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

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A MEASUREMENT OF THE EFFECT OF TECHNICAL CHANGE ON THE PRODUCTIVITY OF THE CANADIAN AGRICULTURAL SECTOR: 1926-58 by HORACE RAYMOND CARBI-SAMUELS B.S.A., U n i v e r s i t y of Toronto, I960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AGRICULTURE i n the Department of AGRICULTURAL ECONOMICS We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia, Vancouver 8, Canada. Date ABSTRACT This study is designed to measure the amount, and character of the change in the economic performance of the agricultural sector of the Canadian economy, over the period 1926 to 1958. The major hypothesis which i t examines is that changes in technology have had a positive effect on the productivity of factors used in the agricultural sector of the Canadian economy. Technological change is defined herein as any change which produces a shift in the production function of the industry, and the concept of the relative shares going to each factor of production has been used to determine the shape of the aggregate production function. In the agricultural industry natural phenomenon such as weather, which are outside the control of management, are capable of causing significant variations in annual output. These fluctuations in output make i t difficult to determine the permanent effects of technological change on input-output ratios. However, the analysis assumes that farmers take into account the possible effects of weather in their decision-making processes, and also assumes that the effects of variations from this source will be randomly distributed over the 33 year period of the study. The production functions were determined by f i r s t assuming that Euler 1s Theorem holds for the agricultural industry. The relative shares of each factor in total inputs were then used as the estimates of the relative share of each factor in total output. By this method the shape of the aggregate production function was determined with a minimum of distortions which may be due to the effects of exogeneous variables. The determining of the aggregate production functions i n the manner used i s f e a s i b l e because of the high degree of competition i n the a g r i c u l t u r a l industry,which contributes to a much lower l e v e l of product or process d i f f e r e n t i a t i o n than that which e x i s t s i n other i n d u s t r i e s . The problems of aggregation of products are therefore i n t h i s case minimized. The l e v e l of aggregate output was determined by expressing as an index the value seri e s which was obtained by d e f l a t i n g the t o t a l value of each type of product by an appropriate p r i c e index which had a 1935-39 base. The annual def l a t e d values were aggregated; and t h i s output s e r i e s was then expressed i n terms of i t s value as at 1926 being made equal to 100. These i n d i c e s of de f l a t e d d o l l a r values were used i n the production f u n c t i o n as estimates of the ph y s i c a l quantity of the output f o r that p a r t i c u l a r year. A s i m i l a r process wa.s used to determine the quantity of each p a r t i c u l a r f a c t o r input which was included i n the production function. The quantity of aggregate inputs, however, was determined by a geometric aggregation of the i n d i c e s of the f a c t o r inputs. In t h i s aggregate the quantity of each f a c t o r was weighted by i t s r e l a t i v e share i n the aggregate input (hence output under the assumptions of the a n a l y s i s ) . This method of geometric aggregation of inputs gives due recognition of the f a c t that changing marginal rates of s u b s t i t u t i o n of f a c t o r inputs are possible i n the a g r i c u l t u r a l industry, and that at d i f f e r e n t l e v e l s of output farmers may e f f e c t a change i n the marginal rates of s u b s t i t u t i o n of fa c t o r s without n e c e s s a r i l y producing a s h i f t of the production f u n c t i o n on which they are operating. i v . The data f o r the analysis were obtained from D.B.S. material, and the changes i n the output-input r a t i o s were examined i n a model of comparative s t a t i c s . Hhen t h i s was done, i t was found that when c a p i t a l was measured i n c l u s i v e of r e a l estate and other improvements the net change i n o v e r - a l l p r o d u c t i v i t y f o r the en t i r e period (1926-58), was not s u b s t a n t i a l l y d i f f e r e n t from that which was cal c u l a t e d when c a p i t a l was measured net of the value of these f a c t o r s . Between 1926 and 1958, the net change i n o v e r - a l l p r o d u c t i v i t y was 33 per cent when c a p i t a l was measured i n c l u s i v e of r e a l estate, and 31 per cent when the value of r e a l estate was removed. Approximately 90 per cent of t h i s observed increase had been recorded between the years 1946 and 1958. Over the period 1950 to 1956 the difference i n the calculated measure of over-a l l p r o d u c t i v i t y from each method showed, however, d i f f e r e n c e s of between 3 and 6 percentage points when compared to the more frequently found difference of 2 percentage points i n favour of p r o d u c t i v i t y when i t was derived from data which included the value of r e a l estate. Technological change between 1926 and 1958 has been associated with an estimated decline of 28 per cent i n the quantity of labour i n use, a 15 per cent increase i n the quantity of t o t a l c a p i t a l as compared with a 4-3 per cent increase i n t he quantity of non r e a l estate c a p i t a l , and a 115 per cent increase i n the quantity of annual non-labour expenses. These expenses are c h i e f l y associated with the use of farm machinery and to a l e s s e r extent with that of f e r t i l i z e r . Feed and seed were omitted from the cal c u l a t i o n s i n order to avoid the problems of double counting. V . The results of the analysis substantiate the main hypothesis of this study, in that technological change has a positive effect on the productivity of factors used in the agricultural sector of the Canadian economy. ACKNOWLEDGEMENT The writer takes this opportunity of acknowledging the assistance in the preparation and presentation of this thesis, which was given by Professor W.J. Anderson of the Department of Agricultural Economics at the University of British Columbia} and also the advice, and assistance, which was given by Professors A.D. Scott, and J.J. RLchter, of the Department of Economics and Political Science, and the Department of Agricultural Economics, respectively. LIST OF TABLES TABLE PAGE I Factor Shares, Canadian Agriculture, 1926-58 34-II Indices; Output and Grouped Inputs, Canadian Agric u l t u r e , 1926-58; 1926 = 100 37 I I I Percentage Annual Current Non-Labour Costs from Various Sources, Selected Years, Canada, 1926-56 . 38 IV Indices; Output, Composite Input, Composite and P a r t i c u l a r Output-Input Ratios, Canadian Ag r i c u l t u r e , 1926-58; 1926 = 100 42 V Factor Shares, Net of Land, Canadian Primary A g r i c u l t u r a l Sector, 1926-58 4-7 VI Indices; Output, Composite Input, Composite and P a r t i c u l a r Output-Input Ratios, Net of Land, Canadian Agriculture, 1926-58; 1926 = 100 . . . . 4-9 VII Relatives; Marginal Physical, and Value Product of Factor Inputs, Canadian A g r i c u l t u r e , 1926-58; 1926 = 100 . . . 53 VIII Indices; Output-Input Ratios, Additional Selected Methods, Canadian Agriculture, 1926-58; 1926 = 100 76 IX Summary Indices; Gross Output-Input Relationships; Various Selected Methods; Canadian Agriculture, 1926-58; 1926 = 100 77 X Relative Changes, M.P.P. Factor Inputs, Canadian Ag r i c u l t u r e , 1926-58; 1926 = 100 78 TABLE OF CONTENTS CHAPTER PAGE I OBJECTIVES OF THE STUDY 1 The Concept of Technology 2 II REVIEW OF LITERATURE 6 The Joan Robinson Model 10 The Solow Model H Points to Note in the Solow Model 17 The Urquhart Model 18 The Pasinetti Model 20 Studies Done on the Canadian Economy . . . . . 22 III THE ANALYTICAL FRAMEWORK OF THE STUDY 26 Inputs 29 Output 30 The Production Function . . . . . 31 IV RESULTS OF THE STUDY 32 Measuring Technological Change Inclusive of Land Capital 32 Output-Input Relationships Inclusive of Land . 39 Measuring Technological Change When Land is Excluded 1<A Output-Input Relationships Net of Land . . . . 46 An Evaluation of the Two Methods 50 Summary 54 BIBLIOGRAPHY . 56 APPENDIX 61 I OBJECTIVES OF THE S T U D Y This study is aimed at measuring the effects of technological change on the output-input relationships of the primary agricultural sector over the 33-year period of 1926 to 1953. It seeks to measure the extent of the changes which have been due to advances in the ability of the Canadian farm sector to convert input into output by analyzing the changes which have occurred in factor-factor and factor-product relationships. An estimate of the amount of change which has been due to technology facilitates a better evaluation of the use that the agricultural industry has made of that portion of society's resources which have been associated with its productive activities. In making policy decisions affecting the future allocation of resources, a knowledge of the past performance of the agricultural industry furnishes a better guide for future decision-making. The hypothesis is that technological change has had a positive effect on the productivity of the factors used in primary agriculture. Various theoretical models for measuring technological change may be found in economic literature. Many of these models are designed to meet particular objectives such as to make measurements for the whole economy or for a particular firm. The data used in this study, and the objectives, required the modification of the available models, which are analyzed later in this study. Although change is a dynamic process in dealing with which dynamic theory is needed, the results of change may be viewed, however, in term3 of static analysis. Samuelson has also pointed out that "... in order for the comparative statics analysis to yield fruitful 2. r e s u l t s we must f i r s t develop a theory of dynamics".^ In t L i s study a model of comparative s t a t i c s i s used with the assumption that the primary a g r i c u l t u r a l sector adjusts each year i n the l i g h t of past experience and future expectations. The input-output data f o r the a g r i c u l t u r a l sector are also c o l l e c t e d and compiled on an annual b a s i s . 5br these reasons technological change w i l l be measured from one year to the next. The Concept of Technology In t h i s study technological change has been defined as any change which makes the adoption of a new production f u n c t i o n economically f e a s i b l e . This means (a) the establishment of an equilibrium p o s i t i o n at a point on a transformation curve not economically f e a s i b l e under previously e x i s t i n g conditions, or (b) a change i n the p o s i t i o n or the shape of the transformation f u n c t i o n . These s h i f t s of the production f u n c t i o n or of the transformation f u n c t i o n are distin g u i s h e d from changes i n f a c t o r combinations which are associated with diminishing marginal p r o d u c t i v i t y as output i s increased. These changes are e f f e c t e d as a r e s u l t of producer decisions to substitute those inputs which have a l a r g e r marginal product at a given cost f o r those which have a smaller marginal product-cost r a t i o . They may also be induced as the r e s u l t of ph y s i c a l s c a r c i t i e s of c e r t a i n f a c t o r s . The new equ i l i b r i u m p o s i t i o n may also produce a p h y s i c a l saving of f a c t o r s . S h i f t s i n the transformation f u n c t i o n as w e l l as changes i n i t s shape cause changes i n the marginal rates of s u b s t i t u t i o n of ^ P.A. Samuelson, Foundations of Economic Analysis, (Cambridge: Harvard U n i v e r s i t y Press, 1955), pp. 262-63. 3. factors. These shifts also cause changes in the shape and position of the cost functions. Some of these cost effects are due to changes in the relative scarcity of factor inputs, while other effects may be due to changes in scale. One such scale effect for example, is a shift in the transformation function which encourages the development of large-scale production, and this may enable these enlarged farm-firms to purchase more efficient machinery from the non-farm sector. At the same time a change in the relative scarcity of factors also results from the reduced demand for certain factors as the number of firms are reduced. The adoption of new production methods may also increase the demand for the products of the farm machinery industry without necessarily encouraging large-scale farming. Having more efficient machinery available tends to free labour time which may be utilized in complementary enterprises, or in shorter hours of work, or which may be transferred to non-farm enterprises. These changes in technology may be induced by innovations which have been developed directly within the sector, as well as by those improvements in the factors of production such as machines, which are purchased from other sectors. Because of the small size of firms, the research for primary agriculture i s paid for out of public funds. This basis for research eliminates patents and other practices which restrict the use of the results of research to certain firms. Thus the results of research tend to be quickly adopted by the entire farm sector through the process of competition. Heady discusses technological innovations in the following terms: In a purely physical and firm sense i t is possible for an innovation to be either factor-saving, factor-using, or output-increasing. The change may also combine factor-using or factor-saving features with output-increasing features . . . . While the notion of innovations which are s i n g u l a r l y f a c t o r - u s i n g may seem a b i t f a r fetched, there i s no reason why t h i s should be so . . . . D i s t i n c t i o n between technological improvements which are output-increasing and those which are factor-saving may apply to an i n d i v i d u a l i n d u s t r y or f i r m but do not e x i s t s i m i l a r l y on an economy-wide basis. The basic nature of technological improvement i s always the same i n the economy as a whole. Aside from the uncertainty exception noted elsewhere, a l l technological improvements are output-inc r e a s i n g f o r given resources, or conversely, input-decreasing f o r a given output. An innovation i s always output-increasing i n the aggregate since although i t may r e s u l t i n the same output from a smaller resource input by a given f i r m or industry, i t f r e e s resources f o r output expansion i n other i n d u s t r i e s . In t h i s sense a l l innovations are l i k e l y to extend economic progress regardless of the industry to which they apply. The greatest portion of t e c h n i c a l innovations i n a g r i c u l t u r e have been of an output-increasing nature to the extent that they have lowered the average per u n i t cost of producing farm products and of a f a c t o r using nature i n the sense that the lovrer marginal costs have caused farm firms to employ more resources (and also to increase output f o r the l a t t e r reason). Changes i n technology w i l l not only s h i f t iso-product curves toward the o r i g i n but w i l l p o s s i b l y also change t h e i r shape. A neutral s h i f t w i l l s h i f t a l l isoquants i n the same proportion, while a non-n e u t r a l s h i f t w i l l change both the p o s i t i o n and the shape of the isoquants. The concept of technological change which w i l l be used i n •a t h i s analysis i s e s s e n t i a l l y Schumpeterian. J In the Schumpeterian system an innovation i n contrast to a f a c t o r adjustment i s regarded S.O. Heady, The Economics of A g r i c u l t u r a l Production and Resource Use. (Inglewood C l i f f s , New Jersey: Prentice H a l l , 1952) pp. 803-04. 3 For a d i s c u s s i o n of the Schumpeterian System see Richard V. Clemmence, and Francis S. Doody, The Schumpeterian System. (Cambridge 42, Mass: Addison Wesley Press Inc., 1950;. 5. as the "setting up of a new production process", i.e. t one based on technical coefficients that did not exist previously. Clemmence and Doody point out that innovation is thus an internal factor from the point of view of the Schumpeterian System} and that innovation with its effects, and with the response of the economy of these effects, i s responsible for the process of economic evolution.^-5 The outlook adopted by Schultz was essentially Schumpeterian, because he associated economic progress with the opening up of new production pos s i b i l i t i e s.