Resource productivity and returns on 160 Acre farms in North-Central Iowa (A production function study of marginal returns on farms with fixed plants)

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1 Volume 31 Number 412 Resource productivity and returns on 160 Acre farms in North-Central Iowa (A production function study of marginal returns on farms with fixed plants) Article 1 July 1954 Resource productivity and returns on 160 Acre farms in North-Central Iowa (A production function study of marginal returns on farms with fixed plants) Earl O. Heady Iowa State College Follow this and additional works at: Part of the Agriculture Commons, Economics Commons, and the Sociology Commons Recommended Citation Heady, Earl O. (1954) "Resource productivity and returns on 160 Acre farms in North-Central Iowa (A production function study of marginal returns on farms with fixed plants)," Research Bulletin (Iowa Agriculture and Home Economics Experiment Station): Vol. 31 : No. 412, Article 1. Available at: This Article is brought to you for free and open access by the Iowa Agricultural and Home Economics Experiment Station Publications at Iowa State University Digital Repository. It has been accepted for inclusion in Research Bulletin (Iowa Agriculture and Home Economics Experiment Station) by an authorized editor of Iowa State University Digital Repository. For more information, please contact digirep@iastate.edu.

2 Resource Productivity and Returns On 160 Acre Farms in North-Central Iowa (A Production Function Study of Marginal Returns on Farms With Fixed Plants) by Earl O. Heaely Department of Economics anel Sociology AGRICU.. TURA.. EXPERIMENT STATION, IOWA STATE CO... EGE RESEARCH BULLETIN 412 JU.. Y, 1954 AMES, IOWA

3 CONTENTS Page Summary Objective of study and method of analysis Method of analysis Sample Elasticity coefficients and scale returns Resources used and factor productivity Equilibrium test for differences between marginal returns and prices of resources..., Returns to labor with variable quantities of resources Resource quantities and returns by strata Machine service-labor substitution Productivity of resources used for livestock Marginal productivity and resource prices Allocation of labor and capital between crops and livestock Productivities for varying quantities of labor Inputs and productivity by labor-capital strata Productivities for 240-acre farms Prices for products and resources Limitations of method Appendix

4 SUMMARY This study is one in which production functions have been derived for a sample of 160-acre farms; a few statistics also are included for 240-acre farms. The elasticities or regression coefficients are acceptable at conventional probability levels for both a crop function and a livestock function. For crops, marginal returns have the following values for mean use of resources: labor, $78 per month; crop capital, $1.08 per $1 used; machinery expenses, $0.93 per $1 used. For livestock, the marginal returns are: labor, $218 per month; capital expenses, $1.04 per $1 used. Further tests show that, with the exception of livestock labor, farmers as an average for the sample used for this study are using resources in quantities to maximize profits. Both labor and capital resources were used in amounts so that the added return was equal to the added cost of a unit of resources. Also, the farmers, as an average, evidently had allocated their labor and capital between crop and livestock enterprises in a manner to give the same return on the last unit of labor used for each-a condition necessary for the maximization of profits. However, farms falling in different capital and labor groups had returns differing greatly from the average for all farms. Farmers using large amounts of labor with little capital realized a low return on their labor, although returns on capital were high. On farms with large amounts of capital and small amounts of labor, returns on funds were low, while labor returns were high. In livestock investment, it appeared that some farms were using too little labor with a given capital investment; better care and management of the same number of animals would give greater returns. The statistics of this study provide the following inference for farms with a small amount of capital: Small amounts of capital give greater returns when invested in crop production than when invested in livestock production; for larger amounts of capital, returns are greatest if funds are invested in livestock. Comparison of substitution rates for machine capital and labor provided predictions showing numerous quantities of the two resources which could be used in producing the same output; costs could be reduced by substituting machine services for labor up through an annual expense of $1,400 for machine services. The type of analysis used in this study provides some extremely useful results in guiding farmers in organizing

5 1068 their farms for maximum profits and in allowing certain suggestions on resource efficiency from the standpoint of the consuming public. However, it does have certain limitations: One limitation is that it shows resource returns for only broad categories of capital; it does not allow predictions for capital and techniques representing particular crop or livestock production practices. However, budget analysis can be used to supplement the production function analysis in solving problems of this kind. Also, the type of function used, like any other particular algebraic model, cannot take into full account the technical relationships of supplementarity and complementarity which exist between products and resources. Finally, while problems of sample homogeneity raise questions of the types of functions traced out, these same problems are inherent in other types of analyses made from sample or record farms.

