quantity added to the t o t a l product by an additional unit of the variable f a c t o r .  I t i s the r a t i o  of the increment i n t o t a l output to the increment i n input of the variable f a c t o r .  This r a t i o can be expressed as AY/AX,  when AY i s the change i n product output and AX i s the change in factor input,  1  The r e l a t i o n s h i p between marginal and t o t a l products i s as follows:  As long as the marginal product i s increasing, the  t o t a l product increases at an increasing rate.  Beyond the  point where the marginal product i s at a maximum, the t o t a l product continues to increase but at a decreasing rate, and • Only an approximation of the marginal product i s obtained by dividing the increment i n t o t a l product by the i n c r e ment i n input of the variable f a c t o r . For example, an increase from s i x t o eight units i n f a c t o r input r e s u l t s i n an increase from 18 t o 26 units i n product output, as shown i n Table 11, The marginal product of four units does not r e l a t e s p e c i f i c a l l y to the eighth unit of input, but rather i t i s the average marginal product of a l l f r a c t i o n a l inputs between s i x and eight units of the variable f a c t o r . This i s true because the change i n input of f a c t o r X i s not i n f i n i t e l y small. However, the exact marginal product at a given l e v e l of f a c t o r input can be calculated by d i f f e r e n t i a t i o n of the mathematical equation that expresses the functional r e l a t i o n s h i p between f a c t o r input and product output. The marginal product as a derivative r e l a t e s to a change i n f a c t o r input that i s i n f i n i t e l y small (approaches the l i m i t zero). L  d7  NEGATIVE RETURNS  DECREASING RETURNS  INCREASING RETURNS  STAGE I (IRRATIONAL)  l  STAGE 2 (RATIONAL)  i !  STAGE 3 (IRRATIONAL)  40k  u  ZD O  o tr a> u. o  30h  Ep > 1.0  I-  Ep < 1.0  Ep < 0  Q. 20l-  tO  Ep = 1.0  Ep =0  I0h Mp Ap  I  0  2  4  6  8  10  12  14  INPUT OF VARIABLE FACTOR X  16  18  FIGURE I. — Relationship of input of a single variable resource to total, average and marginal products.  >  88  reaches a maximum when the marginal product i s zero.  Then, as  the t o t a l product declines, the marginal product becomes negative. The ranges of increasing, decreasing and negative returns to a single variable f a c t o r can be defined i n terms of the marginal product.  Returns t o an additional unit of input i n -  crease u n t i l the maximum marginal product i s reached, are constant at that point, and decrease thereafter.  Negative returns  are indicated by a marginal product less than zero. Certain relationships also exist between the average and marginal products.  The average product of a variable f a c t o r  increases as long as i t i s exceeded by the marginal product, even though the marginal product may be d e c l i n i n g .  The average  and marginal products are equal at the maximum average product. F i n a l l y , the average productivity of a resource decreases i f the marginal product i s less than the average product. The e l a s t i c i t y of production i s defined as the percentage change i n product output as compared with the percentage change i n f a c t o r input.  I t can be expressed i n equation form as  Ep * A T / Y . AX/X This equation can also be written as n Ep  _ AY/ X,  - zxrr  which shows that the e l a s t i c i t y of production equals the r a t i o of the marginal product t o the average product. The value of the e l a s t i c i t y of production depends on the nature of the input-output r e l a t i o n s h i p .  Production e l a s t i c i t y  89 i s equal to 1,0 when returns t o the variable f a c t o r are constant. An e l a s t i c i t y of less than 1.0 i s always associated with decreasing returns t o the v a r i a b l e f a c t o r .  However, when the  e l a s t i c i t y of production i s greater than 1.0, either increasing or decreasing returns may p r e v a i l .  Although increasing returns  can only occur when the e l a s t i c i t y exceeds 1.0, decreasing r e turns also are possible under t h i s condition of e l a s t i c i t y . The range of decreasing returns associated with a production e l a s t i c i t y greater than 1.0 extends from the maximum marginal product t o the maximum average product (see Figure 1 ) . Certain relationships between the e l a s t i c i t y of production and the t o t a l , average and marginal products can also be defined.  The e l a s t i c i t y of production i s equal t o 1.0 at  the maximum average product, at which point the average and marginal products are equal.  I t i s greater than 1.0 up to the  maximum average product, and l e s s than 1.0 between the maximum average product and the maximum t o t a l product.  Production  e l a s t i c i t y equals zero at the maximum t o t a l product and becomes l e s s than zero (or negative) as the t o t a l product declines.  P r i n c i p l e s of Resource A l l o c a t i o n As outlined i n the following, the p r i n c i p l e s of resource a l l o c a t i o n r e l a t e t o the transformation of a single v a r i a b l e f a c t o r into a single product when a l l other resources are held constant, with the objective of maximizing  profits.  The general input-output relationship which includes increasing, decreasing and negative marginal returns can be  90 divided into segments denoted as the three stages of production. As i l l u s t r a t e d i n Figure 1, stage 1 extends to the input of the variable f a c t o r that r e s u l t s i n the maximum average product. Stage 2 covers the range of inputs between the maximum average product and the maximum t o t a l product.  Stage 3 includes a l l i n -  puts that have a negative marginal product and extends over the entire range of declining t o t a l product.  An input-output r e -  l a t i o n s h i p with increasing marginal returns throughout would f a l l e n t i r e l y i n stage 1.  However, when decreasing marginal  returns occur at a l l l e v e l s of input, the input-output r e l a t i o n ship might include a l l three stages of production. A l e v e l of resource use that f a l l s i n stage 1 i s uneconomic because greater returns can always be obtained by using a larger quantity of the variable resource.  The application of  a d d i t i o n a l amounts of the variable resource i n stage 1 increases the average productivity of a l l previous inputs.  Also, a l a r g e r  product i s obtained from the f i x e d factors as well as from each additional unit of the variable f a c t o r .  Thus, the product of  neither the variable f a c t o r nor the f i x e d factors can be maximized i n stage 1.  Instead of r e s t r i c t i n g the application of a  variable resource to the f i x e d factors before the l i m i t of stage 1 i s reached, the combination of fixed and variable r e sources can always be rearranged within stage 1 to secure a larger product.  A greater product from given resources can be  gained by leaving i d l e some of the f a c t o r that was otherwise considered as " f i x e d " .  This i s possible even when the available  amount of the variable f a c t o r i s l i m i t e d .  For example, suppose  91 that column 1 of Table 11 r e f e r s to pounds of f e r t i l i z e r applied to an acre of grain land and column 2 i s the y i e l d per acre. Also assume that only 800 pounds of f e r t i l i z e r are a v a i l a b l e f o r use on 200 acres of land.  I f the f e r t i l i z e r i s applied to a l l  of the land at the rate of four pounds per acre, the t o t a l production i s 1600 bushels.  However, i f h a l f the land i s l e f t i d l e  and the f e r t i l i z e r i s applied to only 100 acres at the rate of eight pounds per acre, t o t a l production increases to 2600 bushels.  Thus, more product i s obtained from the same quantity  of f e r t i l i z e r and l e s s land.  