^ Schumpeter did not mention the special case in which the setting up of a new production process does not change the shape of the production function. Hicks called this one a "neutral 7 technological change". This study recognizes that either neutral or non-neutral technological changes can occur. Since change i s taking place over time i t cannot be judged a priori what is the nature and the extent of the change. The study, therefore, examines the data and formulates a model based on economic theory and on the structure of the agricultural industry. The purpose is to measure the changes in factor-product conversion ratios that have occurred. I b i d * t P» 36 ^ T.W. Schultz, The Economic Organization of Agriculture (New York: McGraw-Hill Book Company, Inc., 1953). 6 Ibid., pp. 99-124 7 J.R. Hicks, Theory of Wages, (London: MacMillan and Co., Limited, 1932), pp. 121-22. II REVIBf OF LITERATURE In a recently published paper Lok mentions two approaches to measuring changes in productivity,(l) the production function method, and (2) the constant dollar method. Domar has presented a more 2 comprehensive classification. He points out that in measuring technological change the practise has been to impute to i t that portion of productivity which cannot be imputed to changes in the quantity of factor inputs. The factors contributing to the change, he goes on, are technological progress in the narrow sense, economies of scale, external economies, improved health, education and s k i l l of the labour force, better management, changes in the product mix, and other non-specific factors. He calls the parameter derived from this method of measurement, which involves taking the differences between actual production and that which i s mathematically determined from a fixed production function a "Residual". The Residual has been calculated in different ways. Domar mentions the f i r s t four-* of the following: (l) It is the difference between the values of outputs and of inputs calculated at constant prices by Hiram S. Davis.^ (2) It i s the ratio between arithmetic Siepko H. Lok, An Enquiry into the Relationships Between Changes in  Over-All Productivity and Real Net Return Fer Farm and Between Changes  in Total Output and Real Gross Return. Canadian Agriculture 1926-57. (Ottawa: " Technical Publication, Canada Department of Agriculture, Oct., 1961), pp. 14-21. S.D. Domar, "On the measurement of technological changes," The  Economic Journal, Volume LXXI (December 1961), pp. 709-29. 3 I b i d«» P« 7 1 ° -^ Hiram S. Davis, Productivity Accounting (Philadelphia: University of Pennsylvania Press, 1955)• i n d i c e s of output and input i n the works of Schmookler, 5 Abramovitz , and Kendrick ; and t h i s Domar c a l l s the S.A.K. method. (3) I t has also been c a l c u l a t e d as a r a t i o between an aggregate arithmetic index of output and inputs embodied i n a l i n e a r and homogeneous production fu n c t i o n . This method was used by Solow.^ (4) The r e l a t i v e percentage rate of growth of the weighted arithmetic average of input c o e f f i c i e n t s between two points i n time as derived by Leontief from h i s input-output studies has also been used as a measure of the rate of growth of the Residual. ^  Domar c a l l s a t t e n t i o n to the f a c t that i n a large slowly grovring economy these methods are l i k e l y to y i e l d s i m i l a r r e s u l t s ; but that i n r a p i d l y growing sectors and i n d u s t r i e s , and i n problems i n v o l v i n g i n t e g r a t i o n and aggregation of i n d u s t r i e s , both the differences i n the r e s u l t s from, and the arguments about each method, may become more s i g n i f i c a n t . This i s because the d i s t o r t i o n s presented by the small amount of s h i f t i n the transformation f u n c t i o n Jacob Schmookler, "The Changing E f f i c i e n c y of the American Economy: 1869-1938," The Review of Economics and S t a t i s t i c s , Volume XXXIV, (August, 1952), pp. 214.-31. Moses Abramovitz,, "Resource and Output Trends i n the United States Since 1870," The American Economic Review, Papers and Proceedings, Volume XLVT, (May 1956), pp. 5-23, r e p r i n t e d as a National Bureau of Economic Research, Occasional Paper 52, (New York, 1956). John W. Kendrick, " P r o d u c t i v i t y Trends: Ca p i t a l and Labour," The  Review of Economics and S t a t i s t i c s , Volume XXXVII, (August 1956), pp. 248-57, r e p r i n t e d as a National Bureau of Economic Research, Occasional Paper 53, (New York: 1956). g Robert M. Solow, ""Technical Change and the Aggregate Production Function, 1 1 The Review of Economics and S t a t i s t i c s , Volume XXXIX, (August 1957), pp. 312-20. Wassily Leontief et. a l . . Studies i n the Structure of the American  Economy, (New York: Oxford U n i v e r s i t y Press, 1952), pp. 27-35. 8. in the slowly growing economy are not large enough to significantly change the results from each method. (5) In agricultural economics research the residual has been calculated by the use of the production function. The relative changes between the output derived from the function and actual output, have been regarded as measurements of the change in productive capacity.-1-0 This approach is an off-shoot of the Solow method. (6) The constant dollar method which Lok describes as having been used also in agricultural economics research is a modification of the method which Domar ascribes to Davis. Quantity indices constructed from deflated value series of inputs and outputs are compared by expressing them as a ratio of each other. Those measurements which express as a ratio input factors to gross output in a growing economy, however, may not measure technological change because factor-factor ratios may change under conditions of constant technology. The result is that single-input-output ratios are mis-leading as measures of changes in technology. Salter points out that the only significance that can be given to these output-single-input-ratios i s that " . . . they are indications of what may be termed 'growth in depth1 as distinct from 'extensive growth'- growth which merely reproduces a given situation. They are measures which crystallize out changes in content as distinct from changes in amount. But because changes in depth are as highly inter-related as other forms of economic change, individual productivity measures, such as labour productivity, have l i t t l e direct significance unless we can relate them to the The production function may be linear or non-linear. The Solow method applies to non-linear production functions. For an application of the production function method in agricultural economics research C f . Vernon W. Ruttan, "The Contribution of Technological Progress to Farm Output: 1950-75,n The Review of Economics and Statistics. Volume XXXVIII, (1956), pp. 61-69. 9. complex process of change of which they are a product . * . . We cannot divorce changes i n the p r o d u c t i v i t y of one f a c t o r from the p r o d u c t i v i t y of other f a c t o r s , or indeed from a l l the elements i n an i n t e r - r e l a t e d economic system. "-^ The objective of t h i s study i s to measure i n quantitative terms the e f f e c t s of change which have been due to technology. Thus a review of some o f the models which have been used f o r measuring changes i n technology i s appropriate. S i g n i f i c a n t contributions to t h i s subject have been made by Joan Robinson,^ Champerowne,-^ P a s i n e t t i , ^ Urquhart,^-' and Solow. Some studies which r e l a t e to the Canadian economy w i l l also be examined. W.E.G. S a l t e r , P r o d u c t i v i t y and Technical Change, (London: Cambridge U n i v e r s i t y Press, I960), p. 3. 12 Joan Robinson, "The Production Function and the Theory of C a p i t a l , " The Review of Economic Studies," Volume XXI, (1953-54-), pp. 81-103. c f . also Volume XXIII (1955-56) p. 24-7. 13 D.G. Champerowne, "The Production Function and the Theory of C a p i t a l : A Comment," The Review o f Economic Studies. Volume XXI, (1953-54.), pp. 112-35. In conjunction with R.F. Khan he also wrote a mathematical addendum to Mrs. Robinson's a r t i c l e op. c i t . , pp. 107-11. L u i g i L. P a s i n e t t i , "On Concepts and Measures of Changes i n Pro d u c t i v i t y , " The Review of Economics and S t a t i s t i c s . Volume XLI, (August, 1959), pp. 270-82. See also h i s "Reply" i n the same pu b l i c a t i o n , pp. 285-86. 15 M.C. Urquhart, " C a p i t a l Accumulation, Technical Change and Economic Growth," The Canadian Journal of Economics and P o l i t i c a l Science, Volume 25, Number 4-, (November 1959), pp. 411-30. Solow, op. c i t . See also R.M. Solow "The Production Function and the Theory of C a p i t a l , " The Review of Economic Studies. Volume XXIII, (1955-56), pp. 101-08: also, "On Concepts and Measures of Changes i n P r o d u c t i v i t y : Comment," The Review of Economics and S t a t i s t i c s , Volume XLI, (August, 1959), pp. 282-85: also, "Reply" The Review of Economics and S t a t i s t i c s , Volume XL, (November, 1958), pp. 411-13. 10. Since Charaperowne's papers were closely associated with Joan Robinson's model, the contributions of both authors will be discussed together. The Joan Robinson Model In Joan Robinson's model, the various levels of technology were derived from capital measured in wage units, i.e., real capital, expressed as a ratio to man hours. In such a model the larger the number of man hours which i s used in conjunction with a given capital measured in wage units, the lower i s the level of technology. If the economy to which her method of measurement i s applied is in equilibrium, the value of capital goods is the present value of the future earnings of the capital discounted as the prevailing rate of interest. Since her model is macro-economic, i t might appear that i t is necessary that the labour which is spent on consumption goods and services should be isolated from that which is spent on the making of producer goods. However, since she was considering an economy in equilibrium, and since equilibrium requires that the stock of capital equipment be maintained, the age composition of the stock in equilibrium is such that the amortization funds provided by the stock as a whole are continuously being spent on replacement. Under these conditions with the stock of capital goods in balance there i s no need to examine whether the particular worker i s engaged in the production of capital goods, or of consumer goods, since the whole economy i s geared to producing a stream of final output for both the present and for the future. 11, There are several weaknesses involved in the Joan Robinson model which Ohamperowne and Solow have pointed out. These weaknesses are associated with (a) the problems which arise when attempts are made to compare two stationary states which have different rates of time preference, and (b) from the presence of factors which have rates of increase that are not necessarily associated with the level of economic activity in the "stationary state 0. The rate of population increase is an example of one such factor. Because of these problems i f comparisons are made between two stationary states, the following erroneous results are likely to appear, (a) Identical quantities of physical capital goods and labour producing each the same quantity of output will appear as different real capital to labour ratios i f there are differences in the rates of interest existing between both states. Each of the stationary states will thus appear to be operating at a different level of technology even though they differ only in time preference. Conversely, i t is possible to find two stationary states with the same quantity of labour but with different techniques. Differing rates of interest will be capable of causing each such stationary state to appear as being operated at the same level of technology, (b) If the level of technology is regarded as being a determinant of the shape of the production function, two states though operating on the same production function will appear under Joan Robinson's criterion as having two different levels of technology. The nature of the production function as well as time preference determines the equilibrium level of interest, therefore, to say that interest in the Joan Robinson model is an 12 additional variable would not solve the problem, (c) $hen one measures the ratio of capital measured in wage units to labour hours in the same stationary state at different points in time, one is actually comparing the relative rates of accumulation of capital and population. Furthermore, i f food supply in the stationary state is not a limiting resource and wages are not at a subsistence level, the increase in population may be greater than the increase in capital accumulation. The stationary equilibrium is thus shifted: but this shift need not affect the customary pattern of conversion of non-labour resources into output. It is for these reasons that Joan Robinson's model will have to 17 be regarded as being applicable only to a completely stationary state, (d) In Joan Robinson's model,assuming that no change in the total quantity of labour hours has occurred, and assuming no change in the rates of interest, her higher level of technology is one which i s more capital intensive than others. If under conditions of constant rates of interest and fixed supply of labour an innovation occurs which has the effect of shifting some of the labour force from the commodity industries into the service industries in which case less labour is needed for production and maintenance of the existing physical capital stock or for a given level of physical output, this shift in the resources is not registered in the model used. This condition arises because the Joan Robinson model cannot register such structural changes which have been effected in the economy. It does not recognize the criterion that 17 The writer once saw this comment in a paper by Solow but has been unsuccessful in relocating the source. This stationary state must be one which i s completely so over time. Autonomous factors would have to be absent. 13. more leisure time as a legitimate output for the economy as a whole. The demand for new services present also problems of measurement in any Indexed series, and thus also exist in Joan Robinson's model. The above weaknesses, therefore, force one to eschew a model which gives labour an especial place in a general equilibrium system where substitution of factor inputs is possible. The basic difficulties presented by the Joan Robinson model involve problems associated with attempts at measuring the quantity of capital, and also problems of indexing. An alternative approach which seems to avoid some of the above problems is suggested by Ohamperowne. A natural method by which to construct an index of quantity of capital in a historical sequence would be to form a chain index, increasing the index at each step by the proportion in which the cost of the capital at current wage and interest rates at the end of the step exceeded the cost of capital at the beginning of the step calculated at the same wage and interest rates. By shortening the steps, the distortion due to choosing wage and interest rates at the end of each step could be made as small as we pleased. The same method can be used to construct an index of quantity of capital in a sequence of stationary states, and provided these are arranged in order so that the difference between the one and the next is always a small step the distortion due to the method can again be reduced to negligible proportions. The method has the advantage that changes of cost merely due to changes in the interest rate do not affect this measure of the quantity of capital.18 Champerovme's suggested method is consistent with measurement attempting to quantify change through a system of comparative statics. Ohamperowne, "Comment," p. 115» u. Solow, however, pointed out that as Champerowne was aware the use of his chain index does not dispel a l l the d i f f i c u l t i e s . The problem of measuring capital Solow asserts, other than i n the circumstance where capital i s regarded as abstract purchasing power uncommitted to a specific form, (hence i n value units) comes not from physical diversity of capital goods but pomes from the inter-twining of the past, the present, and the future. The measurement problem i s such a d i f f i c u l t one to handle that although a theory of capital built on the assemption of perfect foresight seems unreasonable, present theory provides no equally precise and definite assumption to take i t s p l a c e . ^ The Solow Model The Solow model may be regarded as one of the chief examples of the production function method.^ Hogan,^1 and Bomar^ have dis-cussed the premises of this model. The stati s t i c s i n his model comprise, Q = Index of the quantity of output. K = A measure of the index of quantity of capital goods. L = Index of labour input i n physical units, t = Time. Solow postulated that the production function was of the following form. Q = F(K, L ; t) (1) 19 Solow "The Production Function, n etc. The Review of Economic-Studies. Volume XXIII, (1955-56), pp. 101-02. on Solow, "Technical Change" etc. ^ Warren P. Hogan, "Technical Progress and Production Functions," The' Review of Economics and Statistics, Volume XL (1958), pp. 4-07-11. See also Solow" s reply to Hogan, pp. 411-13. 