6 Resource Productivity and Returns on Acre Farms in North... Central Iowa (A Production Function Study of Marginal Returns On Farms With Fixed Plants) By EARL O. HEADY The major management task of farmers is to organize their limited resources into the most profitable operating unit. Ordinarily, the goal in the farm business is to maximize returns for the business as a whole j it is not a goal of maximizing income for one particular segment such as cattle, hogs, chickens, soybeans, corn, soil or labor. Each different practice and crop or livestock enterprise is an activity in which the farmer can invest his capital and labor. Where funds are limited, the farm manager must decide which practice or enterprise will give the greatest return j if resources and funds are always invested where their marginal returns are greatest, returns for the farm as a unit will be at a maximum. Profit maximization, then, is an attainable condition only if the farmer has some rough notion of the marginal returns of each possible practice or enterprise. By the term "marginal" we refer to the added return forthcoming as each added unit of resource is put to a specific use. Farm profits can be at a maximum only if the following marginal (added) conditions are attained: 1. The marginal rate of substitution between any pair of crop or livestock enterprises is equal to the price ratio of the two enterprises (or is equal to the net price ratio -the per unit price less the per unit cost-if costs differ between the enterprises and resources are not fixed in quantity). 2. The marginal rate of substitution between any pair of resources, representing different practices or techniques of production, must be equal to the price ratio of the two resources. 3. The marginal rate of transformation, the marginal product of the resource, must equal the resource/product price ratio for each particular product; a corollary statement is this: The marginal cost of the last unit of product must equal its price or marginal return.

7 The marginal conditions above must hold true between two activities in time, with price ratios referring to discounted quantities, if the present value of future returns is to be at a maximum. These conditions can be stated alternatively for a farmer with limited capital: Each unit of resource must, under the competitive conditions of farming, be used where its marginal value productivity is greatest; it must be used where it adds the greatest amount to gross income. When a farmer has limited capital, he should substitute one resource or practice for a second if the marginal rate of substitution of the first for the second is greater than the price of the first divided by the price of the second; he should substitute one enterprise for another if the marginal rate of substitution of the first for the second is less than the price of the first divided by the second. Given these necessary conditions for farm profit maximization, farmers can attain greatest incomes only if the marginal quantities are known at least in a rough manner. While most farmers do not know exactly the conditions outlined above, they do know the principles in a "rule-of-thumb" manner. Then, too, many are prevented from maximizing profits because plans must be made in advance of production. Since marginal quantities, in terms of prices and yields, must be "guessed" or "estimated," profits are seldom at a maximum. However, increased knowledge of marginal returns and resource productivity is still needed for guiding farmers in the most efficient use of resources. These data can be obtained from farm budgets, from physical research, from empirical production functions such as those of this study or from other methods. OBJECTIVE OF STUDY AND METHOD OF ANALYSIS This study has been made to help provide greater knowledge of resource returns and marginal productivity in Iowa agriculture. As a marginal productivity study, it shows the added return forthcoming from use of different quantities of resources for a particular sample of farms. It also shows the rate at which selected resources substitute for each other. Finally, it tests whether farmers, as an average for the sample, were using quantities of different resources in a manner to maximize their returns under the prices and yield conditions of a particular year. The data obtained in this study are useful in recommendations to farmers in management of their farms; they

8 1071 are useful in inferring the degree of economic efficiency found in a particular sample. Finally, they can be used as a basis for certain policy recommendations. The results are presented in the following pages in a semi-technical manner for purposes of brevity. They can be interpreted with simplicity by extension personnel and other economists for use in meetings with operating farmers and program administrators. METHOD OF ANALYSIS The statistical procedure of this study revolves mainly around regression analysis in the estimation of production functions. Certain arithmetic averages also are presented for the farm sample. The production functions employed are of the Cobb-Douglas type, Y = cc Xl~l Xl' X3~3, where Y refers to the value of production and the X's refer to specified resources. In this function, the f3 which serves as the exponent for each resource is the elasticity of production; it indicates the percentage by which the value of product increases with each I-percent increase in use of the particular resource. If the sum of the f3's is greater than 1.0, an increase in all resources by 1 percent will increase the value of output by more than 1 percent; a sum equal to 1.0 means constant returns; while a sum of f3's less than 1.0 indicates that the value of output increases by a smaller proportion than the increased input or use of resources. In the analysis which follows, two production functions, one for crops and one for livestock, have been derived. The crop function is of the form Ye = CC LeI Mom Co" where Ye refers to the value of crops produced, Le refers to the quantity of labor measured in months, Me refers to value of all machinery expenses or inputs of the particular year (including repairs, depreciation, fuel, oil, etc.), and Co refers to all annual expenses on crops (including seed, fertilizer, lime, seed treatment, etc.); labor inputs are measured in months and machinery and crop inputs are measured in dollars. The livestock function is of the form Y\ = cc L\I C\" where Y 1 refers to the value of livestock output during the year (sales + home used + appreciation of young and fattening stock) while L\ is labor in months used on livestock, and C 1 is all annual capital inputs, measured in dollars, used on livestock. SAMPLE The sample upon which this study is based was drawn from the North-Central Cash Grain Area of Iowa. Soils of the Clarion-Webster association predominate in the area;