Economic returns also must i n -  crease, except when the product has no value attached to i t . Stage 3 also i s an area of uneconomic and i r r a t i o n a l production where the t o t a l product can be increased by using a smaller quantity of resources.  The only difference, compared  with stage 1, i s that some of the variable f a c t o r i s withdrawn from use.  Again assuming that Table 11 i s an input-output r e -  l a t i o n s h i p of f e r t i l i z e r applications on grain land, 3600 pounds of f e r t i l i z e r applied to 200 acres at 18 pounds per acre would r e s u l t i n a t o t a l product of 6000 bushels.  However, i f only  2800 pounds of f e r t i l i z e r are used at 14 pounds per acre, the t o t a l production increases to 7600 bushels.  In t h i s case, a  larger product i s gained by adjusting the combination of f i x e d and variable resources through reduction of the variable r e source ( f e r t i l i z e r ) .  As long as the product has a value,  economic returns also increase when resources are recombined i n t h i s manner within stage 3. Consequently, i r r a t i o n a l and t e c h n i c a l l y i n e f f i c i e n t  92 production exists i f resources can be rearranged to give either (1) a larger product from the same resources, or (2) the same product from a smaller aggregate of fixed and v a r i a b l e r e sources.  This condition exists f o r any resource  f a l l i n g i n stage 1 and stage 3»  combination  In cases of i r r a t i o n a l pro-  duction, the adjustment i n resource combination required to i n crease economic returns can be s p e c i f i e d without knowledge of the resource and f a c t o r p r i c e s .  P r o f i t s are always increased  when any rearrangement of resources results i n a larger product from the same resources or the same product from less resources. I r r a t i o n a l production indicates that a greater value of product can always be produced with the same or a smaller aggregate of resources. Because stage 1 and stage 3 are i r r a t i o n a l ranges of production, the problem of resource a l l o c a t i o n i s often considered only within stage 2, or i n terms of an input-output r e l a t i o n s h i p with a production e l a s t i c i t y of less than 1.0 but more than zero.  This, however, does not suggest that farm r e -  sources are not combined i n an i r r a t i o n a l manner. combinations  Irrational  of resources can and do exist f o r several reasons,  including c a p i t a l l i m i t a t i o n s , i n d i v i s i b i l i t y of resources, uncertainty, ignorance, and even an apathetic attitude of the farm operator. Even without knowledge of resource and product prices, i t i s evident that p r o f i t s can be maximized only when the variable f a c t o r i s applied to the f i x e d f a c t o r at a rate that f a l l s within stage 2.  However, i t i s impossible to determine  93 the exact combination of variable and f i x e d resources required within stage 2 to maximize p r o f i t s without reference to the prices of the variable f a c t o r and the product. . Economic e f f i c i e n c y requires a resource combination that w i l l maximize p r o f i t s .  Attainment of t h i s condition involves a  decision to use one of the several resource combinations that are possible within stage 2, the r a t i o n a l area of production. The problem i s t o specify the amount of a variable f a c t o r to be combined with f i x e d resources i n order to maximize p r o f i t s . Selection of the most e f f i c i e n t combination of resources can be made only i n terms of the appropriate  price r a t i o .  In the  transformation of a s i n g l e variable f a c t o r into a single product, the relevant price r a t i o i s the factor-product  price r a t i o . I t  i s expressed as Px/Py, when Px i s the p r i c e of the variable f a c t o r X, and Py i s the p r i c e of the product I . The l e v e l at which a variable f a c t o r should be applied to f i x e d factors f o r p r o f i t maximization i s determined by the following condition:  The factor/product  price r a t i o must equal  the marginal physical productivity of the variable f a c t o r .  This  condition can be expressed i n equation form as Px/Py = AY/AX. Another way of writing t h i s equation i s (Px)(AX) * (Py)(AY), which indicates that p r o f i t s are maximized when the change in. the variable input and the change i n the product output are equal i n value. The necessary conditions f o r maximum p r o f i t s are i l l u s -  94 strated i n Table 12. As presented there, p r o f i t s are maximized when four units of the variable f a c t o r are used.  At t h i s l e v e l  of variable input, the factor/product price r a t i o equals the marginal physical product, or Px/Py = AY/flX = 50. Also, the changes i n value of the variable f a c t o r input and the product output are equal, or (Px)GflX) = (Py)(4Y) = 50. In other words, the increase i n cost of the variable f a c t o r i s equalled by the increase i n value of the product. TABLE 12 OPTIMUM LEVEL OF APPLYING A VARIABLE FACTOR TO FIXED FACTORS (HYPOTHETICAL DATA) Input of Variable Factor X  Output of Product Y  Marginal Physical Product 4Y/AX  Value of Added. Factor* (Px)(AX)  Value of Added Product (Py)(AY)  0 1 2 3 4 5 6  142 214 284 347 397 440 475  72 70 63 50 43 35  #50 50 50 50 50 50  #72 70 63 50 43 35  0  a  P r i c e of the variable factor, Px = #50 per u n i t ,  b  P r i c e of the product, Py = #1 per u n i t .  Inequality of the factor/product p r i c e r a t i o and the marginal physical product indicates a variable input that i s inconsistent with a maximum p r o f i t .  When the factor/product  p r i c e r a t i o i s greater than the marginal physical product, or  95 Px/Py> AY/AX, the cost of an additional unit of the variable f a c t o r exceeds the value of the additional output of product.  In t h i s case,  p r o f i t s can be increased by using less of the variable f a c t o r . I f the factor/product price r a t i o i s less than the marginal physical product, or Px/Py «c AY/AX, the cost of adding a unit of input i s l e s s than the value of the additional product.  Consequently, using a larger amount of the  variable leads to increased p r o f i t s . The conditions defining the most p r o f i t a b l e quantity of a variable resource to be combined with f i x e d resources can also be presented graphically.  As a f i r s t step, i t i s necessary to  explain the nature of factor/product price r a t i o s .  Lines A and  B i n Figure 2 indicate the quantities of a f a c t o r and a product that are equal i n value under p r i c e r a t i o s of 25/1 respectively.  and  50/1,  As the f a c t o r p r i c e increases r e l a t i v e to the  product price, Px/Py becomes l a r g e r and the p r i c e r a t i o l i n e assumes a steeper slope.  Conversely, a decrease i n the f a c t o r  price r e l a t i v e to the product price causes Px/Py to become smaller and reduces the slope of the price r a t i o l i n e .  However,  variations can occur i n the prices of both f a c t o r and product, either simultaneously or independently, and i n the same or opposite d i r e c t i o n .  Consequently, the factor/product price  r a t i o and the slope of the price r a t i o l i n e change with every disproportionate v a r i a t i o n i n f a c t o r and product p r i c e s . The input of a variable f a c t o r required f o r maximum  Px/Py = 50/1  f  2  3  UNITS OF FACTOR X FIGURE 2.— Factor/product price ratios. 400Px/Py = 25/1 A  10  20 30 40 50 60 70 INPUT OF VARIABLE FACTOR X FIGURE 3.— Equation of the factor/product price rotio and the marginal physical product for maximum profits.  97 p r o f i t s i s denoted by tangency of the t o t a l product curve and the price r a t i o l i n e .  The slope of the input-output curve de-  notes the marginal product of the variable factor, and the p r i c e r a t i o l i n e indicates the factor/product price r a t i o .  