22 Domar, Loc. c i t . 15. In his model with neutral changes in technology the Marginal Rates of Substitution (M.R.S.) remain unchanged. In this case the production function takes on the special form; Q = A (t) £ (K,L) (2) A (t) is a multiplicative factor which measures the cumulative effects of shifts of the production function over time. Solow was seeking to measure the rate of change of technology and not the amount of change which has occurred. An examination of a section of the development of his technique of measurement i s never-theless fruitful. To get the rate change of Q over time, i t *ras necessary to express additional output as a ratio of the amount in the base period. Each preceding year was used as a base for that succeeding. Q, there-fore, was differentiated with respect to time and the result divided through by Q. • ^ = A (^I dK + £ £ dL ) + f ( dA ) . . dt (dK dt gt dt ) ( dt ) Solow let the derivitives of each factor with respect to time be Q, . . . A, K, L, respectively. = cL£ £ + ^£ I» + f A , v £>K f bL f Yk Ub) = ^ f K A + ^ f L _ A + f i [ i c\ f A £>L £ A f ~ A ^ ' 16 = 4 £ K A + a_f L + A ( / D ) = ^ Q K + ^ Q L + A /.v i s Q 51 I A U E ; = K K + ^ L L + A . 3 K Q K «> L Q L A K 4 1 J = ^ J K K + ^ Q L L + A o_\ dK E § S>L L Q A ^ In the above system of equations i t can be noted that K, Q, L, are identifiable factors. The gross rate of change of output is seemed to be made up of the weighted sum of the rates of change in the input factors (equation 4g). That due to technology i s made explicit and identifiable. That portion of the gross change which cannot be allocated to identifiable changes in the other measurable inputs is thus allocated to technology. In order to further isolate the identifiable changes Solow defines the following quantities: W K = K (5) = L (6) L I These quantities are the relative shares of each factor which are also equal to the elasticities of production for each factor input (marginal product divided by average product). In terms of input-output analysis using a linear and homogeneous production function the relative share i s the ratio marginal product to the average product. 17. The' values of equations 5 and 6 were substituted i n t o equation 4g* t h i s produced the fol l o w i n g equation: g - V K + W L + A / 7 N q KK L L A K ' The change i n output i s therefore observed to be the weighted sum of the rates of change of the components. W i s regarded as being equal L to (1 - ^g). In terms of a production f u n c t i o n Solow 1s model therefore consists of a production function which i s l i n e a r and homogeneous of degree unity. Rearrangement of equation 7 produces the f o l l o w i n g equation which expresses the rate of change i n technology. A - g - W K - W_ L A ® K L L Points to Note i n the Solow Model . A I t must be observed that A (which i s a measure of the rate of change i n technology) i s a r e s i d u a l and not a dynamic prime mover. I t absorbs l i k e a sponge, Domar says, a l l increases i n output not accounted f o r by the growth of e x p l i c i t l y recognized inputs. He goes on to point out that A i s thus not an input i n t o technological progress; so the A model does not measure the nature and the magnitude of inputs which . would r e s u l t i n a given increment of A . The magnitude of the A technological change i s thus divorced from c a p i t a l accumulation. Ca p i t a l accumulates but does not serve as an instrument f o r the i n t r o d u c t i o n of technological change i n t o the productive process. These c r i t i c i s m s of Solow's model which Domar has advanced appear to be strong. A, however, i s derived from equation 2, which i s 18, a special form of equation 1. That being the case, with technology assumed neutral, any changes in the level of technology are assumed to leave shares constant as well as to leave marginal rates of substitution unchanged. This i s because of the way Solow defines a neutral technological change. The model does not preclude changes in technology which may be due to changes in the quality or the quantity of capital goods as capital accumulation proceeds. It must also be bourne in mind that the isolation of capital formation from technological progress i s empirically impossible. It should also be noted that the deflation methods tend also to understate the case for capital formation, in that changes in the quality of capital are not measured in the indexed time series data. The rate of change of capital formation ( § ) and also of labour in use ( h ) are K L therefore understated. The result is that the residual is overstated. If the measured amount of technological change is not to be over-estimated any attempts to use a model based on the production function approach must find a means whereby errors due to this indexing problem are minimized. 23 The Urquhart Model This model uses a linear and homogeneous production function . 7 3 .18 . 0 9 of the form Q = L C T where L, C, and T, are indices of labour capital and land respectively. Technological change i s a residual calculated in a manner different from that of Solow. Urquhart's definition of a neutral change in technology was also different. Since 23 Urquhart, op. cit. 19. his neutral change was one in which the shape of the production function was left unchanged he did not preclude changes in the Marginal Rates of Substitution of factors, given that the original factor relationships were non-linear. Over-all productivity was obtained by solving the production function for each year given the levels of each category of input, and the composite index derived from solving the production function was divided into the index of observed output. The effects of technology on the productivity of individual categories of inputs were obtained in the following manner. Urquhart kept two of the factor inputs constant at the base year quantities. The production function was then solved for each year using the observed quantity of the third input which was allowed to vary. The process was repeated for another factor input. The effect of technology on the productivity of a factor input held invariant at the base period level of input was determined by taking the unweighted product of the indices which had been derived by solving the production function in the manner just described. This method of determining the effect of technology on the productivity of the individual factor is superior to that which is calculated by dividing the individual indices of factor inputs into output, because i t makes allowances for the effects of the increases in co-operating input factors, and does not merely record the effects of relative changes in the rates of increase of individual inputs as compared to gross output. Since the quantity of the input whose productivity response is being measured i s kept at the base period quantity, however, Urquhart's method does not cope with technological change which accompanies simultaneous increases in a l l factors. 20. Changing price cost relationships were removed from the data by using price indices to deflate current values of input and output. Returns to scale were assumed to be held constant since he used a Cobb-Douglas function. Changes in the ratio of actual output to the calculated joint input were then ascribed to changes in technology. The Pasinetti Model2^ Pasinetti emphasized that input-output data were usually limited to one point on the production function. This fact made i t difficult to distinguish a change in the level or shape of the production function from a movement along i t . He preferred to avoid making assumptions as to the nature of the particular production function, or postulates as to ways different functions at different points of time are related to each other, and instead gave up the distinction between the change of the production function and a movement along i t . Solow criticized him for this with the following comment: The notion of a production function is not simply a matter of formality or convenience. It is meant to express the fact (if i t i s a fact) that at any time the firm or industry or economic system is faced with a range of technological alternatives any one of which might be chosen, and that given enough time any previously made choice can be changed without appealing to new knowledge . . . . Nobody has yet proposed giving up the distinction shifts or and movements along demand and supply curves although a l l we ever observe for one market at any one time is one p and one q . . . By abandoning the production function Mr. Pasinetti has in effect abandoned the possibility of substituting capital for labour as of given technical knowledge. If Pasinetti, op_. cit. a. technology were r e a l l y l i k e that no one could complain. But to believe t h i s seems to be to be f o l l y , e s p e c i a l l y f o r periods as long as a decade.^5 What P a s i n e t t i d i d was to abandon the Hicksian d e f i n i t i o n of a neutral t e c h n i c a l change. Instead he compared the r a t i o s of output to f a c t o r inputs. His neutral change was one i n which the output-input r a t i o s of a l l f a c t o r s or more s p e c i f i c a l l y of a composite K and L changed i n the same proportion. His labour saving e f f e c t was one i n which the change of the r a t i o g was greater than the change i n K the r a t i o £J. The converse was a c a p i t a l saving e f f e c t . He regards L the analysis by Solow which has j u s t been presented as being "roughly along these l i n e s 0 . 2 0 Solow denied that t h i s method was s i m i l a r to h i s . Solow also pointed out the basic weakness involved i n the attempt to use r a t i o s rather than shares; and t h i s he stated as follows. "Suppose that changes i n K and L over time r e f l e c t e x c l u s i v e l y or p r i m a r i l y impulses from the side of the supply of saving and the growth of population. Then whatever happens to Q, P a s i n e t t i ' s judgement about the nature of t e c h n i c a l change w i l l i n f a c t r e f l e c t nothing about technology but only the r e l a t i v e speeds at which population and 27 c a p i t a l accumulate." This c r i t i c i s m i s s i m i l a r to one of those which has been made e a r l i e r i n t h i s t h e s i s about the Joan Robinson model. R.M. Solow, "Concepts and Measures of Change i n P r o d u c t i v i t y , " The Review of Economics and S t a t i s t i c s , Volume XLI, (August, 1959), p. 283. 2 ° P a s i n e t t i , o j % c i t . , p. 272. 27 Solow, "Concepts", etc., p. 283. 22. Studies Done on the Canadian Economy The studies done by Hood and S c o t t , ^ Anderson,^ and Lok,-^ have been chosen f o r c l o s e r examination. The study by Hood and Scott, was designed to forecast the ranges wit h i n which the measures of population, labour force, output, c a p i t a l and c e r t a i n of t h e i r constituent elements might be expected to l i e . ^ Their study also contains a discussion of the p r i n c i p l e s and the problems of measurement that are associated with the economic analysis of a growing economy. They measured output i n d o l l a r s per man hour. For t h i s study the u n i t of measurement i s output per calendar year. Hhereas the study of Hood and Scott encompassed the Canadian economy, that by Anderson was p r i m a r i l y concerned with the p r o d u c t i v i t y of labour i n a g r i c u l t u r e as compared with i t s p r o d u c t i v i t y . i n the non-a g r i c u l t u r a l sector. Anderson, though recognizing the l i m i t a t i o n s involved i n the use of the r e s i d u a l method f o r the c a l c u l a t i o n of f a c t o r p r o d u c t i v i t y , points out that the absence of a more precise method made the procedure appropriate f o r the task at hand. The study by Lok and t h i s present study apply to the a g r i c u l t u r a l sector. Lok's study was published a f t e r most of the c a l c u l a t i o n s of the present study were completed. Since both these studies to a large extent use the same data, i t i s appropriate that the ^ Wm. C. Hood, and Anthony Scott, Output. Labour and C a p i t a l i n the  Canadian Economy, (Ottawa: Queen's P r i n t e r , 1957). This study i s a part of report of the Royal Commission on Canada's Economic Prospects. 29 W.J. Anderson, "P r o d u c t i v i t y of Labour i n Canadian A g r i c u l t u r e , " Canadian Journal of Economics and P o l i t i c a l Science, Volume XXI, (May,' 1955), pp. 228-36. 30 Lok, l o c . c i t . 31 Hood and Scott, op. c i t . , i n t r o d u c t i o n p. i . 23. sources of the differences in the results should be made clear. The objectives of each study are dissimilar and so too are the models used. The best statement of this fundamental difference is found in the following statement by Lok. "It is not the purpose of this study to describe, and interpret fully the relative changes over time in the input and output and the output structure of Canadian Agriculture.' One of the aims of this present study is to make this interpretation. Lok's study demonstrates the weight period bias which is a part of the index number problem. Lok shows the differences which arise between the different indices which were calculated. Four of these were fixed base indices, and the two variable base indices were calculated on the bias of the Paasche and the chain index number formulae. The weight periods used were 1935-39, 194-0-44-, 194-5-4-9, and 1950-54-. Lok'a fixed base quantity index formulae were of the form Vn / In / Iw Vo / lo / Iw ; where Vn = Aggregate current value. In = Price index number of the commodity in year n. Io = Price index of the commodity in the base year (1926). Vo = Aggregate value of output in the base year. Iw = The average price index number in the base period of the quantity index. Lok's calculated output index series for the 1935 to 1939 fixed base period differs from the gross output index calculated in this study. These differences arise from the price indices used to 32 Lok, op. cit., p. 68. 24. deflate output and from the method in which feed and seed were treated in each study. Lok recognizes that farm price indices rather than oo wholesale price indices should be used to deflate output. The unavailability of farm price indices before 1935 prompted his decision to make two sets of calculations: one using farm price indices from 1935, and another using wholesale price indices from 1926. These two sets of calculations were presented in his study. In this study an index farm price was calculated for the years 1926-34 by linking the wholesale price index to the farm price index. Lok also recognized the problem of intermediate products in 0/ a production function. Feed and seed as an example were mentioned. In his study feed and seed were included in input and not removed from output. In the present study feed and seed are recognized as an intermediate product by neglecting the value on the input side and removing i t from the output product. In this manner only final output of the agricultural sector was considered. If the proportion of livestock in the agricultural economy is changing, in view of the manner in which the quantity indices were calculated, the method which includes feed and seed and that which excludes i t , produce each different results. The major difference, however, i s the method of aggregation of inputs. Lok used a linear function to add together input quantities weighted by prices of the base period. In this study a linear and homogeneous production function Lok, op. cit., p. 61. op. cit., pp. 59 & 63* 25. was used. This made i t possible to add geometrically i n d i c e s of f a c t o r inputs and to a r r i v e at a measure of gross input which i s a geometric aggregate i n which the exponents are the weights used. This method f a c i l i t a t e s the use of stock c o e f f i c i e n t s rather than flow estimates, and so avoids some of the problems of measurement associated with the determining of the amount of c a p i t a l i n use.-^ In seeking to t e s t h i s hypothesis Lok's method possesses high degrees of auto-correlation, because he was r e l a t i n g o v e r - a l l p r o d u c t i v i t y to r e a l net return. P r o d u c t i v i t y i s a fun c t i o n of output, and net return i s also a function of outputj therefore, Y, as used i n t h i s analysis, i s involved on both the ho r i z o n t a l and the v e r t i c a l axes. That being the case, the r e l a t i o n s h i p s which Lok was t e s t i n g were both funct i o n a l s of output. The changes i n p r o d u c t i v i t y cannot be regarded as being independent of r e a l net return. In t h i s analysis input i s cal c u l a t e d independent of the ca l c u l a t i o n s made f o r output; and although some amount of auto-c o r r e l a t i o n i s involved i n a l l measurements of pr o d u c t i v i t y , because composite inputs are a r r i v e d at by t h i s geometric aggregation, and because no e x p l i c i t regression or c o r r e l a t i o n methods w i l l be attempted, i t i s hoped that many of the problems of auto-correlation w i l l be avoided. 