9 1072 only farms with all land tillable were included in the study. As a further step in introducing homogeneity into the sample, production functions were derived only for 160-acre farms (farms falling in the range of 140 to 169 acres). The 160-acre farms include 41 from a 1950 survey and 67 from a 1951 survey, giving a total of 108 farms. These farms were included in two random samples from the entire area in which farms of all sizes were enumerated-except that only 160-acre units were included in the current study. The physical inputs and outputs refer to the particular year of each sample, but all prices used are those of Inferences in this study, therefore, are restricted to 160-acre units; land input is considered as a fixed resource in the production functions presented later. ELASTICITY COEFFICIENTS AND SCALE RETURNS The value of the regression coefficients or elasticities for the two production functions are presented in table 1 along with related statistics. All but one of the elasticities are significant at the 5- or I-percent level of probability; the coefficient for crop service capital was significant at a probability level approaching 5 percent and is, with recognition of a slightly wider probability range for inferences, accepted for the analysis which follows. Each of the elasticities for crops or livestock is less than 1.0-indicating that diminishing returns hold true for the particular re- TABLE 1. ELASTICITIES AND RELATED STATISTICS FOR BASIC FUNCTIONS. Item Crop function Livestock function Yalue of constant a: Yalue of elasticities' I c m Sum of elasticities Yalue of t for elasticities' I 1.98~ 3.65t c t m 3.89t The figure for c refers to crop capital for crops and to all capital for livestock; m refers to machine capital for crops but this category of inputs has been included with all capital for livestock. Probability level for t's: t l>p>o :l:5>p>1 10>P> 5

10 1073 source. A 1-percent increase in input or use of the particular resource results in an increase in value of production by less than 1 percent; the return per unit of the particular resource will decline to lower magnitudes as more of the resource is used. For labor used on crops, for example,a l-percent increase in labor results, as an average over the sample, in an increase of only 0.07 percent in the value of crop production. For crops, the sum of the elasticity coefficients differs significantly from 1.0-indicating diminishing returns as more and more of the various resources are used for crops on a given land area.,since all of the crop acres were in cultivation on all farms in the sample but different quantities of capital and labor resources were used on a given acreage, diminishing returns are indicated for each resource and all resources in combination. On the other hand, the sum of the elasticities for livestock does not differ significantly from 1.0. As an average for farms in the sample, more resources can be put into livestock with returns as great as the mean quantity now being realized. While diminishing returns might be expected on the 160-acre farms if they carried an extreme amount of livestock, few farms approached programs of this intensity. RESOURCES USED AND FACTOR PRODUCTIVITY The average value of production, the mean quantity of resources used and the marginal productivity of crop resources at the mean are shown in table 2. The marginal product figures have this meaning:1 "one more unit" of the particular resource, with its input and that of other resources at the mean of the quantities shown in the top of the table, will add the indicated quantity to total value of production. An increase in crop services will add to total value of production at the rate of $1.08 for each added $1 input of capital services; a $1 input in crop capital services returns itself plus $0.08 in profit. The marginal product per month of labor is $77. In other words, the use of "one more month of labor" beyond the mean quantity per farm in the sample, would add this amount to total value of product. The computed marginal product of machine capital services is $0.93, a marginal return of this amount for each $1 of annual input or expense. 1 The marginal value production figures are the derivatives of value of total product In respect to the particular resource with all resources at mean inputs, from the production functions. Hence, the marginal product ClY equation for crop labor Is ill :::: L- "l71.