Since two  l i n e s have the same slope at a point of tangency, the f a c t o r / product p r i c e r a t i o and the marginal product are equal at the point of tangency of a price r a t i o l i n e and the physical inputoutput curve. ^his condition i s presented i n Figure 3, where A and B are price r a t i o l i n e s and the curve Ip represents an input-output relationship.  When Px/Py i s 25/1, tangency of the price r a t i o  l i n e A with the t o t a l product curve Yp indicates that p r o f i t s are maximized with an input of 45 units of the variable f a c t o r X.  The marginal physical product (curve Mp) i s 25 units at t h i s  input, so that Px/Py equals AY/AX. An increase i n the f a c t o r price r e l a t i v e to the product price i s represented by a s h i f t i n the p r i c e r a t i o l i n e from A to B (Figure 3 ) .  As a r e s u l t , input of the variable f a c t o r  must be reduced to regain the condition of maximum p r o f i t s .  On  the other hand, i f the f a c t o r price decreases r e l a t i v e to the product price, p r o f i t s can be maximized only by increasing the input of the variable f a c t o r . The more or less continual f l u c t u a t i o n of most, i f not a l l , factor/product price r a t i o s has certain implications i n resource a l l o c a t i o n .  F i r s t , these changes necessitate frequent  adjustments i n the proportion of variable and f i x e d resources i n order to maximize p r o f i t s .  In addition, variations i n f a c t o r  98  and product prices create uncertainty about the future.  Since  producers, as users of resources, can only anticipate future prices, t h e i r a b i l i t y to maximize p r o f i t s depends on the accuracy of t h e i r estimates of price changes. Value productivity relationships d i f f e r from physical input-output relationships only i n the unit of measurement; the output of product i s measured i n d o l l a r s instead of a physical unit such as pounds or bushels.  Consequently, the t o t a l value  product (Tv) i s equal to the t o t a l physical product m u l t i p l i e d by the product price, and Yv = (Yp)(Py). The average value product (Av) i s derived by multiplying the average physical product by the product price, or by dividing the t o t a l value product by the input of variable factor, and Av = (Ap)(Py) =  Yv/X.  The marginal value product i s derived by multiplying the marginal physical product by the product price, or by c a l c u l a t i n g the change i n t o t a l value product associated with an additional unit of variable input, and, Mv • (Mp)(Py) = AYv/4X. The condition f o r maximum p r o f i t s , stated i n terms of value productivity, requires equality of the marginal cost and the marginal value product of a resource.  Likewise, p r o f i t s  are maximized when the marginal cost and marginal revenue of a unit of product are equal.  However, the optimum input of a  variable resource i s not indicated d i r e c t l y by an input-output relationship that relates the physical input of a variable r e -  99 source t o the value of output.  I t can be specified only by  reference t o marginal cost of the resource and the marginal value product. The marginal cost of a resource i s the cost of the l a s t unit added to the t o t a l input.  Since any quantity of a resource  can generally be purchased at the current price by farm operators, the marginal cost of a resource i s equal to the price of the resource regardless of the quantity used.  Consequently,  variations i n marginal cost of a resource w i l l occur only through changes i n the p r e v a i l i n g price of a resource. P r o f i t maximization i n terms of value productivity can be i l l u s t r a t e d by the data i n Table 13.  With the price (and  marginal cost) of the variable f a c t o r at #50, an input of four units w i l l maximize p r o f i t s when marginal value productivity i s based on a product price of #1.00 per u n i t .  I f the f a c t o r price  r i s e s t o $70 and the product price remains unchanged at $1.00, the optimum f a c t o r input i s reduced t o two u n i t s .  However, an  increase i n product price t o $2.00 per unit would require a variable input of s i x units f o r maximum p r o f i t s .  Thus, any  change i n either the f a c t o r p r i c e or the product p r i c e compels an adjustment  i n the variable input that w i l l equalize the  marginal cost of the f a c t o r and the marginal value product; otherwise, the maximum l e v e l of p r o f i t s cannot be maintained. Up t o t h i s point, an unlimited supply of the variable resource has been assumed i n determining the input required f o r maximum p r o f i t s .  However, the quantity of any s p e c i f i c r e -  source, such as f e r t i l i z e r , land or labor, available to a farmer  100 i s f r e q u e n t l y l i m i t e d by t h e f u n d s a t h i s d i s p o s a l . ble  This availa-  s t o c k o f a r e s o u r c e may be i n s u f f i c i e n t t o p r o v i d e t h e l e v e l  o f i n p u t n e c e s s a r y f o r maximum p r o f i t s .  The problem t h e n i s t h e  a l l o c a t i o n of a l i m i t e d stock of a resource t o obtain the largest possible profit.  S i n c e any q u a n t i t y o f product  c a n be  s o l d a t t h e same p r i c e under t h e c o m p e t i t i v e c o n d i t i o n s o f a f a r m , any i n c r e a s e i n t h e t o t a l p h y s i c a l product f r o m g i v e n r e s o u r c e s w i l l a l s o i n c r e a s e n e t income, because t o t a l c o s t o f t h e r e s o u r c e s remains c o n s t a n t .  Consequently,  organization of the  r e s o u r c e s t o o b t a i n t h e l a r g e s t p h y s i c a l product w i l l r e s u l t i n t h e l a r g e s t p r o f i t , a l t h o u g h n o t n e c e s s a r i l y t h e maximum p r o f i t . TABLE 13 MARGINAL COST OF A FACTOR AND MARGINAL VALUE PRODUCT (HYPOTHETICAL DATA) Input of Variable Factor  0 1 2 3 4 5 6  Output of Product  142 214 284 347 397 440 475  Marginal Physical Product  72 70 63 50 43 35  M a r g i n a l Cost o f Variable Factor when P r i c e i s  Marginal Value Product when. Price i s  $50  $70  $1.00  $2.00  $50 50 50 50 50 50  $70 70 70 70 70 70  $72 7P 63 50 43 35  $142 140 126 100 86 70  Suppose t h a t o n l y 12 u n i t s (cwt.) o f f e r t i l i z e r a r e a v a i l a b l e f o r u s e on s i x a c r e s o f l a n d t h a t i s i d e n t i c a l i n quality.  The most e f f i c i e n t u s e o f t h i s l i m i t e d s u p p l y o f  f e r t i l i z e r i s a t t a i n e d when t h e m a r g i n a l p h y s i c a l p r o d u c t i v i t y  101 of f e r t i l i z e r i s the same on each acre of land.  This p r i n c i p l e  can be i l l u s t r a t e d with the marginal physical products shown i n Table 13.  Each additional unit of input r e s u l t s i n a smaller  marginal physical product, or successively smaller increments to the t o t a l product.  Consequently,  the f e r t i l i z e r must be  applied at the same rate per acre i n order t o equalize i t s marginal physical product on each acre.  By applying two units  of f e r t i l i z e r to each of the s i x units of land, the t o t a l product i s 1704 u n i t s .  Any other a l l o c a t i o n of the f e r t i l i z e r  r e s u l t s i n a smaller t o t a l product because the marginal product of part of the f e r t i l i z e r would not be as large as possible.  The Factor-Factor Relationship The f a c t o r - f a c t o r or resource substitution relationship r e f e r s to the transformation of two or more variable resources into a product.  The problem now centres on determination of the  optimum combination of a number of variable resources i n producing some constant amount of product.  In the interests of  simplifying the following outline, only two factors are considered to be variable, while a l l others are held at some f i x e d l e v e l , i n the production of a single product.  