35 cf., John ¥. Kendrick, "Some Theoretical Aspects of C a p i t a l Measurement," The American Economic Review: Proceedings and Papers, Volume LI, (May, 1961),, 102-11. I l l THE ANALYTICAL FBAMEHORK OF THE STUDY In a study such as this one which seeks to measure the changes which have occurred in the position and the shape of the production function, a major problem is the determining of the production function from the limited amount of information availablej since without making any assumptions as to the nature of the production function,the available annual data furnishes information about a point on the production function rather than the whole function. On the basis of the theory that a family of isoquants may be derived from each production function, and the twin assumption of diminishing marginal productivity of factor inputs under conditions of constant technology, and of the condition that factors are paid as wages an amount equal to the value of their marginal product, a means of deriving the production function for the agricultural industry i s available. This means utilizes the concept of factor shares. The concept of a single production function for the industry as a whole represents a simplification of the conditions of production operating in the industry, and the derivation of a function for the industry as a whole presents problems of aggregation. A further assumption as to the type of production function is necessary. Under conditions of constant technology agricultural production i s characterized by diminishing marginal rates of substitution of factors and diminishing returns; therefore the production function i s non-linear. For this study i t is assumed that a Cobb-Douglas type production function characterizes the agricultural industry. 27. This type of function has the advantage of allowing for diminishing returns and changing marginal rates of substitution. Since i t is linear in a logarithmic form, the computation methods which are applied a linear production function may be readily adopted to the data when they are expressed in a logarithmic form. This type of function i s also homogeneous, so that returns to scale are held constant. Other conveniences conveyed by the use of the Cobb-Douglas type function arose from the fact that the exponents of the function are estimates of both the elasticity of production coefficients, and the relative share of the particular factor. It is thus possible to determine the function from time-series data in which only one observation of factor combinations is given for each year, because the exponents can be determined by calculating the relative share of each factor. The production function used in this study assumes that the total wage payments to a l l identifiable factors would exhaust total production i f there were no changes in technology. But the total output of the agricultural industry is influenced to a large extent by weather and other exogeneous variables. Consequently, the variability in agricultural output will at times be due to the influence of the exogeneous variables rather than to the influence of the prevailing level of technology. With the assumption that the total product is exhausted in wages to factors under conditions of constant technology, the aggregate wage payments to factors may be used as an alternative means of measuring output. In this event the difficulties which the interaction of the exogeneous variables and changes in technology 28 present i n the way of determining the short-run production function are eliminated; since under conditions of constant technology when the production f u n c t i o n i s of the Cobb-Douglas type, and f a c t o r s are paid the value of t h e i r marginal product, the value of t o t a l input i s equivalent to what the value of t o t a l output would be under the e x i s t i n g l e v e l of technology and market conditions. Divergences of the value of t o t a l input from t o t a l output would be the r e s u l t of (a) exogeneous v a r i a b l e s , or (b) changes i n technology which r e s u l t i n the in c r e a s i n g of the gross output from the a v a i l a b l e f a c t o r s . In these circumstances, r e a l i z e d gross product may be as a r e s u l t d i f f e r e n t from a n t i c i p a t e d t o t a l product a r r i v e d at on the b a s i s of the i n i t i a l production function. The shares were c a l c u l a t e d on the basis of current d o l l a r values. However, since changing p r i c e - c o s t e f f e c t s w i l l influence the t o t a l value of inputs and output, and since technological change deals with the changes i n the conversion r a t i o s between given qu a n t i t i e s of p h y s i c a l inputs and outputs, the p r i c e - c o s t e f f e c t s were removed from the aggregate value s e r i e s by measuring the quantities as i n d i c e s of d e f l a t e d (1935-39) d o l l a r inputs i n which the deflated value as at 1926 was set at 100. The r e l a t i v e shares of the current d o l l a r value of p a r t i c u l a r f a c t o r inputs i n aggregate input (aggregate output under conditions of constant technology and i n a system f r e e of exogeneous v a r i a b l e s ) , may be s a t i s f a c t o r i l y used as the share of the f a c t o r i n the expected l e v e l of aggregate output i f technology remains constant.^ A more precise development of the model used i n t h i s t h e s i s i s presented i n Appendix A. 29 Inputs Three independent variables were included in the production function used; namely, capital (C), current inputs (K), and labour (L). In this analysis capital was treated as a stock. The value of capital goods as at any point in time was regarded as being determined by the expected value of the, future stream of production discounted at some rate of interest (not necessarily the prevailing market rate). Those inputs other than labour whose claims on output must be met from current production were regarded in this study as current inputs. This category included depreciation, and operating expenses which were incurred for items which were not the intermediate products of agricultural industry. Feed and seed were thus excluded from this category; and for the third input category, D.B.S. data on the agricultural labour force were used. Because of the problems associated with the inclusion of land inputs (which constitute a major portion of the value of agricultural capital), two sets of calculations were carried out. In one set of calculation the value of land was included, its value being excluded from the other set. Because many of the characteristics which make agricultural land technologically productive are produced capabilities, the arguments for the inclusion of agricultural land as a capital good, are very substantial. In a manner similar to that which was used by Lok capital was also measured as.an indexed series of the flow of interest payments to capital stock. However, in this study, since depreciation on capital stock has already been charged to current inputs the use of an index of the aggregate i n t e r e s t payments as an i n d i c a t o r of the l e v e l of c a p i t a l input does not recommend i t s e l f . This i s because of the f a c t that the market rate of i n t e r e s t of i t s e l f depends upon time preference as w e l l as upon the marginal e f f i c i e n c y of c a p i t a l , and although being a means of measuring the equilibrium l e v e l of net investment, i s thus an u n s a t i s f a c t o r y measure of the quantity of c a p i t a l i n use at any given l e v e l of technology. A l l these inputs were c a l c u l a t e d i n terms of i n d i c e s of the t o t a l value of the u n i t s f o r each year. The items i n each category were defl a t e d by the appropriate p r i c e index (1935-39 = 100). The d e f l a t e d value of each category was summed, and t h i s aggregate was transformed i n t o an indexed seri e s 1926 = 100.* Since the d e f l a t i o n process removes those e f f e c t s due to price (within the l i m i t a t i o n s of the index number problem) the index of t o t a l d e f l a t e d value may be regarded as being equivalent to an index of physical q u a n t i t i e s . Output Output includes cash farm income as well as income i n kind. Each category was treated i n the same manner as were inputs. Each i n d i v i d u a l category of output of the farm sector was d e f l a t e d by i t s appropriate p r i c e index. The def l a t e d values were aggregated; and the quantity i n d i c e s of the t o t a l output were obtained by a process s i m i l a r to that used i n c a l c u l a t i o n of the i n d i c e s of input.3 The composite output f i g u r e , however, represented an arithmetic aggregation of d e f l a t e d d o l l a r values, rather than a geometric aggregation of the components. 2 The d e t a i l s of the items i n each category and the i n d i c e s used are included i n Appendix A. 3 I b i d . The Production Function The Cobb-Douglas function which is used in this study is of the form 1 = X Q Xg X^ where X Q , Xg , and X^ , represented the indices of capital, current inputs, and labour inputs respectively, and where Y is an index of the quantity of gross farm output. The exponents <x , /3 t and-tf , represent the calculated shares of capital current inputs and labour respectively, and the sum of the exponents equals unity. These wage payments were determined from the data. The aggregate annual wage payment to labour was estimated by the product of the annual wage rate and the size of the farm labour force. The monthly farm wage rate without board as at May 15 was used in this analysis to determine the estimate of the annual wage rate. This wage rate was chosen because the D.B.S. estimate of the annual farm labour force refers to this period. The aggregate of the wage payments to other current inputs was determined from the annual expenditures on the items which make up this input category. 4-The wage payment of capital inputs was determined by the product of the aggregate current dollar value of farm capital (in one case inclusive of land and in the other case exclusive of land) and the current market rate of the rate of interest on farm mortgages. The share of each factor was then determined by the ratio that the wage payment to each, is of the aggregate wage payments to a l l factors. In this manner the share going to each factor was determined net of many of the effects that are produced by exogeneous variables and additional shifts in technology. ^ The details are included in Appendix A . IV RESULTS OF THE STUDY In this section the results of the study will be examined within the framework of the model which has been developed. The results of technological change which economic resource use would lead one to expect are associated with the producing of a larger quantity of output from a given stock of resources. The innovation which this study has introduced i s the method of determining the shape of the production function and from i t the quantity of resources being used at any point in time. Changes in the product mix, and in the input mix, are also associated with changes in technology; but within the framework of the model which has been developed for use in this study the major step is the determining of the production function; and from this point the other steps follow. The results of the study will be presented in a sequence which involves the presentation of the derived production functions in the one case using capital resources inclusive of land and in the other case using capital resources exclusive of land. Those calculations which were made from the production functions in which the quantity of capital was measured as an index of the annual flow of interest payments will be presented in the Appendix. Measuring Technological Change Inclusive of Land Capital Table 1 , indicates the relative shares which were calculated from data in which the value of land and buildings was included in the value of capital stock (C 5). Examination of the table shows that the 33. r e l a t i v e shares of the f a c t o r s had been changing over time. I t followed from the method chosen that these changes must i n d i c a t e changes which have taken place i n the shape of the production fun c t i o n . Since neutral changes are those i n which s h i f t s of the production function do not involve changes i n i t s shape, i t follows that the technological changes which had been adopted were non-neutral. Examination of the data of Table 1 shows that there i s no consistent trend i n the changes of the shares. The r e l a t i v e share of c a p i t a l during the period 1928 to 1932 rose from 30 to 33 per cent, then declined s t e a d i l y to 14 per cent i n 1946, and rose again to 19.6 per cent i n 1958. Although there has been an upward tendency i n the r e l a t i v e share of c a p i t a l since 1946, the share i n 1958, was s t i l l s u b s t a n t i a l l y lower than i t s share of approximately 29 per cent i n the pre-depression era. The proportion of t o t a l expenses represented by current inputs follows by a s i m i l a r pattern to that of c a p i t a l . The r e l a t i v e share increased from 21.8 to 28.2 per cent over the period 1926 to 1932, declined to 22.6 per cent i n 1945, and increased to 38.6 per cent by 1958. Although the r e l a t i v e share of current inputs had declined i n the immediate post-war years of 1944 and 194-5 to w i t h i n 1 percentage point of i t s 1926 l e v e l , the subsequent increase i n the most recent years of the analysis was s i g n i f i c a n t l y above the r e l a t i v e share which i t had i n 1926; having increased from 21.8 per cent to 38.6 per cent. When t h i s increase i s compared with that of the r e l a t i v e share of c a p i t a l TABLE I FACTOR SHARES, CANADIAN AGRICULTURE, 1926-58 Including Land (Oo) <K2) ( L 2) Current Year Capital Inputs Labour 1926 .298 .218 .484 1927 .292 .221 .487 1928 .300 .229 .471 1929 .301 .237 .462 1930 .294 .255 .451 1931 .316 .262 .422 1932 .333 .282 .385 1933 .332 .277 .391 1934 .317 .277 .406 1935 .300 .271 .429 1936 .270 .267 .463 1937 .248 .266 .486 1938 .227 .271 .502 1939 .223 .272 .505 1940 .199 .251 .544 1941 .190 .264 .546 1942 .180 .256 .564 1943 .172 .236 .592 1944 .158 .228 .614 1945 .151 .226 .623 1946 .140 .230 .630 1947 .145 .245 .ao 1948 .147 . 2 a .592 1949 .153 .280 .567 1950 .161 .312 .527 1951 .175 .327 .498 1952 .172 .341 .487 1953 .177 .353 .470 1954 .176 . 