11 1074 TABLE 2. MEAN QUANTITY OF RESOURCES USED ON CROPS. MARGINAL AND GROSS AVERAGE PRODUCTIVITY OF SPECIFIED RESOURCES. Item Average value of production per farm Average Input per farm: Crop services Machine services Labor Marginal products at resource means: Crop services ($ /$) Machine services ($ /$) Labor ($/mo.) Gross average products at resource means Crop services ($/$). Machine services ($/$) Labor ($/mo.) Land ($/acre) Amount $6452 $ 334 $ mos. $ 1.08 $ $ $ $ 4.82 $1041 $ EQUILIBRIUM TEST FOR DIFFERENCES BETWEEN MARGINAL RETURNS AND PRICES OF RESOURCES While these return figures may appear low, except for crop services, two things should be remembered: First, the marginal returns are measured with resource inputs at the mean. Because of the diminishing-return nature of the productivity coefficients, marginal returns will be greater than the indicated amounts for labor inputs smaller than 6.2 months, for crop service inputs smaller than $334 and for machine service inputs smaller than $1,260. Second, the estimates are made from a set of data involving sample variance, and, while probability tests suggest that the elasticity coefficients differ significantly from zero, we may inquire whether they differ significantly from a level necessary to give marginal productivities equal to the market price or cost of each of the resources. In other words, does the marginal return of $77.87 per month of labor differ significantly from $132.44, the market wage rate (without board) for labor in northern Iowa; do the capital returns of $1.08 and $0.93 differ significantly from the $1.06 cost ($1 principal plus 6 percent interest) for crop service and machine service capital respectively? As a test of these possibilities, the elasticities of production necessary to give marginal products equal to the market cost of the resources have been computed. Probability tests have been made for the differences between the elasticities derived in the study and those necessary to give marginal

12 1075 products equal to the market price of the resources.2 statistics for this test are given in table 3. The TABLE 3. TEST OF DEPARTURE BETWEEN MARGINAL RESOURCE RETURNS AND MARKET,PRICE OF RESOURCE. Resource Value of elasticity to give marginal product equal to market price of resource Value of t Crop services Machine services Labor Probability level: *p< 50 tp' < * * t Since none of the t values are significant at the 30-percent level of probability, we cannot say that the marginal returns per month of labor, as an average for farms in the sample, differed significantly from the market wage rate of $ per month for labor or of $1.06 per $1 input for crop or machine capital. While the condition need not hold true for all farms in the sample, inferences based on the above statistics are these: Farmers were, on the average, maximizing returns under the particular prices and yields of the year; efficiency in production had been attained in the sense that the cost of resources approached the added return for more of these resources used beyond the per farm mean. These results seem reasonable in view of the fact that farmers in northcentral Iowa have a capital position about as favorable as those of any other area in the United States. Also, neither of the years included were outstanding in crop yield. Had crop yields been equal to the lo-year average, marginal returns on resources would likely have been significantly greater, given the particular price of the year, than the cost or market price of the resources to the farmers. (Productivity or return of resources would have exceeded the cost of the resources.) The elasticity, e'. necessary to give a marginal product for mean resource inputs equal to the market price of the resources has been computed as e' =PR/Y where P is the market price ($ for labor and $1.06 for capital) for the particular resource, R is the mean input of the resource and Y is the mean value of output. 'the value of t has been computed as t = e - e' where e is the elasticity or regression coefficient derived from Sb the sample and Sb is the standard error of estimate.

13 1076 RETURNS TO LABOR WITH VARIABLE QUAl'l'TITIES OF RESOURCES The productivity figures in the previous section show marginal returns when all resource inputs (quantities used) are at the sample mean. Because of the diminishing-returns nature of the elasticity coefficients, returns for this quantityof resources are expected to be lower than for smaller quantities; larger quantities of resources are expected to have smaller marginal products than indicated at the mean. Table 4 shows marginal returns for different quantities of crop labor, with crop and machine capital services set at different levels. With labor input at 4 months and capital use at the mean of the sample, the marginal product of 1 month of labor is $115; with labor input at 8 months, marginal labor product is only $61. TABLE 4. MARGINAL PRODUC1'IVITY OF LABOR IN CROP PRODUCTION WITH CAPITAL RESOURCES AT DIFFERENT LEVELS. Months of labor Marginal return per month of labor with input of other resources at: Average for One-half the 50% greater all farms average for than the all farms average for all farms 2 $ $ $ Mean The predicted effect of the quantity of capital on labor productivity and returns is illustrated across the rows of table 4. With labor input at 4 months, it is predicted that a farm with capital equal to only one-half the sample average would have a marginal return to labor of only $98- approximately 10 percent less than a farm with average capital. With capital services 50 percent greater than the sample mean, labor returns would, with input at 4 months, increase to $127. This "interaction" between farm resources is highly important in management programs by individual farms and for educational and policy programs. From the standpoint of the farmer, this "interaction" means that the return to one resource, labor in this case, will be low if he has insufficient quantities of other resources to go with it. From the standpoint of educational and action