Although more  than two variable resources are o r d i n a r i l y involved i n a production process, the two-factor relationships are equally applicable to any number of variable resources. The relationship between the input of two variable factors,  and X , and the output of a single product Y can be 2  shown as a two-way table such as Table 14.  This table a c t u a l l y  102 consists of a series of single f a c t o r input-output relationships with either X-^ or/ X  2  f i x e d at d i f f e r e n t l e v e l s and input of the  other allowed to vary. be increased,  I t shows that input of both factors can  either proportionately  larger output of product.  I t also indicates that  d i f f e r e n t combinations of Xj_ and X same l e v e l of output.  or otherwise, to gain a  2  several  can be used t o a t t a i n the  Consequently, three d i s t i n c t types of  adjustment i n the f a c t o r inputs are possible! (1) Input of one f a c t o r can be increased  or decreased while the other i s held  constant; (2) Input of both factors can be either increased or decreased simultaneously; (3) One f a c t o r can be increased and the other decreased i n quantity to produce the same amount of product.  The l a s t of these adjustments involves the f a c t o r -  f a c t o r or resource substitution relationship i n which the r e placement of one f a c t o r with the other i s possible within a certain range i n the production of a constant output of product, A two-factor input-output r e l a t i o n s h i p can also be presented graphically as a series of isoquants or iso-product curves (Figure 4),  Each iso-product curve indicates a l l of the  possible combinations of X-^ and X quantity of product Y,  2  that y i e l d a s p e c i f i e d  Figure 4 also shows that X^ and X are  substitute resources because a range of input  2  combinations,  wherein an increase i n one resource replaces a decrease i n the other, exists at each l e v e l of input. The rate of f a c t o r substitution may be either constant or decreasing i n the production of a f i x e d output of product. Under a constant rate of substitution, one f a c t o r replaces the  103  other at the same r a t i o throughout a l l f a c t o r combinations at a f i x e d l e v e l of output,  A continuous and l i n e a r isoquant i s  c h a r a c t e r i s t i c of resources that substitute at a constant rate. Factor s u b s t i t u t i o n at a decreasing rate exists when successive increments i n the input of one f a c t o r replace a decreasing quantity of the other f a c t o r .  In t h i s case, the isoquant i s a  curved l i n e convex to the axes of the graph.  As indicated i n  Figure 4, i t assumes a greater slope as f a c t o r X^ i s increased, with each a d d i t i o n a l unit of X^ replacing a smaller amount of X . 2  Conversely, the curve declines i n slope as X  2  i s substi-  tuted f o r X^, but only at a decreasing rate, TABLE 14 RELATIONSHIP BETWEEN INPUT OF TWO VARIABLE FACTORS AND OUTPUT OF PRODUCT (HYPOTHETICAL DATA) Input of Factor X Input of T?A /*+"  A M  0  1  2  A.  0 1 2 3 4 5 6 7 8 9  3  7  4  5  2  6  7  8  9  -Output of Product Y0 0 0 0 0 0 0 0 0 0  0 6 10 12 12 11 10 9 8 7  0 7 12 16 20 22 24 24  24 23  0 8 13 18 22 26 30 32 34 36  0 8  14 19  24 28 32 36 40  41  0 7  15  20 25 30 35 39 42 45  0 0 6 6.5 16 16.5 21 22 26 27 32 31 36 37 42 41 46 44 48 50  0 5.5 16 23 28 33 38 43 48 52  0 5  15.5  24 29 34 39 44 49 54  The marginal rate of s u b s t i t u t i o n r e f e r s to the amount by which one resource (X ) i s decreased 2  as input of the other  104  r e s o u r c e (X^) i s d e c r e a s e d by one u n i t . t h e r a t i o A X / A X ^ , when A X 2  AX  i s t h e change ( d e c r e a s e ) i n X  2  i s t h e change ( i n c r e a s e ) i n X  1  I t can be e x p r e s s e d as 2  and  C a l c u l a t e d by t h i s methodj  1 #  t h e m a r g i n a l r a t e o f s u b s t i t u t i o n i s an a v e r a g e between two d i s t i n c t combinations  of r e s o u r c e s .  1  When two f a c t o r s  substi-  t u t e f o r each o t h e r a t a c o n s t a n t r a t e , t h e m a r g i n a l r a t e o f s u b s t i t u t i o n does n o t v a r y .  However, i f t h e r a t e o f f a c t o r  s u b s t i t u t i o n d i m i n i s h e s , t h e m a r g i n a l r a t e o f s u b s t i t u t i o n becomes p r o g r e s s i v e l y s m a l l e r as one f a c t o r r e p l a c e s t h e o t h e r i n the p r o d u c t i o n of a constant product  (Table  15).  TABLE 15 DIMINISHING RATE OF FACTOR SUBSTITUTION WITH OUTPUT FIXED AT 100 UNITS (HYPOTHETICAL DATA) Input of Factor l  Input of Factor  50 55 60 65 70 75 80  62 49 40 34 29 25 22  x  X  Change i n F a c t o r Xn  2  Change i n Factor X AX  2  2  -13 - 9 - 6 - 5 - 4 - 3  5 5 5 5 5 5  M a r g i n a l Rate, o f Substitution  -2.6 -1.8 -1.2 -1.0 -0.8 -0.6  The e l a s t i c i t y o f s u b s t i t u t i o n i s d e f i n e d as t h e r e l a t i v e change i n t h e q u a n t i t i e s o f two r e s o u r c e s w h i c h combine i n The exact m a r g i n a l r a t e o f s u b s t i t u t i o n r e f e r s t o a s i n g l e p o i n t on t h e i s o - p r o d u c t c u r v e . I t must be computed as a d e r i v a t i v e o f t h e i s o q u a n t e q u a t i o n , e x p r e s s e d as dX /dX^ o r dX^/dX , where t h e change i n X o r X-^ becomes i n f i n i t e l y s m a l l . 2  2  2  1  2  3  4  5  6  7  INPUT OF VARIABLE FACTOR FIGURE 4 . — Isoquants or iso-product  curves.  X  2  106 producing a f i x e d amount of product. for X ,  the e l a s t i c i t y of substitution can be calculated  2  where X^ and X AX^ X .^ 2  In substituting f a c t o r X-^  2  are the o r i g i n a l quantities of the two  i s the change i n f a c t o r X^ and The  AX  2  as  factors,  i s the change i n f a c t o r  e l a s t i c i t y of substitution i s always negative f o r  substitute resources, and indicates how iso-product curve changes or how  f a s t the slope of the  r a p i d l y the marginal rate of  substitution declines. Resources can be either technical substitutes or technic a l complements.  The  extreme condition of technical comple-  mentarity involves resources that combine only i n a f i x e d proportion.  In t h i s case, there i s only one combination of re-  sources f o r producing each quantity of product.  I t i s impossi-  ble to maintain a given l e v e l of output by f a c t o r s u b s t i t u t i o n . Also, the t o t a l product i s unaffected by adjustments to the i n put of one f a c t o r alone. simultaneous increases  A larger output i s obtained only by  i n the input of both f a c t o r s .  There are other cases of technical complements where further reduction i n input of one f a c t o r cannot be replaced an increase i n another f a c t o r .  by  Many resources employed i n  agriculture are of t h i s nature, serving both as  substitutes  and technical complements over d i f f e r e n t ranges of input combiT h i s method of c a l c u l a t i o n gives the average e l a s t i c i t y f o r a range of f a c t o r combinations, or f o r a portion of the iso-product curve. The e l a s t i c i t y at a s p e c i f i c point on the product curve must be computed by calculus and i n reference to an i n f i n i t e l y small change i n resource inputs. 1  107 nations.  Iso-product curves f o r complementary or l i m i t a t i o n a l  resources of t h i s nature are shown i n Figure 5. to be maintained at 10 units, f a c t o r X  2  I f output i s  can be substituted f o r  only up to the point where the iso-product curve becomes  vertical.  Conversely, replacement of X^ with X  iso-product curve becomes h o r i z o n t a l .  2  ends where the  Thus, f a c t o r substi-  t u t i o n i s possible over a range of input combinations but, beyond a certain point, some minimum input of one f a c t o r i s required to maintain the l e v e l of output. The two resources are substitutes within the range of input combinations delineated by the ridge l i n e s OA and OB (Figure 5), and they are complements f o r a l l combinations f a l l i n g outisde of the ridge l i n e s .  