3 a .463 1955 .184 .376 .440 1956 .185 .384 .431 1957 .184 .370 .437 1958 .196 .386 .418 35. i t must be observed that the most recent and l a r g e s t r e l a t i v e share of c a p i t a l since 1946 i s s t i l l 10.2 percentage points belot* i t s 1926 share of 29.8 per cent. The r e l a t i v e share of labour has v a r i e d from a low of 38.5 per cent i n 1932 to a high of 63 per cent i n 1946. Since the t o t a l of the r e l a t i v e shares i s 100 per cent, labour's share has v a r i e d i n v e r s e l y to that of the other two f a c t o r s . From 48.4 per cent i n 1926, the share declined to 38.5 per cent i n 1932, rose to 63.0 per cent i n 1946, and declined to 41.8 per cent i n 1958. Since the shares are dependent on the marginal p r o d u c t i v i t y of the f a c t o r as well as the quantity of the f a c t o r the changing r e l a t i v e shares i n d i c a t e the changing r e l a t i v e importance of f a c t o r s i n the production of output. The i n c r e a s i n g r e l a t i v e share of current inputs represents the increased importance of short-term c a p i t a l to the industry. This i s r e f l e c t e d i n the increased l e v e l of use of current inputs. An examination of the changes i n the quantity of the various inputs as compared to the changes i n the r e l a t i v e shares i n d i c a t e s the type of adjustment which changes i n technology have required. These adjustments to c a p i t a l , current inputs, and labour r e s p e c t i v e l y , may be observed i n Columns 2, 3 and 4 of Table I I , which reveal an o v e r - a l l gradual increase i n the quantity of c a p i t a l i n use, a s u b s t a n t i a l increase i n the l e v e l of current inputs, and a l e s s s u b s t a n t i a l but noticeable decline i n the quantity of labour i n use. 36. The quantity of current inputs has more than doubled since 1926; however, from Table I, i t can be observed that the share as at 1958 was l e s s than double i t s share as at 1926. Other s t r i k i n g observations are the f a c t s that although the quantity of labour i n use as at 1958 had declined by nearly 4-0 per cent, i t s share had declined by only 14 per cent, and that the quantity of c a p i t a l had increased by 15 per cent, while i t s share had declined by 34 per cent. The d i f f e r e n c e s between the changes i n the f a c t o r shares as compared to changes i n f a c t o r quantities r e f l e c t some of the e f f e c t s of technological change on the p r o d u c t i v i t y of the f a c t o r s used i n the a g r i c u l t u r a l industry, and the nature of some of the s t r u c t u r a l adjustments which had taken place. Mien the quantity of current inputs i s broken down i n t o i t s main components (Table III) i t becomes evident that s i g n i f i c a n t increases have occurred i n the proportion of annual cash expenses which are associated with farm mechanization and with expenditures on f e r t i l i z e r . On f u r t h e r examination the reduced proportion of farm cash expenses associated with depreciation and r e p a i r s showed s i g n i f i c a n t increases i n the absolute cost of farm machinery depreciation and r e p a i r s as w e l l as that of b u i l d i n g depreciation and r e p a i r s . Thus i n the presence of a decreased proportion one concludes that the increases i n the other operating expenses have been greater than the increases i n those expenses associated with depreciation and r e p a i r s . TABLE I I INDICES: OUTPUT AND GROUPED INPUTS, CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1) (2) (3) (4) (I) (c2) (K) (L) Year Output C a p i t a l Current Inputs Labour 1926 100.0 100.0 100.0 100.0 1927 107.2 104.7 108.8 101.2 1928 112.6 107.8 115.1 101.4 1929 89.4 110.5 119.5 102.7 1930 96.0 111.6 121 .4 102.5 1931 77.9 114.4 113.0 106.2 1932 100.0 114.9 103.8 106.2 1933 88.8 113.9 100.7 110.2 1934 91.0 114.7 100.4 110 .9 1935 99.6 112.6 100.8 113.5 1936 92.3 108.6 99.7 114.7 1937 85.2 107.1 100.1 114.8 1938 102.2 110.7 103.0 118.0 1939 129.5 101.4 106.7 117 .9 1940 127.6 101 .9 107.0 116.5 1941 112.1 96.4 110.1 99.8 1942 161.8 99.8 116.1 91.9 1943 113.5 102.6 121.7 88.2 1944 137.2 102.0 127.0 99.2 1945 109.2 104.2 135.3 99.1 1946 116.7 103.6 146.0 103.3 1947 118.7 103.5 154.4 97.5 1948 130,0 101.5 159.7 95.2 1949 125.8 102.7 166.3 93.7 1950 119.7 105.5 181 .3 89.7 1951 153.3 107.5 190.7 81.5 1952 160.1 108.7 193.9 77.0 1953 163.4 109.2 204.3 75.2 1954 129.3 110.6 206.4 76.0 1955 149.6 110.8 211.9 70 .9 1956 167.3 111.4 221.1 67.3 1957 140.1 111.0 213.7 66.0 1958 150.6 115.4 214.6 61.7 TABLE III PERCENTAGE ANNUAL CURRENT NON-LABOUR COSTS FROM VARIOUS SOURCES, SELECTED YEARS, CANADA, 1926-56 Years Source 1926 1931 1936 1941 1946 1951 1956 (Percentages) Depreciation and repairs on farm buildings and" machinery 44.7 43.2 42.9 37.1 41.0 39.3 37.7 Tractor, truck, auto engine and combine expenses 17.1 21.2 22.4 27.2 23.9 28.3 28.8 Taxes 21.2 21.8 21.0 16.7 14.6 13.1' H-6 Fertilizer cost .• 2.0 3.2 2.9 3.9 5.0 5.0 4.7 Miscellaneous expenses .. 15.0 10.6 10.8 15.1 15.5 14*3' 14.2 Source: Handbook of Agricultural Statistics Part II, Farm Income 1926-1957 (Revised Edition Reference paper No. 25-Part II), D.B.S., Agricultural Division, Farm Finance Section, pp. 68-69. 39. The percentage of farm cash expenses made up of taxes has also declined. Miscellaneous expenses have been r e l a t i v e l y constant since 1941 at t h e i r 1926 l e v e l of approximately 15 per cent, but during the depression miscellaneous expenses were down to 10 per cent of current expenses. Changes i n technology i n the a g r i c u l t u r a l sector, therefore, have been associated with increases i n the use of f e r t i l i z e r and machinery. The greater increase of operating expenses r e l a t i v e to depreciation also r e f l e c t s the i n t e n s i f i c a t i o n of the use of farm machinery. Output-Input Relationships Inclusive of Land The data from which the output-input r e l a t i o n s h i p s may be calculated, have already been presented i n Table I I . Column 1 presents i n d i c e s of actual output which were calculated from aggregating the de f l a t e d d o l l a r values of each type of output, and by expressing the de f l a t e d aggregate of d o l l a r values i n terms of a r e l a t i v e i n which the value as at 1926 was set at 100. This quantity index follows reasonably c l o s e l y the published Index of Physical Volume of A g r i c u l t u r a l Production. The index calculated i n t h i s study i s , l e s s than the published s e r i e s i n 1953, 1954, and 1958, the calculated index i s r e s p e c t i v e l y 6, 10, and 5 percentage points higher. The i n d i c e s of c a p i t a l , current inputs, and labour input r e s p e c t i v e l y are presented i n Columns 2, 3, and 4» The calculated predicted output (hence composite input i n t h i s study, Z2.) from each production f u n c t i o n i s presented i n Table IV, Column 2. The difference between the marked v a r i a b i l i t y of output and the l e s s marked v a r i a b i l i t y of the ca l c u l a t e d j o i n t input i s noticeable. AO. iii though the effect of changes in technology is to alter output-input ratios an exogeneous variable such as rainfall may markedly affect the ratio in any single year. Consequently, since the choice of a production function is based on rational considerations, and since the possible effects of the exogeneous variables enter into the decision-making process of the entrepreneur, although i t may be reasonable to assume that their effects are randomly distributed in the long run, the effects of changes in technology are best studied by observing whether there has been any pattern in output-input relationships, and what changes have occurred in the pattern. These output-input relationships showing the calculated annual values of the average as well as the marginal productivity of each of the three independent variables used in each of the production functions that had been determined, are presented in Table 17,and in Tables IX, and X, Appendix A. Table IV, however, shows figures representing the average product of composite and particular inputs. Output has increased beyond its 1926 level. Under conditions of diminishing returns and constant technology, when output is increasing average and marginal products are inverse functions of the quantity of the particular resource in use. That being the case since the quantity of labour in use had declined over the period of the analysis, in these circumstances i t follows that its average and marginal productivities would show a positive change. If technology is changing, an increase in the quantity of any input need not result in a decline in its average or marginal productivities, and changes in the marginal productivities need not be 41. proportional to changes i n the average p r o d u c t i v i t i e s . Labour saving technological innovations w i l l increase the marginal p r o d u c t i v i t y of labour more than the marginal p r o d u c t i v i t y of other inputs; and innovations which are '"very labour saving" w i l l be accompanied by a reduction of the quantity of labour i n use. These "very labour saving" innovations w i l l contribute s i g n i f i c a n t l y to increases i n the average p r o d u c t i v i t y of labour. The average p r o d u c t i v i t y of other f a c t o r s may also be increased. The e f f e c t s of the technological innovations which had been adopted by the a g r i c u l t u r a l industry can be seen i n Table IV. Those periods i n which the output-input r a t i o s had been d e c l i n i n g show the f a c t o r using nature of the innovations which were adopted. The f a c t o r saving nature of innovations may be observed from the r e l a t i v e changes i n the average and the marginal p r o d u c t i v i t i e s of f a c t o r s , i n that these w i l l be r a i s e d . The lowered output-input r a t i o s of a l l f a c t o r s f o r the 1929 to 1937 period are due p r i m a r i l y to the low l e v e l of output. Column 1 shows the high v a r i a b i l i t y of output, whereas Column 2 shows that composite input ha3 v a r i e d between very narrow l i m i t s . When the period as a whole i s examined, Table IV shows that output shot-red a net change of 50.6 per cent, whereas composite input showed one of 12.9 per cent g i v i n g an increase of 33.3 per cent i n the output-input r a t i o s . I t i s also i n t e r e s t i n g to note that the peak years d i f f e r f o r each of these three s e r i e s represented i n Columns 1, 2, and 3: however, i f the r e s u l t s obtained f o r the year 1942 are regarded as abnormal i t can be observed from these columns that the greater proportion of the increase i n p r o d u c t i v i t y has been achieved subsequent to the year 1950. TABLE IV INDICES} OUTPUT, COMPOSITE INPUT, COMPOSITE AND PARTICULAR OUTPUT-INPUT RATIOS, CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1) (2) (3) (4) (5) (6) Y S I / K 2 vH V V Output-Output- Output- Current- Output-Composite Input C a p i t a l Input Labour Year Output Input Ratio Ratio Ratio Ratio 1926 100.0 100.0 100.00 100.0 100.0 100.0 1927 107.2 103.8 103.28 102.4 98.5 105.9 1928 112.6 105.5 106.73 104.5 97.8 111.0 1929 89.4 108.8 82.17 80.9 74.8 87.0 1930 96.0 109.7 87.51 86.0 79.1 93.7 1931 77.9 110.5 70.50 68.1 68.9 73.4 1932 100.0 108.3 92.34 87.0 96.3 94.1 1933 88.8 108.6 81.77 78.0 88.2 80.6 1934 91.0 109.0 83.49 79.3 90.6 82.1 1935 99.6 109.5 90.96 88.5 98.8 87.8 1936 92.3 108.9 87.76 85.0 92.6 80.5 1937 85.2 108.8 78.31 79.6 85.1 74.2 1938 102.2 112.1 91.17 92.3 99.2 86.6 1939 129.5 110.8 116.88 127.7 121.4 109.8 1940 127.6 110.8 115.16 126.3 119.3 109.5 1941 112.1 101.2 110.77 116.2 101.8 112.3 1942 161.8 99.0 163.43 162.1 139.4 176.1 1943 113.5 97.7 116.17 110.6 93.3 128.7 1944 137.2 105.4 130.17 134.5 108.0 138.3 1945 109.2 107.1 101.96 104.8 80.7 110.2 1946 116.7 111.0 105.14 112.6 79.9 112.8 1947 118.7 110.0 107.91 114.7 76.9 121.7 1948 130.8 110.0 118.91 128.1 81.4 136.6 1949 125.8 111.6 112.72 122.5 75.6 134.3 1950 119.7 114.7 104.36 113.5 66.0 133.4 1951 153.3 113.0 135.66 142.6 80.4 188.1 1952 160.1 111.9 143.07 147.3 82.5 207.9 1953 163.4 114.3 142.96 149.6 80.0 217.3 1954 129.3 116.4 111.08 116.9 62.6 170.1 1955 149.6 116.2 128.74 135.0 70.6 211.0 1956 167.3 114.8 145.73 150.2 75.6 248.6 1957 140.1 113.4 123.54 126.2 65.6 212.3 1958 150.6 112.9 133.39 130.5 70.2 244.1 43. The "very labour saving" nature of technological innovations may be observed from the results recorded in Column 6 of Table IV. Since 1946 the average productivity of labour has shown marked increases, the index of average product having moved from 112.8 in 1946 to 244*1 in 1958, a net increase over the thirteen year period of 131.3 percentage points, and at an average annual increase of 10.1 per cent of its 1926 level. When the period as a whole was examined the average productivity of labour showed a net increase of 144*1 per cent. This long-period increase in contrast to that just presented for the 1946 to 58 period provides an average annual increase of approximately 4.37 per cent of the 1926 level. The data in Column 6 which has just been examined- may be contrasted with those results shown in Columns 4 and 5. The fact that output had increased at a faster rate than that of the increase in the quantity of capital in use, while i t was at the same time increasing at a slower rate than the quantity of current inputs in use, may be deduced from the increasing average productivity of capital and the declining average productivity of current inputs. For the period as a whole the net increase of 30.5 per cent in the average productivity of capital may be contrasted with the net decrease of 29.8 per cent in the average productivity of current inputs. Additional comparisons may be made between the increase of 7.9 percentage points since 1946 in the average productivity of capital with the decline of 9.7 percentage points in the average productivity of current inputs for the same period. These changes when viewed with those that have already been observed for labour point to the heavy reliance of 44. agricultural industry on short term investment which is measured in this study as current inputs. A very instructive contrast i s also provided by examining the close relationship displayed here in the changes of the over-all productivity (Column 3) and those of capital in the two forms capital stock, and current input; i.e., long term capital, and short term investment with depreciation. This relationship is seen in the fact that over-all productivity as measured here showed a net increase of 33.3 per cent; and this may be compared with a closely similar net increase of 30.5 per cent in the average productivity of capital, and the similar amount but negative change of 29.8 per cent in the average productivity of current inputs. Measuring Technological Change When Land is Excluded In this section the analytical procedure will be similar to that used previously in this study. The modification which will be introduced is that capital as measured here will be the figure derived from aggregating in constant 1935-39 dollars the value of machinery and livestock. Since the value buildings and other improvements to land are included in the reported value of land, when this data for land was removed from the value of capital used in the previous section, that of buildings and other improvements, unfortunately, was also removed. Changes in technology are instrumental in causing variations in the quantity and quality of machinery and livestock which are combined with a given quantity of land. Variations of capital in the form of machinery and livestock are therefore sensitive to changes in technology. £5. M t h the value of land and buildings removed the r e l a t i v e share of c a p i t a l was diminished and that of the other inputs accordingly increased. As the quantity of l i v e s t o c k and machinery increases, other things being equal, the share of c a p i t a l increases. However, under the assumptions of the model used i n t h i s a n a l y s i s t h i s cannot be the case unless the increase i n the quantity of c a p i t a l i s achieved under conditions of constant, or in c r e a s i n g marginal p r o d u c t i v i t y ; so that an increase i n the quantity of c a p i t a l does not automatically l e a d to an increase i n i t s share. Each table which i s presented i n t h i s section compares with a s i m i l a r one i n the section previously presented. Table V, gives the shares which were calculated net of land, and compares with Table I. In t h i s table i t can be observed that the share of c a p i t a l as at 1958 was approximately the same as i t s share as at 1926, although i t had v a r i e d oyer the period, having f i r s t increased and subsequently decreased to lower than i t s 1926 l e v e l before i t returned to t h i s l e v e l . This phenomenon of having i n 1958 a share s i m i l a r to what i t had i n 1926 may be compared with the lower than 1926 l e v e l of the share of t o t a l c a p i t a l stock as at 1958, i n order to observe one of the e f f e c t s of the change i n the method of measurement. The r e l a t i v e share of labour i n 1926 although being 15 per-centage points higher than i t s share which was calculated i n Table I, declined by 1958 to within 6 percentage points of i t s share i n t o t a l inputs i n c l u s i v e of land (as shown i n Table I ) . This provides an i n d i c a t i o n of the s u b s t a n t i a l increase i n the p r o d u c t i v i t y and importance of the non labour inputs. 46. The relative share of current non-labour inputs shows an increase in Table V above its 1926 levels. Since the relative shares are also the coefficients of the elasticity of productivity, with the exclusion of land the elasticity of production of labour had declined over the years. This has been especially so since 1946. The elasticity coefficients (and hence also the shares) of a l l factors had been continually changing over the period of the analysis; and these changing coefficients reflect the changing emphasis which changes in. technology exert on factor inputs. Output Input Relationships Net of Land Since capital i s the only variable which is measured differently in this section the average productivities of labour inputs and current inputs will be identical with those recorded earlier. Table VI, except for Column 1, presents data which have not been put forward earlier in this thesis. Column 2 records the calculated quantities of composite input net of land and is analogous to a similar column which has been presented earlier in Table IV. Columns 3 and 5 of Table VT, also compare with Columns 3 and 4 respectively of Table IV. The remaining column of Table VI (Column 5), i s analogous to Column 2 of Table II. On analyzing each column of Table VI in turn, the following comparisons may be made with the data previously studied. Column 1 which records observed output i s unchanged from the data examined earlier since i t i s the identical series. The net change in composite inputs can be observed in Column 2, and this for the entire period as a whole was approximately two percentage points higher in the TABLE V FACTOR SHARES, NET OF LAND, CANADIAN PRIMARY AGRICULTURAL SECTOR, 1926-58 Excluding Land ~ (Ci) (%) (LIT" Current Year Capital Inputs Labour 1926 .085 .285 .630 1927 .082 .287 .631 1928 .090 .298 .612 1929 .092 .307 .601 1930 .090 .328 .582 1931 .093 .347 .560 1932 .102 .380 .518 1933 .102 .372 .526 1934 .094 .367 .529 1935 .092 .351 .557 1936 .084 .335 .581 1937 .078 .326 .596 1938 .073 .325 .602 1939 .074 .324 .602 1940 .068 .299 .633 1941 .063 .305 .632 1942 .064 .292 .644 1943 .067 .266 .667 1944 .059 .255 .686 1945 .056 .251 .693 1946 .052 .254 .694 1947 .055 .271 .674 1948 .056 .289 .655 1949 .063 .310 .627 1950 .069 .346 .585 1951 .081 .364 .555 1952 .078 .380 .542 1953 .076 .396 .528 1954 .075 .405 .520 1955 .077 .425 .498 1956 .076 .436 .488 1957 .076 .427 .497 1958 .083 .441 .476 48. new s e r i e s presented here than that which was observed f o r composite inputs i n c l u s i v e of land. There i s here a l a r g e r d i f f e r e n c e i n the calculated i n d i c e s of composite inputs f o r the years 1950 to 1956 from those differences of the data which were presented e a r l i e r . The net change i n j o i n t input f o r the e n t i r e period, however, was i n t h i s case 14 per cent above i t s 1926 l e v e l s as compared with the 12.9 per cent recorded i n Table IV. As a consequence of the s l i g h t l y higher l e v e l s of composite input, the output-input r a t i o s i n d i c a t i n g o v e r - a l l p r o d u c t i v i t y are s l i g h t l y narrower f o r t h i s s e r i e s which has excluded the value of land and b u i l d i n g s . This i s p a r t i c u l a r l y true of the 1950-56 period. A net change i n o v e r - a l l p r o d u c t i v i t y here of 31.4 per cent, compares with one of 33.4 which was observed e a r l i e r . The much more s i g n i f i c a n t change i n the quantity of non r e a l estate c a p i t a l than that of t o t a l c a p i t a l becomes evident when Column 4 of Table VI i s compared with Column 2 of Table I I . In the former the net increase of 4 2 . 