14 1077 programs, it means that emphasis on one resource alone, (i.e., a practice or technique which is represented mainly by one resource) cannot have maximum efficiency. The productivity. of one resource or practice depends on the quantity and form of other practices or resources with which it is combined. Tables 5 and 6 indicate marginal returns for crop and machine services respectively, with resources other than the one examined "fixed" at various levels. Returns are extremely high for small crop-service inputs under each column. However, they decline quite rapidly beyond the mean quantity of crop capital services. The column with machine and labor services equal to one-half the sample average suggests low returns to crop capital when labor and machinery are available in small quantities. Crop capital returns are maintained at a relatively high level with large inputs of labor and machine services (i.e., those 50 percent greater than the sample average in table 5), but the ad- TABLE 5. MARGINAL PRODUCTIVITY OF CROP CAPITAL SERVICES WITH QUANTITY OF OTHER RESOURCES AT SPECIFIED LEVELS. Marginal return per dollar input of crop services with input of other resources at: Input of crop services Average for ($) / One-half averagc all farms for all farms I I 50 % greater than average for all farms 100 $3.36 I $2.82 I $ I Mean I I 0.62 I 0.81 I TABLE 6. :MARGINAL PRODUCTIVITY OF MACHINE CAPITAL SERVICES IN CROP PRODUCTION WITH QUANTITY OF OTHER RESOURCES AT SPECIFIED LEVELS. ;\Iarginal return per dollar input of machine services with input of other resources at: Input of machine services Average for / One-half average /50% greater than ($) all farms for all farms the average for all farms 700 $ $1.38~ I $ , , I 0.95fi1 1.09n 1, n Mean 0.93 I , I I , I I I

15 1078 dition to returns would not be great enough to support labor and machinery at this level of use. Farmers could not afford to increase labor inputs and machinery investment by 50 percent to increase the marginal return of crop services (with input of the latter at the mean of $334) from $0.93 to $1.08. Similarly, while machine service returns are increased when used with more capital services and labor, 50 percent more of the latter two resources could not be justified in increasing mean marginal return of machine capital services from $0.93 to $1.08 (when input of machinery is at the mean of the sample). Errors of inference may, of course, be greater for productivity estimates based on resource inputs away from the mean. It is doubtful that any single algebraic model adequately describes the complex agricultural production process with its ranges of complementarity and competition between resources and products. The estimates provided above, for inputs at other than the mean, therefore should be looked upon as those for the particular algebraic form of model; two algebraic forms of production functions may give quite similar estimates at the mean but quite different figures for inputs at the extremes. These statements also apply to the predicted returns of the next section. However, the analysis of a later section suggests that the function used appears to conform with the algebraic nature of the data throughout various strata of the sample. RESOURCE QUANTITIES AND RETURNS BY STRATA The data in table 7 show selected input and output figures for the farms stratified by labor and capital.s Each stratum or cell of the table contains 12 farms-one-ninth of the total sample. These figures have been computed to suggest the manner in which total production and resource returns differ for 160-acre farms using different quantities of resources. Any movement down a column represents an increase in the per-farm use of capital, with labor held approximately constant. A movement across a row represents an increase in labor with "constancy" in the quantity of capital; a di. agonal movement from northwest to southeast represents an increase in both capital and labor. It is apparent that the use of (1) more of one resource alone (a movement down a column or across a row), or (2) more of both labor and capital together (movement down Farms were first divided Into three labor groups: each of these were then divided Into three capital groups. Capital groups were broken down on the basis of the sum of machine and crop services.

16 1079 diagonally) increases total value of crop production. However, this increase in value of production is less than proportional to the increase in the quantity of resources used; farmers with a limited acreage encounter diminishing returns regardless of the resource which is increased. These relationships are consistent with the diminishing-returns figures predicted from the production function in previous tables. With capital approximately constant, the average gross product per unit of labor declines as we move across the row of any capital group; the decline is relatively rapid. On the other hand, as we move down a column within a labor group, we have the equivalent of adding capital on a given farm with a fixed amount of labor; in this case, the average gross product of labor increases. These findings of the predicted changes in resource productivity in previous sections are consistent with these average conditions' actually found in each strata of the sample. Gross capital returns decline similarly within a labor group-indicating diminishing returns to capital as it is increased relative to a fixed amount of labor; it has a tendency to increase as labor is increased within a capital group. TABLE 7. INPUT OF LABOR AND CAPITAL SERVICES AND GROSS PRODUCTIVITY RATIOS ON CROPS. Capital service Labor Input group input group Low labor Medium labor, High labor Low capital I $5775 $6221 I $ mo mo., 8.29 mo. $ 198 $ 215 $ 406 $ 757 $ 888 $ 924 S 9;;5 ~1103 F 330 $ I 764 $ 5.47 $ 5.90 $ 4.76 $6249 $6323 I $ mo. S.83 mo mo. Medium capital $ 250 $ 314 I $ 278 $1252 $1183 $1502 $ $1460 $1090 i 741 $ 4.16 $ $6894 I $7062 I $ mo mo mo. High capital $ 419 $ 497 $ 448 $1779 $1513 I $1772 $2198 I f 2010 $2220 p I t I $ The figures in each cell are, reading from top to bottom: value of crop production; months of labor; dollars of crop capital services; dollars of machine capital services: sum of crop and machine capital services: gross labor product per month of labor and gross product per $1 machine and crop services. (Gross labor productivity Is obtained by dividing value of crop production by months of labor; crop capital productivity Is obtained by dividing gross product by sum of Inputs of crop and machine services. Figures are per farm.means.)