Factor X  2  i s complementary  with X^ f o r the v e r t i c a l portions of the iso-product curves above OA because (1) no further substitution of X^ f o r X possible without a decrease i n t o t a l product, and (2) X  2  2  is must  be increased along with X-^ to gain an increase i n t o t a l product.  These conditions also apply i n respect to the r e -  l a t i o n s h i p of X^ with X  2  f o r the portions of the iso-product  curves f a l l i n g below OB. The difference between technical substitutes and technic a l complements i n resource combination can now be stated more specifically.  Resources are technical substitutes when t h e i r  marginal rate of substitution i s negative or less than zero.  In  Figure 5, the sign of AXg/AX^ i s negative f o r a l l factor combinations that are indicated by the portion of each i s o product curve f a l l i n g within the ridge l i n e s OA and OB.  Within  O  10  20 INPUT  OF  30 FACTOR  X  40 2  FIGURE 5 . — Ridge lines and isocline indicating rates of output.  substitution  at  different  equal marginal levels  of  109  these l i m i t s , an increase or p o s i t i v e change i n X^ i s always associated with a decrease or negative change i n X . 2  Resources  are t e c h n i c a l complements when the marginal rate of substitution i s zero or greater.  The s u b s t i t u t i o n r a t i o i s zero along the  v e r t i c a l portion of each iso-product curve (above OB i n Figure 5) because none of the minimum amount of X  2  required to maintain  a l e v e l of output can be replaced by an increase i n the input of Xj_.  In some extreme cases, i t i s possible f o r the input of one  f a c t o r to be carried to such a high l e v e l that the other f a c t o r must also be increased to maintain a constant output of product. Under t h i s condition, the r a t i o of change i n f a c t o r inputs i s positive. An i r r a t i o n a l combination of resources i s indicated by a marginal rate of s u b s t i t u t i o n that i s equal to, or greater than zero.  Under conditions of l i m i t e d substitution, the area  of i r r a t i o n a l resource use begins at the point on an iso-product curve where the two f a c t o r s become complementary.  Any f a c t o r  combination f o r a constant product that f a l l s outside of the ridge l i n e s (OA and OB i n Figure 5) i s i r r a t i o n a l because i n creased input of one f a c t o r either allows no reduction i n input of the other f a c t o r or requires that input of the other f a c t o r also be increased.  Conversely,  the same quantity of product  be obtained by using l e s s of one or both resources.  can  The l i m i t s  of r a t i o n a l resource combination are marked by the ridge l i n e s , which define the points of zero f a c t o r substitution on a family of iso-product curves.  Factor combinations f a l l i n g between the  ridge l i n e s are r a t i o n a l because a larger input of one f a c t o r  110 permits a reduced input of the other f a c t o r at a given l e v e l of output. As already noted, the marginal rate of substitution usually diminishes as more of one f a c t o r and l e s s of another f a c t o r i s used to produce the same quantity of product.  However;  as output i s raised to higher l e v e l s , f a c t o r substitution may be at a greater or l e s s e r rate.  The slope of iso-product curves  f o r successively larger products may become steeper or f l a t t e r , depending on whether the marginal rate of substitution declines more r a p i d l y or more slowly than at the preceding output.  Also,  a change often occurs i n the range of f a c t o r combinations within which substitution i s possible.  Nevertheless, the marginal rate  of substitution can be equal at d i f f e r e n t l e v e l s of output. These conditions are i l l u s t r a t e d by the iso-product contours i n Figure 5«  The l i n e 0T defining the points of equal  marginal rate of substitution i s c a l l e d an i s o c l i n e . AX^/^X  2  The r a t i o  i s equal at a l l points where the i s o c l i n e intersects  an iso-product curve,  T  here i s a continuous i s o c l i n e f o r each  marginal rate of substitution that i s common to a l l constant product curves.  The ridge l i n e s also are i s o c l i n e s i n the sense  that they denote a substitution rate of zero.  Equal substi-  t u t i o n rates, however, do not necessarily occur on a l l i s o product curves; rates of substitution may be found at lower l e v e l s of production which do not exist at a higher l e v e l .  Ill  Resource Combination and Cost Minimization Resource substitution presents the problem of combining factors i n a way to minimize the cost of producing a given amount of product.  A l t e r n a t i v e l y , the maximum economic product,  measured i n p r o f i t s at the farm, i s obtained from given r e sources only when each unit of output i s produced with the minimum cost or outlay of resources.  Resources that  substitute  continuously i n the production of a given output constitute a major area of resource substitution r e l a t i o n s h i p s .  Confronted  with the many f a c t o r combinations that are possible under conditions of continuous substitution, some c r i t e r i o n i s required to indicate which of the several alternatives i s most desirable. The relevant  indicator f o r p r o f i t maximization i s the f a c t o r  price r a t i o . Knowledge of the f a c t o r p r i c e r e l a t i o n s h i p i s unnecessary f o r making adjustments i n f a c t o r combinations when the marginal rate of f a c t o r substitution i s equal t o or greater than zero.  Such i r r a t i o n a l resource combinations can be rejected as  uneconomic because the aggregate input of resources could be reduced without lowering the l e v e l of output.  As long as the  same physical output can be produced with less of one or more factors, net p r o f i t i s not at a maximum.  Rational  combinations  of resources are associated with the portion of the iso-product curve characterized  by negative and diminishing  of f a c t o r substitution.  marginal rates  Since a smaller input of one f a c t o r  must be compensated by a larger input of another f a c t o r within  112 the range of r a t i o n a l resource combinations, the optimum combination cannot be selected without reference to the f a c t o r price relationship. The p r i n c i p l e of cost minimization can be stated as follows:  I f two or more factors are employed i n the production  of a single product, cost i s at a minimum when the r a t i o of f a c t o r prices i s inversely equal to the marginal rate of s u b s t i t u t i o n of the f a c t o r s .  This condition i s expressed by the  equation AXg/AX-L = P / P x , Xl  2  where AX^/AX^ i s the marginal rate of substitution of f a c t o r X-^ f o r faetor X , Px^ i s the price per unit of X^, and Px i s 2  2  the p r i c e per unit of X . 2  This p r i n c i p l e of cost minimization i s best i l l u s t r a t e d when two factors substitute at a diminishing  marginal rate.  average marginal rate of substitution of X^ f o r X  2  The  under an  assumed f a c t o r - f a c t o r relationship i s shown i n Table 16. When f a c t o r prices are $1.80 per unit of X^ and $1.00 per unit of X , 2  100 units of output are produced at a minimum cost with an i n put combination of 55 to 60 units of X^ and 40 to 40 units of X2.  The average marginal rate of f a c t o r substitution  ( A X / A I ^ ) of 1.8 within t h i s range of inputs equals the f a c t o r 2  p r i c e r a t i o (Px^/Px ) of 1.8. 2  A single least-cost f a c t o r combi-  nation i s not indicated because the substitution rate i s an average f o r the range of inputs rather than the exact s u b s t i t u t i o n rate at a s p e c i f i c input  combination.  