9 per cent over i t s 1926 l e v e l s i s recorded, and i n the l a t t e r one of 15.4 per cent. The d i f f e r e n c e s i n the l e v e l s of these measures of c a p i t a l input a f f e c t e d the measure of the average p r o d u c t i v i t y of c a p i t a l accordingly; i n that the average p r o d u c t i v i t y of c a p i t a l stock i n c l u s i v e of land was higher than that of c a p i t a l net of land. In f a c t , the close r e l a t i o n s h i p between the l e v e l s of output and those of non land c a p i t a l i s evident from the f a c t that since 1946 the average p r o d u c t i v i t y of c a p i t a l net of land may be regarded as f l u c t u a t i n g around 1. The data from t h i s section of the analysis, i n d i c a t e that the change i n the method of measuring the quantity of c a p i t a l a f f e c t s s l i g h t l y the index of the amount of c a p i t a l i n use. The r e s u l t i n g changes are not great enough to s e r i o u s l y a f f e c t the o v e r - a l l p r o d u c t i v i t y TABLE VI INDICES; OUTPUT, COMPOSITE INPUT, COMPOSITE AND PARTICULAR OUTPUT-INPUT RATIOS, NET OF LAND, CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1) (2) (3) (4) (5) (I) ( V T ) (Oj.) Tear Composite Output-Input Output-Capital Output Input Ratio C a p i t a l Ratio 1926 100.0 100.0 100.00 100.0 100.0 1927 107.2 104.0 103.08 109.3 98.1 1928 112.6 106.3 105.93 112.3 100.3 1929 89.4 108.6 82.32 113.8 78.6 1930 96.0 109.0 88.07 109.3 87.8 1931 77.9 109.0 71.47 111.4 69.9 1932 100.0 105.7 94.16 110.9 99.2 1933 88.8 106.3 83.15 113.0 78.6 1934 91.0 105.4 86.34 98.0 92.9 1935 99.6 108.2 92.05 105.9 94.1 1936 92.3 108.6 84.99 105.4 87.6 1937 85.2 108.9 78.07 103.4 82.4 1938 102.2 111.5 91.66 99.2 103.0 1939 129.5 113.3 114.30 106.6 121.5 1940 127.6 112.9 113.02 107.2 119.0 1941 112.1 101.8 110.12 94.3 118.9 1942 161.8 98.9 163.60 99.4 126.8 1943 113.5 99.8 113.73 114.1 99.5 1944 137.2 106.6 128.71 115.1 119.2 1945 109.2 108.2 100.92 118.6 92.1 1946 116.7 113.7 102.64 120.1 97.2 1947 118.7 111.9 106.08 123.6 96.0 1948 130.8 111.9 116.18 118.3 109.0 1949 125.8 114.1 110.25 126.3 99.6 1950 119.7 117.9 101.53 138.6 86.4 1951 153.3 116.4 131.70 145.4 105.4 1952 160.1 115.2 138.98 150.0 106.7 1953 163.4 117.7 138.83 150.2 108.8 1954 129.3 119.3 108.36 151.4 85.4 1955 149.6 119.7 124.98 152.5 98.1 1956 167.3 119.8 139.68 145.3 115.1 1957 140.1 115.4 121.40 140.6 99.6 1958 150.6 114.6 131.41 142.9 105.4 50 measurement. However, the changes i n the average p r o d u c t i v i t y of c a p i t a l when land i s excluded are d i f f e r e n t from those changes observed by the other method. An Evaluation of the Two Methods Used Tables IV and VI in d i c a t e that so f a r , the p r i n c i p a l difference between the two methods of measuring the quantity of c a p i t a l i s that when c a p i t a l i s measured exclusive of land the r e s u l t i s a smaller change i n the average p r o d u c t i v i t y of non r e a l estate c a p i t a l than that of t o t a l c a p i t a l . The net change i n o v e r - a l l p r o d u c t i v i t y between 1926 and 1958 was very s i m i l a r i n both circumstances although the data from both methods provide d i f f e r e n t estimates over the 1950 to 1956 period. A change i n the production f u n c t i o n has been the c r i t e r i o n which t h i s analysis has regarded as being i n d i c a t i v e of technological change. The e f f e c t s of the changes i n the production f u n c t i o n are not evident i n the observed changes i n the average product of each f a c t o r , because the r e s u l t s would have been the same whether the production fu n c t i o n had remained stationary or not. The p r i n c i p a l e f f e c t of the differen c e i n the methods of measurement, may be observed by comparing the former r e s u l t s with those which were obtained when the marginal p r o d u c t i v i t y of f a c t o r s was calculated. This comparison i s f a c i l i t a t e d by the r e s u l t s presented i n Table VII. An analogous comparison may also be made from the r e s u l t s reported i n Table X, Appendix A. Table VII records the cal c u l a t e d i n d i c e s which show how much change occurred i n the p r o d u c t i v i t y of the marginal u n i t s as technology changed. These i n d i c e s may be compared with those which showed the 51 change in the average productivity of each factor. Over-all productivity has been already presented, and from the calculations made the conclusion has been drawn that the inclusion or the exclusion of land did not significantly affect the measure of the extent of the change in over-all productivity. Table VII also indicates the changes which have been observed in the marginal productivity of factor inputs when land was included in total capital, and also when i t was excluded. Within each method Golumns 1 and 4 respectively indicate that the change in the marginal productivity of capital has been less than that of other inputs. The change in that of labour was the greatest; and this is bourne out in Columns 3 and 6« This result, is different from that observed earlier, in that i t was current inputs and not capital which had shown the smallest increase in average productivity; and in fact, this change was a decline rather than the observed increase in marginal productivity which is recorded here. Betx/een method comparisons, show that the net change in the marginal productivity of capital stock net of land was not as great as that for total capital stock. The marginal physical productivity of labour, and current inputs, was higher when capital included land; and this result is similar to that observed for the average productivity. The net change for current inputs was 24.3 per cent over i t s 1926 level in the one case, and 8.6 per cent in the other case when capital was measured net of land. ii/hen total capital was considered, the net change in the marginal productivity of labour was 110.8 per cent above its 1926 level; inhereas the net change of its marginal product when land and buildings were removed was 85.6 per cent above its 1926 level. The comparisons made from the method of measurement which deletes the value 52. of land and buildings from c a p i t a l stock, i n d i c a t e a more than favourable adjustment process i n the a g r i c u l t u r a l sector i n so f a r as the use of c a p i t a l i s being considered. Column 1 shows that the new equilibrium p o s i t i o n s to which the farm sector had moved, had been attained with l e s s e r s a c r i f i c e i n the p r o d u c t i v i t y of a d d i t i o n a l u n i t s of c a p i t a l than those s a c r i f i c e s of p r o d u c t i v i t y as the output expands that are suggested by Column 4* These varying r e s u l t s therefore i n d i c a t e that the choice of the method of measuring c a p i t a l does a f f e c t the conclusions which may be drawn as regards the p r o d u c t i v i t y of the additions to the available stock of resources. The v a r i a t i o n s which are observable i n each column of Table VII point to the e f f e c t s of changes which have been due to both technology and to exogeneous v a r i a b l e s . I t i s noticeable that i n the 1929 to 1938 period the marginal p r o d u c t i v i t y of labour was lower than that of the other inputs, and thus i n d i c a t e s that the changes i n technology over the period were labour using. On the other hand, the labour saving technological changes of the 1946 to 1958 period are revealed i n the s u b s t a n t i a l changes that the marginal p r o d u c t i v i t y of labour has made from i t s 1926 l e v e l . The e f f e c t s of technological change may also be observed i n the r e l a t i o n s h i p s between the calculated changes i n the average p r o d u c t i v i t y of current inputs over the period 1946 to 1958, and the c a l c u l a t e d changes of i t s marginal p r o d u c t i v i t y over the same period. The one when measured i n c l u s i v e of land, showed a net decline of 9.7 percentage points over the period, having gone from an index of 79.9 to one of 70.2j whereas the other (marginal p r o d u c t i v i t y ) showed a net increase of 4-0 percentage points, by having gone from an index of 84.3 to one of 124.3. TABLE VTI RELATIVES^ MARGINAL .PHYSICAL.AND VALUE PRODUCT OF FACTOR INPUTS, CANADIAN AGRICULTURE, 1926-58,-1926 = IOO (1) (2) (3) M (71 EXCLUDING LAND INCLUDING LAND M.P. P. Ca p i t a l (Ol) M.P. P. M.P.P. Current M.P.P. M.P. P. Current M.P. P. M.V.P. Inputs Labour Ca p i t a l Inputs Labour C,K,L, (%) ( L l ) (C 2) (K 2) ( L 2 ) 1926 100 100 100 100 100 100 100 1927 94.6 99.2 106.1 100.3 99.9 106.5 99.4 1928 106.2 102.2 106.9 106.1 102.8 108.0 99.7 1929 85.1 80.6 883.0 81.7 81.3 83.0 81.2 1930 92.9 91.0 86.5 86.5 84.8 92.5 80.8 1931 76.5 83.9 65.2 71.3 82.8 64.0 64.3 1932 108.2 128.4 77.4 97.2 124.6 74.8 71.4 1933 , 94.4 115.1 67.3 86.9 112.1 65.1 69.4 1934 102.7 116.7 70.2 84.4 115.1 68.9 82.6 1935 101.9 121.7 77.6 89.1 122.8 77.8 85.1 1936 86.6 108.8 74.2 77.0 113.4 77.0 86.2 1937 75.6 97.3 70.2 66.2 103.8 74.5 93.2 1938 111.6 113.1 82.7 70.3 123.3 89.4 98.2 1939 105.7 138.0 104.9 95.0 151.5 114.6 104.4 1940 95.2 125.-2 109.6 84.3 140.6 123.1 100.0 1941 88.1 108.9 112.7 74.1 123.3 126.7 99.6 1942 122.6 142.8 180.0 97.9 163.7 205.2 139.8 1943 78.4 87.1 136.3 64.0 101.0 157.4 109.7 1944 82.7 96.6 150.6 71.3 112.9 175.5 123.6 1945 60.7 71.1 121.2 53.1 83.6 141.8 100.7 1946 59.4 71.2 124.3 52.9 84.3 146.8 108.4 1947 62.1 73.1 130.2 55.8 86.4 153.4 103.1 1948 72.4 82.5 142.0 63.2 97.5 167.1 128.5 1949 73.8 82.2 143.3 62.9 97.1 157.3 120.3 1950 70.1 80.1 123.9 61.3 94.4 145.2 114.8 1951 100.5 102.7 165.7 83.8 120.6 193.5 141.8 1952 97.9 110.0 178.9 85.0 129.0 209.1 140.1 1953 97.3 111.2 182.1 88.8 129.5 211.0 125.8 1954 75.3 88.9 140.4 69.0 103.7 162.7 102.6 1955 88.8 105.3 166.8 83.4 121.8 191.8 117.2 1956 102.9 115.6 192.6 93.3 133.1 221.4 123.2 1957 89.1 98.3 167.5 77.9 114.0 191.7 104.2 1958 102.9 108.6 185.6 85.6 124.3 210.8 117.0 54. Column 7 records the changes in the marginal value productivities of the factor inputs. These were calculated from inserting the current dollar values of each factor in the production function. It shows that the changes in the physical product of each factor have been in most cases greater than the value change. Summary Tables I, and V, show that the relative shares of the factors have been changing. Under the criterion used in this analysis these changes indicate the shifts which have taken place in the production function. Tables IV, and VI, indicate that the inclusion or the exclusion of land does not substantially affect the calculated measure of joint productivity, in that in the one case a net change of 33.4 per cent above the 1926 level was recorded, and in the other case one of 31.4 per cent. Both methods of calculating capital show that the greatest proportion of this increase (approximately 28.5 per cent above 1926) has been achieved since 1946. In view of the two abnormal economic periods (the Great Depression, and Tforld ¥ar II) which preceded 1946, i t is unwise to draw any conclusions as regards the efficiency of operation of the agricultural industry as a whole between the years 1926 and 1945. The data must be regarded as indicating the adjustments which were effected under the conditions which these two periods imposed on the industry. The changes in technology have had a positive effect on the productivity of factors used in the agricultural sector. These changes have been accompanied by substantial increases (115 per cent) in the use of current inputs (Table II)j and these inputs have'been chiefly associated with the expenses associated with farm mechanization, and 55. also with use of f e r t i l i z e r (Table I I I ) . Other changes have been net increase i n the amount of machinery and l i v e s t o c k of approximately 43 per cent above i t s 1926 l e v e l (Table VI)j and t h i s has been associated with a net decline of approximately 28 per cent i n the quantity of labour i n use. The s h i f t s i n the production functions have been instrumental i n combining more resources with land at higher l e v e l s of o v e r - a l l e f f i c i e n c y (Table IV, Column 4$ and Table VII, Columns 5 and 6). The r e s u l t s of the i n v e s t i g a t i o n have substantiated the main hypothesis of t h i s t h e s i s ; i n that technological change has had a p o s i t i v e e f f e c t on the p r o d u c t i v i t y of f a c t o r s used i n the a g r i c u l t u r a l sector of the Canadian economy. BIBLIOGRAPHY A. BOOKS Ackley, Gardner. Macroeconomic Theory. New York: The Macmillan Company, 1961. American Economic Association. Readings i n the Theory of Income  D i s t r i b u t i o n . E d i t o r s , F e l l n e r , William, and Haley, Bernard P. A r t i c l e s number 8, 9, 10, 20, and 21. P h i l a d e l p h i a : The Blackston Company, 1951. . Readings i n Price Theory. Edi t o r s , S t i g l e r , George J., and Boulding, Kenneth E. A r t i c l e s number 9, 11, and 12. Baumol, William J.- Economic Dynamics. 2nd E d i t i o n . Nex* York: The Macmillan Company, 1959. Economic Theory and Operations Analysis. Englewood C l i f f s , N.J.: Pr e n t i c e - H a l l , Inc. 1961. Bohn^-Bawerk, Eagene von. Po s i t i v e Theory of C a p i t a l . Translated with a Preface and Analysis by William Smart. New York: G.E. Stechert & Company, 1923. Boulding, Kenneth. Economic Analysis, t h i r d e d i t i o n . New York: Harper & Brothers, 1955. Chamberlain, Edward Hastings. Towards a More General Theory of Value. New York: Oxford U n i v e r s i t y Press, 1957. Clemmence, Richard V., and Doody, Francis S. The Schumpeterian System. Cambridge 42, Mass.: Addison Wesley Press, Inc., 1950. Conference on Research i n Income and Wealth. Input-Output Analysis; An Appraisal. - Studies i n Income and Wealth, Volume Eighteen. A report of the National Bureau of Economic Research, New York. Princeton: Princeton U n i v e r s i t y Press, 1955. Croxton, F r e d r i c E., and Cowden, J . J . Applied General S t a t i s t i c s , 2nd e d i t i o n . New York: Prentice-Hall, Inc., 1955. Davidson, Paul. Theories of Aggregate Income D i s t r i b u t i o n . New Jersey: Rutgers U n i v e r s i t y Press, 1959. Davis, Hiram S. P r o d u c t i v i t y Accounting. Phil a d e l p h i a : U n i v e r s i t y of Pennsylvania Press, 1955. Douglas, Paul H. The Theory of Wages, New York: The Macmillan Company, 1934-F e l l n e r , U l l i a m . Modern Economic Analysis. New York: McGraw-Hill Book Company, Inc., I960. 57. Fossati, Eraldo. The Theory of General Static Equilibrium. BI., G.L.S.: Shackle. Oxford: Basil Blackwell, 1 9 5 7 . Friedman, Milton. Essays in Positive Economics. Chicago: The University of Chicago Press, 1 9 5 3 . Heady, Earl 0 . Economics of Agricultural Production and Resource Use. Euglewood Cliffs, N.J.: Prentice-Hall, Inc., 1 9 5 2 . Henderson, James M., and Quandt, Richard E. Microeconomic Theory. New York: McGraw-Hill Book Company, Inc., 1 9 5 8 . Hicks, J.R. The Theory of Wages. London: Macmillan & Co., Limited, 1932. . Value and Capital, second edition. London: Oxford University Press, 1 9 3 9 . Higgins, Benjamin. Economic Development. New York: 3ff.