17 1080 The productivity figures of table 7 are gross averages alone. As averages, they can decline only as marginal returns of the particular resources decline. To provide an estimate of the marginal returns, as based on the particular production function employed, for resources used in the proportions of each of the labor-capital strata, the figures of table 8 have been derived. The first figure in each column is the total value of product derived from the production functions presented previously; the two total value products are quite similarthus giving support to the particular algebraic function applied to this sample and used in deriving marginal return figures. The second figure is the marginal return per month of labor, while the third and fourth are returns figures for crop and machine services respectively. The marginal returns to labor show exactly the same pattern as the gross average products in table 8. The capital services show a somewhat similar pattern, but the change between cells is not so consistent. Gross average products in table 7 are for machine crop services aggregated into one input column; in table 8, marginal returns are computed for each category of resource separately. TABLE 8. PREDICTED TOTAL PRODUCT AND MARGINAL RETURNS OF LABOR. CROP SERVICES AND MACHINE SERVICES BY LABOR CAPIT AL STRATA. Labor input group Capital input Low labor ~Iedlum labor High labor group $ I $ I $ Low capital I I I I 1.21 I 1.24 Medium capital I I I I High capital I 0.74 First figure in each column of each cell is predicted total value of crop production; second, third and fourth are the marginal returns for labor, crop services and machine services, respectively. These figures suggest that farms in certain of the strata use resources in an "unbalanced" manner, if profit maximization is the criterion. Those using a small quantity of all resources (i.e., the northwest cell of table 8) have a high marginal return on capital resources; returns also are high for labor (even when we consider that our previous I

18 1081 test showed that, at mean labor inputs, the marginal return of labor did not differ significantly from the wage rate of $132). These farms could borrow more funds for investment in machinery, fertilizer and seed; the return would be greater than the short-run interest rate of 6 percent.4 Farms using a large amount of all resources (the southeast cell of the table) have a relatively low return on all resources; the computed marginal return is less than the cost of the resources. One possibility is that these farms simply are not using efficient techniques or practices and therefore could change the form of their capital resources and the use of their labor. In terms of the data and functions, the more logical possibility is that the quantity of resources used by this one-ninth of the farms is so great as to give very low marginal returns. Machine capital services have a low marginal return in each of the high capital strata. It is possible and likely that many of the farms in this group have driven machine investment beyond the most profitable level. Investment in machinery to a point where the return is less than the cost may be made to allow farm work to include less drudgery and more leisure; maximization of family satisfactions rather than profits then is the goaj.5 MACHINE SERVICE LABOR SUBSTITUTION Using the original crop production function as a basis for estimating, the data of table 9 have been derived. These TABLE 9. MACHINE LABOR SUBSTITUTION IN CROP PRODUCTION. Value of labor replaced Combination of rna by $100 in annual chine service and Marginal rate of machine services at labor to produce substitution of average crop out machine services 50% put of $6,545 for labor (mos.) greater % Labor replaced by 1951 than wage $100 machine wage wage rate Input of Quantity of service inpu t rate rate of machine labor in of 1951 services months 1951 ($) (mos.) (mos.) ($) ($) I I ($) I I 277 I I I 62 I 21 'For most of the extrcme cells, the computed elasticity necessary to give marginal resource returns equal to the market prices of the resources with inputs at the means of the cells differed significantly from the derived elasticity of the production function. S The costs of all electricity and electrical equipment is included in crop machine services. These items could not be separated readily.