Adjustments i n the f a c t o r inputs are required to r e t a i n  113 a least-cost combination when a v a r i a t i o n i n one or both f a c t o r prices causes a change i n the price r a t i o . of $1,60 f o r X and $2.00 f o r X 1  (Px^/Px ) becomes 0.8. 2  With f a c t o r prices  (Table 16) the price r a t i o  2  Equating t h i s price r a t i o with the  marginal rate of substitution indicates that costs are minimized with an input combination of 70 to 75 units of X units of X .  1  and 25 to 29  A l l other combinations of f a c t o r inputs involve  2  a larger t o t a l cost under these f a c t o r prices. TABLE 16 MINIMIZATION OF COSTS UNDER A DIMINISHING MARGINAL RATE OF FACTOR SUBSTITUTION (HYPOTHETICAL DATA) Input of Resources Marginal Rate Cost of Producing 100 Units Required t o Produce of Substitution with Factor Prices of: 100 Units of Output of XJL f o r X X - $1.80 X i = $1.60 2  x  X  x  l  2  62 49 40 34 29 25 22  50 55 60 65 70 75 80  Z\X /AX 2  X  1  2  « $1,00  $152 148 148 151 155 160 166  2.6 1.8 1.2 1.0 0.8 0.6  %2  s  $2.00  $204' 186 176 172 170 170 172  An iso-cost l i n e represents graphically a l l the possible combinations of two factors that can be purchased at a given t o t a l cost.  I f two factors X^ and X  2  cost $3 and $1 per unit,  respectively, the iso-cost l i n e AB i n Figure 6 shows the d i f f e r ent quantities of X^ and X expenditure of $30.  2  that are available f o r a constant  Iso-cost  l i n e s are always l i n e a r f o r .  114 factors that can be purchased i n any the market p r i c e .  quantity without a f f e c t i n g  The slope of the iso-cost l i n e denotes the  f a c t o r price r a t i o .  The  slope of l i n e AB  (or Px /Pxi) i s 2  1/3,  indicating that one unit of X^ can be purchased at the same cost as three units of  X. 2  An iso-cost l i n e can be constructed f o r any constant t o t a l outlay f o r the two f a c t o r s .  Line CD i n Figure 6 represents  the iso-cost l i n e f o r an expenditure of $60 f o r X^ and X prices remaining at $3 and $1, respectively.  2  with  I t has the same  slope as AB because the f a c t o r price r a t i o i s unchanged. However, since CD represents a larger t o t a l outlay, i t f a l l s at a higher l e v e l than  AB.  Any disproportionate f a c t o r price r a t i o and,  change i n f a c t o r prices a l t e r s the  consequently, causes a change i n the  slope of the iso-cost l i n e .  This effect i s shown i n Figure 7  by the iso-cost l i n e s AB and CD,  both of which represent a  constant expenditure of $60 f o r X^ and X . 2  Line AB  indicates  a price r a t i o (Px /Px^) of 1.0/1.5 at prices of $6 f o r X^ 2  $4 f o r X . 2  X  2  and  I f the price of X^ decreases to $2 and the price of  increases t o $10,  the price r a t i o i s changed to 5.0/1.0.  iso-cost l i n e , as represented by CD,  The  then assumes a steeper  slope and rotates toward the axis of the f a c t o r that has become r e l a t i v e l y cheaper.  Line AB indicates that only 0.67  X-j_ can be purchased f o r the cost of 1.0 with f a c t o r prices as indicated by CD, i n cost to 1.0  unit of  unit of X . 2  unit of However,  5.0 units of X^ are equal  X. 2  The least-cost combination of f a c t o r inputs f o r a given  QUANTITY OF FACTOR X2 FIGURE 6— bo-cost lines for constant factor prices.  0  20  2 5 3 0  QUANTITY OF FACTOR X FIGURE 7.— Iso-cost for different factor prices. 2  3 5 4 0 4 6  INPUT OF  FACTOR  50 X  55  60  2  FIGURE 8.— Least-cost combination of factor inputs as indicated by tangency of iso-cost lines and iso-product curves.  65  116 output of product i s denoted by the point of tangency of an i s o cost l i n e with an iso-product  curve (Figure 8).  At t h i s point,  the f a c t o r price r a t i o and the marginal rate of f a c t o r substit u t i o n are equal.  Line AB i s an iso-cost l i n e with a slope  (Px /Px ) of 1.0/1*8, when the factor prices are $1.80 2  1  and $1.00  for X .  for X i  I t i s tangent to the iso-prpduct curve f o r  2  100 units of output at point M, i n d i c a t i n g inputs of 57*5 units of X^ and 44 units of X  2  f o r minimum t o t a l cost.  prices change to $1.60  f o r I.^ and $2.00 f o r X , the iso-cost 2  l i n e s h i f t s to CD with a slope of 1.0/0.8, iso-product  Tangency with the  curve at point N indicates that 71.5  27.5 units of X  I f the factor  units of X-^ and  minimize the t o t a l cost of factor inputs.  2  As  would be expected, the r e l a t i v e l y cheaper f a c t o r X^ i s substituted f o r the more expensive f a c t o r X ation i n f a c t o r prices. 71.5  2  as a r e s u l t of the v a r i -  Input of X-^ i s increased from 57.5  units, and input of X  i s decreased from 44 to 27.5  2  to  units.  The f a c t that more than two variable factors are required i n most a g r i c u l t u r a l production processes does not i n validate the conditions f o r minimizing the cost of factor i n puts.  The p r i n c i p l e can be extended to any number of f a c t o r s .  I f three substitute resources, X-^, X , 2  and X3, are used i n a  production process, the t o t a l cost of factor inputs f o r a given l e v e l of output i s minimized when AX!/AX AX!/AX  2  3  = Px /Px , 2  x  = Px3/Px!, and  A X 2 / A X 3 = Px3/Px . 2  117  Conditions of Optimum Resource Combination i n the Short  Run  The p r i n c i p l e s of f a c t o r substitution have been presented up to t h i s point under the assumption of a l i m i t e d supply of resources f o r the producing u n i t . a v a i l a b l e i n unlimited  quantities, then two  combination must be considered. ship involving two factor-product  However, i f resources are problems i n resource  Since an input-output r e l a t i o n -  or more variable factors includes both the  and the f a c t o r - f a c t o r relationships, the optimum  l e v e l of output and the optimum combination of variable resources must be selected.  This requires a decision on (1)  how  to combine resources with a f i x e d technical unit as output i s expanded from zero to the most p r o f i t a b l e l e v e l (the f a c t o r product r e l a t i o n s h i p ) , and  (2) how  to combine the variable re-  sources f o r minimum costs at each l e v e l of output (the f a c t o r factor relationship). The attainment of minimum costs as output i s expanded to the most p r o f i t a b l e l e v e l poses the question of whether resource inputs should be increased portion.  i n a f i x e d or i n a variable pro-  The answer depends on the f a c t o r price r a t i o and  on  changes i n the marginal rate of f a c t o r substitution when the l e v e l of output i s raised, as i l l u s t r a t e d i n Figure 9»  The  l i n e s marked IP are iso-product curves f o r d i f f e r e n t l e v e l s of production.  The f a c t o r price relationship i s indicated by  slope of the iso-cost l i n e s denoted as EC,  the  Tangency of the i s o -  cost l i n e and the iso-product curve s p e c i f i e s the least-cost  118 combination of inputs f o r each output.  The expansion l i n e  B  1  drawn through these minimum cost points shows that a r e l a t i v e l y greater proportion of f a c t o r X-^ should be employed as output i s increased, when costs are minimized f o r each p a r t i c u l a r output, This results from the higher rate of substitution of X^ f o r X  2  that i s associated with increased output. Limitations on c a p i t a l f o r the a c q u i s i t i o n of additional resources, among other conditions, prevent most farmers from extending production to the optimum l e v e l .  