\W. Norton & Company, Inc., 1 9 5 9 . Hood, Win. C, and Scott, A.D. Output, Labour and Capital in the Canadian Economy. Ottawa: Queen's Printer, 1 9 5 7 . Jevons, William S. The Theory of Political Economy. Third Edition. London: Macmillan & Co., Limited, 1 8 8 8 . Keynes, J.M. The General Theory of Employment Interest and Money. London: Macmillan & Co., Limited, 1 9 3 6 . Knight, Frank. Risk Uncertainty and Profit. New York: Houghton Mifflin Company, 1 9 2 1 . Learner, Abba P.The Economics of Control. New York: The Macmillan Company, 1 9 4 6 . Leftwich, Richard. The Price System and Resource Allocation. Revised Edition. New York: Holt, Rinehart and Weston, I 9 6 0 . Leontief, Wassiley 1W., and others. Studies in the Structure of the  American Economy. New York: Oxford University Press, 1 9 5 3 . Marshall, Alfred. Principles of Economics. Eighth Edition. London: Macmillan & Co., Limited, 1 9 5 0 . . Economics of Industry. Third Edition. London: Macmillan & Co., Limited, 1 9 5 8 . Patinkin, Don. Money, Interest, and Prices. Evaston, Illinois: ROXJ Peterson and Company, 1 9 5 6 . Ricardo, David. On The Principles of Political Economy and Taxation. Edited by P. Sraffa. Cambridge, England: Cambridge University Press, 1 9 5 2 . 58 Robinson, Joan. The Accumulation of C a p i t a l . London: Macmillan & Co., Limited, 1956. S a l t e r , ¥.E.G. P r o d u c t i v i t y and Technical Change. Cambridge, England: Cambridge U n i v e r s i t y Press, I960. Samuelson, Paul A. Foundations of Economic Analysis. Cambridge, Mass.: Harvard U n i v e r s i t y Press, 1947. Schultz, T.W. The Economic Organization of Agriculture. New York: McGraw-Hill Book Company, Inc., 1953. Schumpeter, Joseph A. The Theory of Economic Development. Translated by Redvers Opie. New York: Oxford U n i v e r s i t y Press, 1961. Walraa, Leon. Elements of Economics, Pure. Translated by 15.111 am Ja f f e e . London: George A l l e n and Unwin, Ltd., 1954* M i c k s e l l , Khut. Lectures on P o l i t i c a l Economy. Translated by E. Classen. Volume One. London, 1934* Zeuthen, F.W. Economic Theory and Method. Cambridge, Mass.: Harvard U n i v e r s i t y Press, 1955. B. PERIODICALS Abramovitz, Moses. "Resource and Output Trends i n the United States Since 1870,° The American Economic Review, Papers and Proceedings, XLVI (May, 195677 5-23. Anderson, H.J. ""Productivity of Labour i n Canadian A g r i c u l t u r e , " Canadian Journal of Economics and P o l i t i c a l Science, XXI (May, 1955), 228-36. Buchman, Kenneth. "The Analysis of Changes i n A g r i c u l t u r a l Supply: Problems and Approaches," Journal of Farm Economics, XLII, (August, 1960), 531-51. Champerowne, D.G. "The Production Function and the Theory of C a p i t a l : A Comment," The Review of Economic Studies, XXI (1953-54), 112-35. , with Khan, R.F. "The Production Function and the Theory of C a p i t a l , a Mathematical Addendum," The Review of Economic  Studies, XXIII (1955-56), 107-11. Domar, S.D. "On the Measurement of Technological Change," The Economic  Journal, LXXI, (December, 1961), 709-29. Gruen, F.H. "Agriculture and Technical Change," The Journal of Farm  Economics, XLIII, (November, 1961), 838-58. 59. Hogan, Warren P. "Technical Progress and Production Functions," The  Revievr of Economics and S t a t i s t i c s , XL, (November, 1958), 407-11. Johnston, B.F., and Mellor, J.W. "Agriculture i n Economic Development^'" The American Economic Review, L I , (September, 1961), 566-93. Kaldor, N. "Alternative Theories of D i s t r i b u t i o n , " The Review of Economic Studies, XXIII, (1955-56), 83-100. Kendrick, John ¥. "Some Theoretical Aspects of Ca p i t a l Measurement," The" American Economic Review: Papers and Proceedings, L I , (May, 1961), 102-11. . "P r o d u c t i v i t y Trends: Cap i t a l and Labour," The Review of Economics and S t a t i s t i c s , XXXVIII, (August, 1956), 248-57. Lok, S.H. An Enquiry Into the Relationships Between Changes i n Over- a l l P r o d u c t i v i t y and Real Net Return Per Farm, and Between Changes i n Total Output and Real Gross Return. Canadian Agriculture 1926-57, Technical P u b l i c a t i o n , Canada Department of Agricu l t u r e , Economics Branch, (October, 1961). Mackenzie, M l l i a m . "The Impact of Technological Change on the E f f i c i e n c y of Production i n Canadian Agr i c u l t u r e , " Canadian Journal of A g r i c u l t u r a l Economics, X, (1962), 41-53. P a s i n e t t i , L u i g i L. "On Concepts and Measures of Changes i n Productivity, The Review of Economics and S t a t i s t i c s , XLI, (August, 1959), 270-82. . "Reply," The Review of Economics and S t a t i s t i c s , XLI, (August, 1959), 285-86. Phelps Brown, E.H. ""The Meaning of the F i t t e d Cobb-Douglas Function," Quarterly Journal of Economics, LXXI,(November, 1957), 546-60. Robinson, Joan. "The Production Function and the Theory of C a p i t a l , " The Review of Economic Studies, XXI, (1953-54), 81-103. Ruttan, Vernon ®. "Research on the Economics of Technical Change," Journal of Farm Economics, XLII, (November, I960), 735-54-. . "The Contribution of Technological Progress to Farm Output: 1950-75," The Review of Economics and S t a t i s t i c s , XXXVIII, (February, 1956), 61-69. Schmookler, Jacob. "The Changing E f f i c i e n c y of the American Economy: 1869-1938,18 The Review of Economics and S t a t i s t i c s , XXIV, (August, 1952), 214-31. Solow, Robert M. "Technical Change and the Aggregate Production Function, The Review of Economics and S t a t i s t i c s , XXXIX, (August, 1957), 312-20. 60 . "Reply" The Review of Economics and S t a t i s t i c s , XL, (November, 1958), 411-13. . "The Production Function and the Theory of C a p i t a l , " The Review of Economic Studies, XXIII, (1955-56), 101-08. . "On Concepts and Measures of Changes i n Produc t i v i t y : Comment," The Review of Economics and S t a t i s t i c s , XLI, (August, 1959), 282-85. . "A Skepti c a l Note on the Constancy of Relative Shares," The American Economic Review, XLVIII, (September, 1958), 618-31. Urquhart, M.C. "C a p i t a l Accumulation, Technical Change, and Economic Growth," The Canadian Journal of Economics and P o l i t i c a l Science, 25, (November, 1959), 411-30. APPENDIX The theoretical model which has been used in the analysis will be presented in this appendix. The data derived from the calculations which were made when capital was measured as an annual flow of interest payments, and also those which were made when a stationary function was used, will be presented. These results may be compared with those presented in the main body of the thesis. The Model Used The elements of the production function are: Y = The gross output of the farm sector. C = Gross quantity of capital. C - Annual input of capital. K = Quantity of current non labour inputs, excluding feed and seed. L = Quantity of labour input. The measurement of the amount of change due to technology involves the comparing of the calculated measures of composite input (which is equivalent to predicted output) from a linear and homogeneous production function of degree unity, with observed levels of output. This calculated measure of composite input may also be regarded as a geometric aggregate in which the quantity of each item in the aggregate is weighted by its relative share. Over-all productivity was measured by dividing observed annual output by the computed measure of composite inputj and the average productivity of each factor input was obtained by dividing the index of observed output, by the index of each factor input, for each of the years 1926-1958. 62, Within the data the effects of weather and other such exogeneous variables are assumed to be randomly distributed over the time period in such a manner as not to introduce any serious bias in the results. Wars and depressions are regarded as being different from random events, and although their effects influence the data of the analysis there is not much that can be done to mitigate their effects, beyond omitting the specific periods from the analysis. A family of isoquants may be derived from each production function. It is further assumed that a smooth production surface characterizes each of the production functions which are used. The production function may be linear i f there are constant marginal rates of substitution, or curvelinear i f there are changing marginal rates of substitution. Changing marginal rates of substitution characterize the agricultural sector. In order to discover the production function at any point in time given the values of Y, K, C, and L, let the function be of the form Y = XQ X L j where X is the quantity of input of the particular factor, and where the sum of the exponents is unity. Let the wage payments to factors exhaust total product. .*. P^ Y = + \%g + ; where W, represents the vrages of the factor, and P, the price. The wage share of the factor was obtained from the followings % ¥ X W X p_ . & : h J are the relative shares of C, K, and L V • y v respectively. As long as the V.M.P. (Value of the Marginal Product) is less than the wage rate in a system in which there are several factors of production, ceteris bar!bus i t will pay the producer to use additional units of each 63. factor up to the point where the following conditions hold true. V.M.Pj^ V.M.PX (a) !1 = 3. = 1 (b) (c) PXn PX~ x l *2 M.P.PX P„ M« P- px« p T *2 x l ^ 2 \ Now = M .P .Px c • P y j where XQ is the unit of the factor X^ and Py is the unit price of output. This condition holds in circumstances of pure competition. The function Y - XQ Xg X£ describes a physical relation-ship. The M.P.Px„ iscV Y Let the M.P.P. = 1 a physical relationship. Y -2 *C = = o£ is a value relationship. Y Py T.V.P. If factor inputs are measured in terms of value relationships, that is to say, i f the physical quantities of input and output are weighted by their respective prices i t is possible to determine the exponents, and to regard the value ratios as representing the physical relationship , since value is a transpose of price and quantity. Y The critical question becomes shifted to the conditions under which the 64. prices of the factor and the product are determined. This analysis assumes that the prevailing prices are equilibrium ones. In the production function which is used in this analysis, the exponent of each factor is also equal to the elasticity of production as well as its relative share. If the relative share of each factor is constant through time, as long as factors are paid at the value of their marginal product, there is only one function. If the relative shares are changing in the time series data, there are changes of the relative shares. Figure 1 illustrates the fact that when units of factors are paid as wages the value of their marginal product and when a Cobb-Douglas type function describes the production relationship, a change in the relative shares of factors represents a change in technology. Consider the agricultural economy as having a fixed stock of resources. ( X^  ), which must be used to induce the services of the other factors of production. Let X2 be a measure of a l l these other factors whose services may be exchanged with the stock at varying marginal rates of substitution. Let the economic conditions be such that larger quantities of X2 are only forthcoming at higher costs in terms of X-j_. Under prevailing conditions the opportunity curve of the agricultural sector i s represented in Figure 1 by the curve LV. The aggregate production function for the agricultural economy under the prevailing conditions is represented by the isoquants 0^, § 2 * . . . On • Under these conditions the optimum equilibrium combination of X]_ and X£ is represented by the combination Ox-^  of X-^  and O X 2 ° ^ ^ 2 * ^ e P r i c e °^ ^ 2 ^ n terms of X]_ under these conditions 65. figure t 66. is represented by the line P]/Pg f o r "the level of output ^ 5. Assume that an innovation makes i t possible to utilize Xj_ but not Xg more fully. With the shift to the new curve MV, under the old price ratio the quantity of Xg in use will be reduced by OXg - Ox' g. At the same time the quantity of Xj_ xri.ll be increased by the amount Ox'-^  - Ox^ . If the quantity of Xg in use vrere kept at Xg the quantity of X-j_ would be increased by Ox^  - Ox^ , a smaller increase than the above. The old price ratio of X 2 in terms of X]_, however, would not be tangential to S. A new price ratio / Pg would be established. At point S the marginal rate of transformation on the new curve is greater than that at point T. Since at equilibrium the marginal cost of Xg in terms of X-^  is also equal to the marginal rate of transformation of X-^  into Xg , with neutral technological change, i f the shares are to remain constant the wages of Xg will have to increase in the same proportion that its marginal rate of transformation is increased. T, is an equilibrium position at the old price ratio. Hith the shift to the new transformation curve MV i f the price ratio remains constant a new equilibrium position xrould be established at R, A solution which requires tangency of the isoquants with the price line Bj. Pg, would involve a change in their shape. At the same time since the quantity of X-j_, which would be kept for use, would be increased, and the amount of Xg, which is bought, decreased. The relative share of X-j_, which is kept by the sector, would be as a consequence increased, and the relative share of X 2 under the old price ratio would decrease. A non neutral technological change, therefore, involves a change in factor shares. Given that there are no discontinuities in 67. the marginal productivity function, the converse may be proved.2 Within the context of the above model i t can also be shown that a change in technology which does not involve the shift of the curve LV may occur. This happens when a shift in the production function results in anew point of tangency of the isoquant whose point of tangency is now at T. Depending on the pressures causing the shift the new point of tangency will be to the left or the right of point T. For further discussion of the effects of technological change on the factor product relationships in agriculture c f . F.H. Gruen "Agriculture and Technical Change," Journal of Farm Economics, Vol. XLIII, Number 4, Part I (November, 1961), pp. 838-58 and references. A discourse on the association of research and technological change is presented by Vernon W . Ruttan in the article "Research on the Economics of Technological Change in American Agriculture," Journal of  Farm Economics, Volume XLII, Number 4, (November, I960), pp. 735-54* Footnote references throughout this article provide a comprehensive guide to work in the field of evaluation and measurement of technological change. Technological change viewed as a supply response is discussed by Mark Nerlove, and Kenneth L. Buchman, "The Analysis of Changes in Agricultural Supply: Problems and^Approaches," Journal of Farm Economics, Volume XLII, Number 3, (August, I960), pp. 531-51. This article provides an extensive bibliography on the subject of technological change. COMPUTATION Output The value of each category of output obtained from the D.B.S. data, was deflated by its price index, 1935-39 = 100. The total value of output was determined by aggregating the deflated values. Since the price indices are supposed to remove the effects of price changes from the aggregate value series, the deflated series represents annual physical quantities weighted by 1935-39 prices. The data were then converted to index numbers, 1926 = 100, from vrhich the changes in the quantity of output over the period could be observed. Specifically total output was obtained as follows: (Cash farm income + Changes in + Income in kind _ Feed and Seed1) (from livestock " inventory f r o m livestock expenses ) / Index number of farm price of ) ( livestock and livestock products. ) (Cash income + Change in + Income in kind ) (from crops _ inventory from crops ) + ( .. •, • . ) ( Index of farm prices ) ( for crops. ) (Cash income from forest + Income in kind from ) ( and maple products forest and maple products ) + ( •• • • - ' • , . i • ) / Price index for lumber and \ / lumber products. \ ( House rent ) + ( = ) ( Index of building materials ) ( taxes and interest rates. ) Feed and seed were removed to avoid couble counting. 