19 1082 are substitution rates which provide estimates of the rate at which machine services and labor replace each other.6 The first two columns of table 9 show numerous combinations of the two resources which might be used in producing the average per-farm crop production of $6,545. In other words, this value of production could be attained with months of labor and a $1,000 annual machinery expense, 6.99 months of labor and $1,200, 4.78 months and $1,400, or any other of the combinations shown. (The upper and lower figures of the two columns are extremes, and, while in the range of observations, they still extend too far for the particular algebraic function; they are included for illustrative purposes.) Column 3 of table 9 shows the marginal rate at which machine services substitute for labor. The figures are computed on the basis of derivatives "at exactly" the combinations indicated in columns 1 and 2; they are not averages between combinations. These figures show declining rates of substitution of machine services for labor; at larger inputs of machine services, the amount of labor replaced by $100 in machine services becomes less and less. As column 4 shows, $100 in machine services is predicted to replace a $359 value of labor (2.71 months at $ per month) when machine service input is $1,000 and labor input is months. Of the combinations shown, it is profitable to substitute machine services through a combination including $1,400 in machine expenses and 4.78 months of labor; costs of the given output of $6,545 can be lessened since the value of labor saved is more than the $100 machine services added. With a 50-percent increase in wage rates, machine service costs remaining the same, machine expenses could be extended through $1,600; whereas they could be extended only through $1,100 with wage rates equal to one-half those of It is of interest that, even with relatively large changes in wage rates (over the range $66 to $198, or from 50 percent to 150 percent of $132), the most profitable machine-labor combination would, within the combinations shown, vary only over a $500 range for machine inputs. In other words, a relatively small machine input is extremely profitable, regardless of wage rates. However, once a complement of These figures are derived from the original function by an isoproduct contour equation. L == [-Y-]...!...-. where the symbols are the same as ",c-:\rm 1 previously indicated except that the subscripts have been omitted. The marginal substitution rates In column 3 thus are the derivative of this dl.1798l equation and have the numerical value: dl\i =.0729;\1

20 1083 machines for tilling, cultivating and certain harvesting operations has been attained, further additions to machine expenses make only limited (a) savings in labor and (b) addition to income. PRODUCTIVITY OF RESOURCES USED FOR LIVESTOCK The farms included in the sample produced a greater average value of livestock than crops. They used considerably more resources in doing so. Even with these large labor and capital inputs, labor returns still were high for livestock-whether the return was measured in average or marginal terms. These figures are in line with the earlier indication of constant returns to scale in livestock production. The average gross productivity of labor used on livestock was $1,126, while the figure for crops was $1,041. Although with analysis of variance tests, the difference in gross labor productivity is not statistically significant between crops and livestock, it is economically important that loa months of labor used on livestock production can return as great an average product as 6.2 months on cropsa much smaller labor input. An average product for labor on livestock as great as that for crops, even with a much greater input, would suggest a greater marginal product for the former enterprise. This fact is indicated by the mean marginal return of $218 per month of labor in table 10. The marginal return per $1 capital in table 10 is of a magnitude comparable to that for crop services in table 2. TABLE 10. MEAN VALUE OF LIVESTOCK PRODUCTION, AVERAGE RESOURCE INPUTS, PREDICTED MARGINAL PRODUCTS AND AVERAGE GROSS PRODUCTIVITY OF RESOURCES. Item Amount Average value of production per farm Average Input per farm: Capital services Labor Marginal products at resource means: Capital services ($/$) Labor ($/mo.) Gross average products at resource means: Capital services ($/$) Labor ($/mo.) $10,531 $ 9, mo $ 1.17 $ 1,126 MARGINAL PRODUCTIVITY AND RESOURCE PRICES We may now ask the question of whether, considering sample variance and the fact that our inferences must be

21 1084 based on probability statements, these marginal resource productivities differ significantly from the market prices of the same resources. In other words, does the marginal capital return of $1.04 differ significantly from the $1.06 market cost of capital or does the marginal labor return of $218 differ significantly from the $133 wage rate? If the answer is "yes" in both cases, we would suppose that the farmers in the sample were, as an average, using too much capital and too little labor. As the probability test in table 11 shows, however, the marginal return of capital definitely does not differ significantly from the market price of borrowed funds. Given the type of sample data, it does appear that the marginal labor return of $218 differs significantly from the wage rate of $132. TABLE 11. TEST OF DEPARTURE OF MARGINAL RESOURCE RETURNS AND MARKET PRICE OF RESOURCES. Resource Value of elasticity to give marginal product equal to market price of resource Value of t Capital ' Labor t 'P> 50 tlo >P > 5 This difference for labor but not for capital seems difficult to explain. It would mean that, with the same capital investment in livestock, farmers could use more labor and add to total gross returns and to net profits. This type of adjustment would perhaps mean better care for existing livestock. Hypotheses as to why farmers have not added sufficient labor to attain these possible ends might include these: Crop and livestock production found on the farms, as an average, employed all of the family help available; besides a small amount of seasonal work for crops, it is difficult to hire an added man for only a small amount of work; the family does not care to have an extra person around; or the farm does not have a hired man's house. An alternative proposition, however, is that differences as great as between the derived and "computed" elasticity coefficients could have arisen by chance, but differences of this magnitude in the two quantities seem unlikely by chance. ALLOCATION OF LABOR AND CAPITAL BETWEEN CROPS AND LIVESTOCK While the computed marginal product for capital inputs on livestock are quite similar to those for crop capital serv-