T y p i c a l l y , they must  attempt to gain the largest possible p r o f i t from a stock of various resources that i s r e s t r i c t e d to rather narrow l i m i t s . Under these conditions, the farmer i s confronted with -the task of (1) a l l o c a t i n g a given quantity of resources between technic a l units producing a single product i n a manner to maximize the physical product and i t s value, and (2) a l l o c a t i n g a given quantity of resources between a l t e r n a t i v e commodities and enterprises i n a manner to maximize the t o t a l value of production. The analysis of Figure 9 indicates that, f o r a farm producing a single product with factors X-^ and X , 2  p r o f i t s can  be maximized by (1) equating the f a c t o r price r a t i o Px /Px^ with 2  the marginal rate of f a c t o r substitution AX-^/AXg at each l e v e l of output, and (2) extending output u n t i l the marginal cost of resources equals the marginal value of product.  When t h i s con-  d i t i o n i s attained, the combination of resources cannot be "'"The expansion l i n e i s a c t u a l l y an i s o c l i n e ; both mark a point on each iso-product curve where the marginal rate of f a c t o r substitution i s the same.  119  E  4  INPUT FIGURE  OF  FACTOR  Xz  9.— Profit maximization and the expansion path.  120 rearranged t o i n c r e a s e net p r o f i t , and t h e m a r g i n a l v a l u e prod u c t i v i t i e s of a l l resources a r e equal.  I f the quantity of r e -  sources n e c e s s a r y t o a c h i e v e t h i s u l t i m a t e p o s i t i o n a r e not a v a i l a b l e and cannot be obtained as t h e r e s u l t o f l i m i t e d  capi-  t a l o r o t h e r c o n d i t i o n s , then output w i l l be r e s t r i c t e d t o some lower l e v e l and t h e f u l l maximization o f p r o f i t w i l l be impossible. At t h e p o i n t s o f tangency  o f t h e i s o - p r o d u c t curves and  t h e i s o - c o s t l i n e s shown i n F i g u r e 9, t h e marginal p h y s i c a l products o f f a c t o r s X^ and X AY/AX  X  2  a r e equal, o r  = AY/4X . 2  Denoting t h e m a r g i n a l p h y s i c a l products as MPx^ and MPx , r e 2  s p e c t i v e l y , t h i s equation can be w r i t t e n as MPX]_ = MPx . 2  S i n c e p r o f i t i s maximized a t each l e v e l of output by employing t h e r e s o u r c e combinations  i n d i c a t e d by t h e p o i n t o f tangency,  t h e marginal p h y s i c a l product of f a c t o r X^ equals t h e f a c t o r / product p r i c e r a t i o , o r MPXQ^  = Px /Py and s i m i l a r l y  MPx  = Px /Py.  MPx ^ MPx  1  2  2  Px,/Py — Px /Py  x = 2  MP*2 MPX]_  2  P =  Then ?x , and Px 1  2  *2  Px]_  I f t h r e e f a c t o r s X-^, X  2  and X^ a r e used t o produce a  s i n g l e product Y, p r o f i t s a r e a t a maximum f o r each l e v e l o f output when  121 MPx]_  Px  MPx  Px '  2  2  MPx-|_ MPx-j MPx  1  Px-,  =  Px^ Px  2  MPX3  , and  2  PX3 *  T h i s c o n d i t i o n o f p r o f i t m a x i m i z a t i o n can a l s o be e x p r e s s e d as MPx-j_  MPx  ixT"  2  MPX3 p^~'  which i n d i c a t e s t h a t , f o r each l e v e l o f o u t p u t , t h e r a t i o o f t h e marginal p h y s i c a l product t o t h e f a c t o r p r i c e i s equal f o r a l l factors. The m a r g i n a l v a l u e p r o d u c t o f a f a c t o r i s o b t a i n e d by m u l t i p l y i n g t h e m a r g i n a l p h y s i c a l product by t h e p r o d u c t p r i c e . F o r example, t h e m a r g i n a l v a l u e p r o d u c t o f Consequently,  i s (Py)(MPx^).  t h e c o n d i t i o n f o r maximum p r o f i t s a t each l e v e l  of output c a n a l s o be s t a t e d as (Py)(MP PX^  X]L  ) _ (Py)(MPx ) _ (Py)(MPx ) _ 2  PX  2  3  PX3  T h i s means t h a t p r o f i t s a r e maximized when t h e r a t i o o f t h e m a r g i n a l v a l u e p r o d u c t t o t h e f a c t o r p r i c e i s t h e same f o r a l l f a c t o r s , and e q u a l s t h e c o n s t a n t "fc". F o r a farm w i t h c a p i t a l , f a c t o r i n p u t s would be i n c r e a s e d  unlimited  i n t h e combinations  i n d i c a t e d b y t h e expansion l i n e u n t i l t h e l e v e l o f output reached t h e p o i n t where t h e m a r g i n a l v a l u e p r o d u c t i v i t y o f each f a c t o r e q u a l s t h e f a c t o r p r i c e , and t h e v a l u e o f "k" i s 1.0. I n o t h e r words, | l i n v e s t e d  i n an a d d i t i o n a l i n p u t  o f any f a c t o r  122 results i n an increase of $1 i n value of the product. However, i f a farm has limited c a p i t a l f o r the acquis i t i o n of resources, output w i l l be r e s t r i c t e d to some lower level.  The conditions f o r maximum p r o f i t are s t i l l denoted by  the above equation, except that the constant "k" has a value greater than 1.0.  The r a t i o of marginal value product to the  f a c t o r price i s the same f o r a l l factors, but i s greater than 1.0.  In t h i s situation, the marginal value productivity of  each resource exceeds the price Consequently,  (marginal cost) of the resource.  more p r o f i t could be gained by expanding output  to a higher l e v e l but, with a l i m i t e d amount .of c a p i t a l , the resources needed f o r t h i s expansion of output cannot be acquired.  Thus, with i n s u f f i c i e n t resources or other conditions  serving to r e s t r i c t the l e v e l of output, the resource combination required f o r maximum p r o f i t s i s attained when the marginal value product/factor price r a t i o i s equal, but greater than 1.0, f o r a l l f a c t o r s .  123  APPENDIX IV AGGREGATION OF TOTAL OUTPUT AND THE INPUT CATEGORIES IN THE PRODUCTION FUNCTION  Total output and the various input categories i n the production functions derived f o r the market egg enterprise were measured and c l a s s i f i e d i n the following manner: X^, t o t a l output measured i n d o l l a r s : egg sales, plus  b i r d sales (fowl, chicken, chicks and breeders),  plus  manure sales,  plus  patronage dividends from co-operatives,  plus  market value of eggs and poultry meat used i n the farm home,  plus  any increase i n f l o c k inventory value at end of the record year as compared with s t a r t of the record year,  minus  any decrease i n f l o c k inventory value at end of the record year as compared with s t a r t of the record year*  X , r e a l estate and equipment input measured i n d o l l a r s : 2  building depreciation (2.5 per cent of estimated replacement cost), plus  interest on investment i n buildings (4.0 per cent of current depreciated value),  124 plus  building repairs,  plus  insurance,  plus  interest on investment i n land (4.0 per cent of current value),  plus  taxes,  plus  equipment depreciation (15.0 per cent of current depreciated value),  plus  interest on investment i n equipment (4.0 per cent of current depreciated value),  plus  equipment repairs,  plus  small t o o l s purchased,  plus  operating costs f o r car, truck and t r a c t o r .  laying f l o c k input measured i n layer years: p u l l e t layer years, plus  hen layer years adjusted t o equivalent of p u l l e t layer years (hen layer years m u l t i p l i e d by the r a t i o of the average value of a hen to the average value of a p u l l e t ; these r a t i o s are 0.647 f o r 1949, 0.588 f o r 1950, and 0.640 f o r 1951, as calculated from the i n i t i a l laying f l o c k inventory)•  labor input measured i n hours: operator labor, plus  family labor,  plus  hired labor.  feed input measured i n d o l l a r s : purchased grain,  125 plus  purchased mash,  minus  refund on feed sacks returned,  plus  feed supplements,  plus  value of farm grown feed.  other cash inputs measured i n d o l l a r s : purchased l i t t e r , Plus  value of farm grown l i t t e r ,  plus  brooder f u e l ,  plus  electricity,  plus  medicine and disinfectant,  plus  shell,  plus  grit,  plus  purchased chicks and other stock,  plus  other cash expenses.  126  APPENDIX V COMPUTATION OF REGRESSION COEFFICIENTS AND TEST OF STATISTICAL SIGNIFICANCE  Solution of the appropriate set of normal equations  1  yields the regression c o e f f i c i e n t s , or value of the b s " f o r n  the production function.  