69 Inputs The value of the input factors G, K, and L, were changed from current dollar terms to constant dollars, and the indices of physical quantities were calculated in the same manner as was output. Here-under are set out the members of each category and the deflator index which was used in conjunction with each member before the aggregate constant dollar value was determined and then indexed in terms of 1926 being made equal to 100. Capital Co = ( Machinery value ) (Value of ( less depreciation ) (livestock ( T„ J„_ ,. ) + { / Index of machinery \ /Index number of / prices \ /farm prices of /livestock and ^livestock products ( Land value ( Index of land ( value per acre c; = (Total current value ) '( of capital goods ) ( Rate of interest on ) ( farm mortgages ) Index of interest rates. &L = C 2 net of land ( Value of capital goods ) ( net of land ) ( Rate of interest on ) ( farm mortgages ) Index of interest rates The other non capital inputs were the following: K = Cost of fertilizer ) and lime ) Index of fertilizer^ prices \ ) + ( (Machinery depreciation) (and repairs ) (Price index of farm ( machinery -) + ) Building de-) preciation ) and repairs ) Price index ) of building ) materials ) 70. ( Tractor truck auto] ( engine and combine] ( expenses | Index of Gasoline ( o i l and grease Taxes ( (-( Index of ( taxes Miscellaneous expenses Index of hard-ware prices ( Canadian labour force ) ( Monthly wage rate ) _ ( in agriculture ) ( without board ) , Index of farm wage rates Capital was calculated in two different ways because there are two schools of thought each with a reasonable set of arguments supporting the claim that land should or should not be left out in an analysis of this sort. The fir s t school is represented by this quotation from Marshall. . . . Uhen regarding capital from the social point of view i t is best to put under separate heads those of the nation's resources which are made by man, and those which are not; and to separate the capital x-rtiieh is the result of labour and saving from those things which nature has given freely. This plan is well adopted for the main purposes of the economist. For indeed his chief concern with capital in general, or social capital, is when he i s considering the way in which the three agents of production, land (i.e., natural agents) labour and capital, contribute to producing the national income . . . , and the way in which this is distributed among the three agents.4-The argument used by the other school of thought is well represented by the following quotation from Fossati. The productive power which land brings to agriculture i s therefore itself produced, in the sense that f e r t i l i t y can be increased by man's labour and knowledge . . . . To ignore this to regard land as merely so much earth, denying its fundamental property, fe r t i l i t y . -> 4 Alfred Marshall, Economics of Industry, (London: Macmillan, 1958 reprint) p. 4-7. Sraldo Fossati, The Theory of General Static Equilibrium edited by G.L.S. Shackle (Oxford: Basil ELackwell, 1957), p. 132. 71 I t i s true that F o s s a t i was r e f e r r i n g to land w i t h i n the context of a diminishing returns controversy, but the f a c t that a g r i c u l t u r a l land i s not required merely f o r i t s s i t e value i s a powerful argument i n support of i n c l u d i n g land as a c a p i t a l good. But as Solow pointed out^ i t i s c a p i t a l i n use and not c a p i t a l on hand which i s important i n the production process. The problem of excess capacity could e a s i l y creep i n i f land value i s included when the value of c a p i t a l i s being determined. A problem involved i n the i n c l u s i o n of land l i e s i n the f a c t that the value of land does not n e c e s s a r i l y r e f l e c t i t s p o t e n t i a l a g r i c u l t u r a l p r o d u c t i v i t y but also r e f l e c t s demand from the non a g r i c u l t u r a l use of the s i t e . Investment i n land i s frequently used as a hedge against i n f l a t i o n , and i n f a c t , many c r e d i t i n s t i t u t i o n s are t i e d to the ovmership of property. The r e s u l t i s that the market value of a g r i c u l t u r a l land may not always represent the p r i c e that a farmer acting i n h i s capacity as a farmer would be w i l l i n g to pay f o r the s i t e . Despite these considerations, however, i t must be recognized that technological improvements are often designed to extract more productive capacity from a given amount of land. The proportion of a g r i c u l t u r a l l a n d whose pri c e i s influenced by non a g r i c u l t u r a l use i s not large; thus at any point i n time the t o t a l value of a l l a g r i c u l t u r a l land r e f l e c t s i t s p r o d u c t i v i t y i n a given state of technology. In t h i s a n a l y s i s c a l c u l a t i o n s were made i n which land was regarded from the two points of view previously expressed. However, i t must be noted that the i n c l u s i o n of l a n d reduces the share going to Solow, "Technical Change" etc. p. 314* 72 labour and current inputs, and increases the share of capital. The effect of its inclusion will also depend upon the behavior of the non-land in relation to land inputs. Simultaneous decreases in the relative importance of land and increases in non land capital inputs will be masked in a value aggregate. Under these circumstances, the changes in the share of capital will be less marked when the value of land is included and as a consequence, since there will be less variation in the relative shares, changes in technology will be less apparent. The analysis done here has therefore made use of both approaches. Estimating Input and Output Relationships Several modifications of the input variables were used in order to describe fully the interaction in the system. The modifications make use of the following variables and parameters. (l) = Capital stock = Depreciated value of buildings and machinery = Capital stock net of land (2) G 2 = = Capital stock including land (3) ~ 1 = : Share of o<2 = = Share of C 2 U) : Share of current inputs (K) when C = = °1 : n II tl tl tt " C = : C 2 (5) = " « labour " (L) tt c = : °L ~*2 = i n n tt ti tt c = : C 2 (6) An analysis using the more traditional approach was also done. The shares were kept constant at 1926 levels and capital input was measured as the interest payments on capital stock inclusive land (Cg). 73. The use of a stationary production function facilitates prediction. If non-neutral technological changes are occurring, the production function is changing as a result. At the same time, i f neutral changes are occurring the predictive accuracy of the stationary production function is restricted. However, i f technology is changing at some known rate reasonably accurate predictions may be made, and information as to the known or expected rate of change of technology, or regarding the expected frequency of its change together with the probable amount of change i f available would be invaluable. There is as yet no means of acquiring such information as regards the expected future rate of changej and as the review of the literature presented in this thesis has shown, there is no consensus as regards the best method of measuring past changes. Under the criterion used by this analysis the data available show that the aggregate production function has been shifting, thus technological changes have been occurring. As a result, those calculations using the stationary production, which were made in this analysis, are presented for purposes of making comparisons of the results with those results of other methods. A Mote on Some of the Price Indices Used Most of the price indices used were compiled by D.B.S.j however, the indices of Farm Price for Crops and also for livestock products for the years 1926-34 were computed by establishing a link relative between the respective Farm Price indices and the Wholesale Price indices for the years 1935 to 1958. The link relative was then used to convert the wholesale price index for 1926 to 1934 into Farm Price indices. The deflator index used for taxes was also computed by-establishing a conversion ratio between the available Index of Tax and Interest rates and the Index of Interest Rates. The annual indices of taxes were then computed out of both series. Additional Results It is instructive to examine the difference vrhich the use of some of the other methods of calculating composite inputs would have made to the results. One method involves the use of a stationary function, that i s to say, the relative shares were not allowed to vary from those values which they had in 1926. In this case the level of composite input has been designated here as X^ .. Another method made use the shifting production function, but capital in this case was measured in terms of an indexed series of the value of interest payments going to capital stock, and in which the deflator index used was an index of interest rates. The designation of this type of capital index i s C', and the composite input which was calculated from this series is designated Xl . The weakness of this method has already been discussed in the main body of this thesis. The results of these calculations are presented in Tables VIII, IX, and X; and the effect of the various methods on the estimate of the change ii.^ver-all productivity may best be examined, in Table IX. This table shows that for the entire period, the estimate of the change in the over-all productivity which was calculated from the use of the stationary function was similar to that which was calculated with the use of the shifting functions. Over the period 1931 to 1946, however, the estimated change in over-all productivity was greater when the measurement was made with the use of the stationary function than the 7.5. amount of change registered by the other methods. During the years 1948 to 1954- inclusive, the greatest amount of change from the base period values was recorded by the function which measured capital as a stock inclusive of real estate. It therefore appears that the changes recorded by these three methods of measurement at times moved together with closely similar results, as characterized the 1926-30 period while at other times they changed in pairs, or independently. For example, between the years 1936 and 194-5 the results which embody the use of and Cg were closely similar; whereas those embodying the use of Cg and Cg were closely similar for the years 1955 to 1958 inclusive. Under these circumstances i t must be concluded that these variations in the calculated results of each method are to a large extent due to the characteristics of the changes which were taking place in the particular periods. The choice of the method of measurement is thus not immaterial; because i f the time series data of this analysis had terminated in a different year the estimates of net over-all change produced by each method would be much more dissimilar. The choice of the method must therefore be determined by the economic logic which can be brought to bear on the particular circumstances: and the method of measurement chosen therefore will depend upon the amount as well as on the type of changes which are occurring in the sector. The data of Columns 3 and 4- of this table were derived from a model whose conceptual weakness has already been discussed; but since this method of measuring capital (as an annual flow of interest payments) has been used at different times by various writers, these columns are included here in order that the results of the use of the shifting production function in conjunction with a geometric aggregation TABLE VIII INDICES; OUTPUT-INPUT RATIOS, ADDITIONAL SELECTED METHODS, CANADSS AGRICULTURE, 1926-58; 1926 = IOO (1) (2) (3) (4) (5)_ STATIONARY FUNCTION* SHIFTING FUNCTION** 1 , Year Output A 2 j Output-Composite- Input Input Ratio L2i Output-Composite- Input Input Ratio 1926 100 100 100 100 100.00 1927 107.2 104.5 102.58 104.5 102.58 1928 112.6 107.2 105.04 107.3 104.94 1929 89.4 108.7 82. 24 109.0 82.02 1930 96.0 109.2 87.91 109.9 87.35 1931 77.9 102.0 76.37 101.9 76.45 1932 100.0 100.1 99.90 94.5 105.82 1933 88.8 96.5 92.02 94.8 93.67 1934 91.0 96.7 94.11 95.5 95.29 1935 99.6 98.2 101.42 97.5 102.15 1936 92.3 97.7 94.47 98.2 93.99 1937 85.2 97.9 87.03 99.4 85.71 1938 102.2 98.1 104.18 101.0 101.19 1939 129.5 97.3 133.09 102.7 126.10 1940 127.6 99.1 128.76 103.3 123.64 1941 112.1 91.9 121.98 95.6 117.25 1942 161.8 92.4 175.11 95.0 170.03 1943 113.5 94.8 119.73 95.3 119.10 1944 137.2 102.6 133.72 103.8 132.18 1945 109.2 104.7 104.3 105.7 103.31 1946 116.7 110.0 105.14 111.1 105.04 1947 118.7 110.8 107.13 110.6 107.32 1948 130.8 114.1 113.94 112.7 115.35 1949 125.8 116.3 108.17 115.3 109.11 1950 119.7 118.7 100.84 119.6 100.00 1951 153.3 119.9 127.86 121.1 126.59 1952 160.1 116.9 136.95 119.5 133.97 1953 163.4 118.0 138.47 112.8 133.06 1954 129.3 118.4 109.21 124.5 103.86 1955 149.6 116.3 128.63 125.3 119.39 1956 167.3 115.2 145.23 124.3 134.59 1957 140.1 113.4 123.54 122.8 114.09 1958 150.6 112.0 134.46 123.6 121.84 * C a p i t a l was measured as an annual flow accruing to a l l c a p i t a l stock i n c l u d i n g land and shares were kept at the 1926 l e v e l s . ** The same as f o r the stationary function except that the shares were vari e d as the data dict a t e d . TABLE IX SUMMARY INDICES, GROSS OUTPUT-INPUT RELATIONSHIPS; VARIOUS SELECTED METHODS CANADIAN AGRICULTURE, 1926-58; 1926 = 100 (1) (2) (3) U) (5) Index of Producti-vity when Index of Index of Index of Index of c = Cg and Productivity Productivity Productivity Productivity function Year when c = C^  when c = Cg when c = C[ when c = Cg Stationary 1926 100 100 100 100 100 1927 103.08 103.28 103.38 102.58 102.58 1928 105.93 106.73 106.03 104.94 105.04 1929 82.32 82.17 81.87 82.02 82.24 1930 88.07 87.51 88.24 87.35 87.91 1931 71.47 70.50 72.67 76.45 76.37 1932 94.61 92.33 97.79 105.82 99.02 1933 83.15 81.77 86.30 93.67 92.02 1934 86.34 83.49 88.09 95.29 94.11 1935 92.05 90.96 94.23 102.15 101.42 1936 84.99 84.76 86.59 93.99 94.47 1937 78.09 78.31 79.26 85.71 87.03 1938 91.66 91.17 - 92.57 101.19 104.18 1939 114.30 116.88 116.98 126.10 133.09 1940 113.02 115.16 113.83 123.64 128.76 1941 110.12 110.77 110.12 117.25 121.98 1942 163.60 163.43 162.45 170.03 175.11 1943 113.73 116.17 114.50 119.10 119.73 1944 128.71 130.17 127.15 132.18 133.72 1945 100.92 101.97 99.7 103.31 104.3 1946 102.64 105.14 101.39 105.04 105.14 1947 106.08 107.91 104.40 107.32 107.13 1948 116.18 . 118.18 112.85 115.35 113.94 1949 110.25 112.72 106.61 109.11 108.17 1950 101.53 104.36 97.7 100.00 100.84 1951 131.70 135.66 124.13 126.59 127.86 1952 138.98 143.07 137.19 133.97 136.95 1953 138.83 142.96 132.09 133.06 138.47 1954 108.38 111.08 102.86 103.86 109.21 1955 124.98 128.70 119.11 119.39 128.63 1956 139.65 145.73 132.78 134.59 145.23 1957 121.40 123.54 115.02 114.09 123.54 1958 131.41 133.39 123.14 121.84 134-46 TABLE X RELATIVE CHANGES, M . P . P . FACTOR INPUTS, CANADIAN AGRICULTURE, 1926-58; 1926 = IOO (1) (2) (3) U) (5) (6) (7) SHIFTING FUNCTION STATIONARY FUNCTION M . P . P . MTPTPT MTPTPT M . P . P . M . P . £ M . P . P . M . P . P . °2 C 2 *2 L 2 C 2 *2 L 2 1926 100 1927 100.3 1928 106.1 1929 81.7 1930 84.8 1931 71.3 1932 97.2 1933 86.9 1934 84.4 1935 89.1 1936 77.0 1937 66.2 1938 70.3 1939 95.0 1940 84.3 1941 74.1 1942 97.9 1943 64.0 1944 71.3 1945 53.1 1946 52.9 1947 55.8 1948 63.2 1949 62.9 1950 61.3 1951 83.8 1952 85.0 1953 88.0 1954 69.0 1955 83.4 1956 93.3 1957 77.9 1958 85.6 100 100 98.3 9 9 . 9 1 0 2 . 0 1 0 2 . 8 81 . 1 81 . 3 84 . 5 9 2 . 5 9 3 . 3 82 . 8 1 4 6 . 6 1 2 4 . 6 131 . 0 1 1 2 . 1 128 . 4 115 . 1 131 . 6 1 2 2 . 8 1 1 2 . 9 113.4 9 5 . 5 1 0 3 . 8 111 .1 1 2 3 . 3 1 3 4 . 6 151 . 5 1 2 0 . 0 1 4 0 . 6 9 9 . 8 1 2 3 . 3 1 2 3 . 7 163 . 7 7 3 . 8 1 0 1 . 0 78 . 4 1 1 2 . 9 5 8 . 2 8 3 . 6 5 5 . 4 8 4 . 3 5 4 . 0 8 6 . 4 46 . 6 9 7 . 5 50 . 8 9 7 . 1 4 7 . 1 9 4 . 4 56 . 4 1 2 0 . 6 5 8 . 1 1 2 9 . 0 5 9 . 2 1 2 9 . 5 4 7 . 1 1 0 3 . 7 5 5 . 2 1 2 1 . 8 60 . 6 133 . 1 5 0 . 4 1 1 4 . 0 54.1 1 2 4 . 3 100 100 106.5 102.4 108.0 104.5 83.0 80.9 88.0 86.0 64.0 68.1 74.8 87.0 65.1 78.0 68.9 79.3 77.8 88.5 77.0 85.0 74.5 79.5 89.8 92.3 114.6 127.7 123.1 126.3 126.7 116.2 205.2 162.1 157.4 110.6 175.5 134.5 141.8 104.8 146.8 112.6 153.4 114.7 167 . 1 128.0 157.3 122.5 145.2 113.5 193.5 142.6 209.1 147.3 211.0 149.6 162.7 116.9 191.8 135.0 221.4 150.2 191.7 126.1 210.8 130.2 100 100 98.5 105.9 97.8 111.0 74.7 87.0 79.1 93.7 68.9 73.4 96.3 94.1 88.2 80.6 90.6 82.1 98.8 87.8 92.6 80.5 85.1 74.2 99.2 86.6 121.3 109.8 119.3 109.5 101.8 112.3 139.4 176.1 93.3 128.7 108.0 138.3 80.7 110.2 79.9 112.8 76.9 121.7 81.4 136.6 75.6 134.3 66.0 133.4 80.3 188.1 82.5 207.9 80.0 217.3 62.6 170.1 70.6 211.0 75.6 248.6 65.6 212.3 70.2 244.1 of inputs may be compared with the results of those studies which make use of a different method. Since changes in the marginal productivities are equivalent to changes in the average productivities when there is no change in the shape of the production function, the data presented in Columns 5, 6 and 7 of Table X, and which represent the indices from which may be observed changes in the marginal productivity when the stationary function is used, may also be regarded as equivalent to the changes in the average productivity of the respective factors. A comparison of the changes from the base period, of Columns 1, 2, A with those of Columns 5, 6 and 7 respectively is analogous to comparing the changes of the marginal productivities of the respective factors with the changes in the average productivities. Therefore these columns do not only present the changes in the respective marginal productivities with the use of the stationary function. The inferences which were made in the body of the thesis with respect to the former comparison, (that i s , comparisons of the changes in the average productivity of factors with those of their marginal productivities), are therefore applicable here. 

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