T  The constant "a" i n the production  function i s calculated by substituting the means of the v a r i ables ( i n logarithms) and the b " values i n the following n  equation: a = %  - b ^2 2  " A  " 3% b  ~ 5^5  " 6*6*  b  b  The standard error of estimate  b  i s a measure of the  2  r e l i a b i l i t y of the production function f o r estimating t o t a l output.  I t indicates the accuracy with which estimates of  t o t a l output may be expected to approximate the actual output values contained i n the sample.  The standard error of estimate  adjusted f o r the s i z e of sample (S[) i s obtained by taking the square root of 3 . 2  £(x ) x  ^2  =  The value of 3  i s given by the formula:  2  |b2(£ l 2) + 3 (1^x3) + x  x  b  b^dx^)  -Hb (Ix x ) + b (Ix x )] 5  1  5  6  1  6  n - m •*-For the method of deriving and solving the normal equations, see Mordecai Ezekiel, Methods of Correlation Analysis (2d ed.; New York: John Wiley and Sons, 1950), pp. 198-205  and 459-469. 2  I b i d . , pp. 328-135 and 208-210.  127 where x^, x , etc. are deviations of the variables X^ and X 2  ( i n logarithms)  2  from t h e i r respective means ( i n logarithms);  n equals the number of sets of observations  or records i n  the sample; m equals the number of constants  i n the production function,  including "a" and the "b's". The c o e f f i c i e n t of multiple determination  1  measures the  proportion of t o t a l variance i n output that i s explained by the several input categories. b  r 2  2  ( ^ X ! X  2  )  I t was calculated from the formula: (1x3X3)  +  +  b ^ C E x - ^ ) 4-  b^dx^)  •fb (Ix x ) 6  :  1  6  t  I(x ) 2  Adjusting f o r the s i z e of sample was obtained by c a l c u l a t i n g f  2  as  H - 1 ~ M - R H n - 1) 2  2  n - m  The adjusted c o e f f i c i e n t of multiple c o r r e l a t i o n (R") i s a measure of the degree of c o r r e l a t i o n between output and the c o l l e c t i v e inputs*  I t was calculated by taking the square root  of the adjusted c o e f f i c i e n t of multiple determination,  The standard  or  error of the c o e f f i c i e n t of multiple  c o r r e l a t i o n was computed from the formula *\/n - ra The t - t e s t was used t o test the s t a t i s t i c a l s i g n i f i c a n c e of the multiple c o r r e l a t i o n c o e f f i c i e n t .  The value of " t " was  Ezekiel, op.cit.. pp. 136-143 and 210-213.  128 computed from the expression  By r e f e r r i n g to a table of t-values, i t i s possible to establish the p r o b a b i l i t y that the multiple correlation c o e f f i c i e n t differs from zero due to chance alone."'"  The multiple correlation  coef-  f i c i e n t i s accepted as s i g n i f i c a n t l y greater than zero i f the computed t-value exceeds the t-value stated i n the table f o r an a r b i t r a r i l y selected  l e v e l of p r o b a b i l i t y  (usually 0 . 0 5 ) , with  the degrees of freedom equal to n - (m - 1). The  standard errors of the regression c o e f f i c i e n t s were 2  obtained from the following formulas:  a  b3  Ob  5  =  ff^3j  = 3'^c^  S t a t i s c a l significance of a regression c o e f f i c i e n t was determined by applying the t - t e s t i n the same manner as f o r the multiple c o r r e l a t i o n c o e f f i c i e n t .  The t-value was obtained by  calculating the r a t i o of the regression c o e f f i c i e n t to the unbiased estimate of i t s sampling standard deviation, that i s  By comparing t h i s r a t i o with the values i n a t-table, i t was x  2  E z e k i e l , op. c i t . . pp. 3 2 2 - 3 2 5 .  Ezekiel,  op. c i t . . pp. 469-472.  129 possible to ascertain the p r o b a b i l i t y that the regression coeff i c i e n t d i f f e r e d from zero due to chance. The marginal value productivity of each resource category was estimated with the l e v e l of a l l inputs f i x e d at t h e i r geometric mean.  The marginal value products were derived by  p a r t i a l d i f f e r e n t i a t i o n of the production function with respect to each input variable.  For the Cobb-Douglas function, the  derivative with respect to X  2  (the marginal value product of  input X ) i s given by the equation 2  where b  2  dX  x  dX  2  _  bX 2  X  1  2  i s the regression c o e f f i c i e n t of input X ; 2  X.-± i s the geometric mean of t o t a l output X^; X  2  i s the geometric mean -of input X . 2  The geometric mean of a variable was computed as the a n t i l o g of the arithmetic mean of the values of that variable expressed i n logarithms.  For example,  geometric mean of X^ ( t o t a l output) = a n t i l o g ^  l o  g n  where ZlogX^ i s the sum of the logarithmic values of X^; n i s the number of records { il-^ values) i n the sample.  x  l  t  130  BIBLIOGRAPHY  Beringer, Christoph. "Estimating Enterprise Production Functions from Input-Output Data on Multiple Enterprise Farms", Journal of Farm Economics. XXXVIII (November,  1956),'pp. $23-930.  Black, John D., et a l . Macmillan Co.,  Farm Management. 1949.  New York: The  Bronfenbrenner, M., and Douglas, Paul H. "Cross-Sectional Studies i n the Cobb-Douglas Function", The Journal of P o l i t i c a l Economy. XLVII (December, 1939J, pp. 761-785. Clarke, J . W., "The Production Function i n Farm Management Research", Canadian Journal of A g r i c u l t u r a l Economics. II (1954), pp. 36-41 Cobb, Charles W., and Douglas, Baul H. "A Theory of Production", The American Economic Review. XVTII (March, 1928), pp. 139-165. : Croxton, Frederick E., and Cowden, Dudley J . Applied General S t a t i s t i c s . New York: Prentice-Hall Inc., 1946. Douglas, Paul H. The Theory of Wages. Co., 1934.  New York: The Macmillan  Ezekiel, Mordecai. Methods of Correlation Analysis. John Wiley and Sons, 1950.  New York:  :  Forster, G. W. Farm Organization and Management. Prentice-Hall, Inc., 1946.  New York:  Gunn, Grace T., and Douglas, Paul H. "The Production Function f o r American Manufacturing i n 1914", The Journal of P o l i t i c a l Economy. L (August, 1942), pp. 595-602. Hansaker, Marjorie L., and Douglas, Paul H. "The Theory of Marginal Productivity Tested by Data f o r Manufacturing i n V i c t o r i a " , The Quarterly Journal of Economics. LII  (1937-38), pp. 1-36 and 215-254.  Heady, E a r l 0. "Production Functions from a Random Sample of Farms", Journal of Farm Economics. XXVIII (November, 1946), pp. 989-1004.  131 Heady, E a r l 0. "A Production Function and Marginal Rates of Substitution i n the U t i l i z a t i o n of Feed Resources by Dairy Cows", Journal of Farm Economics. XXXIII (November, 1951), pp. 485-498. Heady, E a r l 0. Economics of A g r i c u l t u r a l Production and Resource Use. New York: Prentice-Hall, Inc., 1952. Heady, E a r l 0. "Use and Estimation of Input-Output Relationships or Productivity C o e f f i c i e n t s " , Journal of Farm Economics. XXXIV (December, 1952), pp. W-736. Heady, E a r l 0., and Shaw, Russell. "Resource Returns and Productivity C o e f f i c i e n t s i n Selected Farming Areas", Journal of Farm Economics. XXXVI (May, 1954), pp. 243-257.  Heady, E a r l 0., et a l . "An Experiment to Derive Productivity and Substitution Coefficients i n Pork Output", Journal of Farm Economics. XXXV (August, 1953), pp. 341-354. Hopkins, John A., and Heady, E a r l 0. Farm Records and Accounting. Ames: Iowa State College Press, 1955. Nicholls, W. H. < Labor Productivity Functions i n Meat Packing. Chicago: University of Chicago Press, 1948. Plaxico, James S. "Problems of Factor-Product Aggregation i n Cobb-Douglas Value Productivity Analysis", Journal_of Farm Economics. XXXVII (November, 1955), pp. 6 6 4 - 6 7 5 . Shaw, H, R., and Wright, P. A. "Alternative Methods of Farm Management Analysis", Canadian Journal of A g r i c u l t u r a l Economics. I l l (1955;, pp. 67-80. Swanson, E a r l R. "Resource Adjustments on 146 Commercial Corn-belt Farms", Journal of Farm Economics. XXXIX (May, 1957), pp. 502-505. Tintner, Gerhard, and Brownlee, 0. H. "Production Functions Derived from Farm Records". Journal of Farm Economics. XXVI (August, 1944), pp. 566^71".  

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