22 1085 ices, we wish to know whether the "apparent" large differences in marginal labor productivity differ significantly. If the marginal returns of crop service capital are significantly TABLE 12. COMPARISON OF MARGINAL RESOURCE PRODUCTS BETWEEN CROP AND LIVESTOCK ENTERPRISES. Capital Resource Labor op> 50 tio>p> 5 Value of elasticity coefficient for livestock necessary to give marginal return in livestock production as in crop production Value of t 0.33* 1.70t greater than those for livestock capital, farmers have not, as an average, allocated given funds between crops and livestock in a manner to maximize profits; they could always withdraw funds from the former, add them to the latter and get a greater return. If the differences are significant for labor, profits could always be increased by shifting some of this resource from crops to livestock. In order to make probability statements in these respects, the "computed elasticities" in table 12 have been derived. These are the magnitude of elasticities necessary to give a marginal return of capital services and labor in livestock equal to those in crop production, when inputs are of the size indicated previously for livestock. The t values shown here have been computed and tested in a probability sense.7 As these statistics show, we can only infer that, as an average for the sample, farmers have allocated capital resources optimally between crops and livestock. Marginal return on capital does not, as near as can be said in a probability framework, differ significantly, and capital has been divided between the two major enterprises in a manner to give equal income on the last dollar used for each. The same cannot be said for labor, however. It appears that the marginal return for labor used on livestock may be significantly greater than that used for crops.,\\x. 1 'l'he computed elasticity, e'. again is e' = e. =-=- where X refers to the Y.X, mean quantity of the particular resource. e. refers to the elasticity for livestock and Y is the mean product for crops (subscript c) and live stock (subscript I). The value of t has been computed as t == e - e Y,x./fex, "' I ~e' - [y'xj' "lex::!;1' where s. is the standard error of estimate for the resource used in crop production and s, is the standard error in livestock production.

23 1086 If it were possible, returns might be increased by shifting a slight amount of labor from crops to livestock production. However, this opportunity may not always exist. The production functions used (or any others which might be used) cannot express supplementarity between enterprises. Crop and livestock enterprises are supplementary in the use of some labor over the year; labor used for livestock in the winter cannot be used for crop production in the summer, and the labor used on crops in the summer cannot be transferred to winter livestock production.. Hence, some difference in labor productivity is possible because of supplementary relationships between the two enterprises; this supplementary labor would not be reallocated between enterprises even with differences in returns. Other possible reasons why labor returns are not equated between the two activities might include (1) lack of knowledge and (2) the fact that, for farmers with limited access to funds, use of labor for livestock often entails a greater capital investment than use of the same labor for crops. PRODUCTIVITIES FOR VARYING QUANTITIES OF LABOR Since the returns functions for capitai suggest constant productivity, we use taole 13 to compare the productivity of labor and capital used for livestock when both are changed in the same proportion. The levels of input are expressed as percentages of the sample means. Because the sum of the elasticities is slightly greater than 1.0, the productivity of the resources increases with total level of use. As mentioned previously, however, the sum of elasticities does not differ significantly from 1.0, and, therefore, we can only infer that the marginal returns remain near the $1.04 level for capital and the $217 level for labor for farms which might add or subs tract capital and labor in the same proportions from the sample means. TABLE 13. PREDICTED MARGINAL PRODUCT OF CAPITAL AND LABOR "VARIED" PROPORTIONATELY AT VARIOUS INPUT LEVELS. Level of Predicted marginal product input as Capital Labor percent of input input of capital of labor mean input m (mo.) ($ per $1 ($ per in table 10 input) month) 80 7, , , , ,

24 1087 Even with constant returns for capital and labor (with both resources increased in the same proportions) diminishing returns are expected for either category of resource increased by itself. Physical production conditions for livestock specify this condition; the magnitude of the individual elasticities (both are less than 1.0 in the original production function) in the basic regression equation also specify it. Table 14 shows predicted marginal returns to labor when capital is "fixed" at the mean and "labor is used" in various quantities.b Small labor inputs on livestock appear to give greater returns than parallel amounts of labor used on crops. The marginal returns of large labor inputs are much greater than those for crops, partly because the elasticity coefficient for livestock labor is greater than for crop labor. The prices for the period sampled were, of course, more favorable for livestock than for crops. The "constancy" of the high returns to labor on livestock would also support the earlier proposition; with the same capital investment some farms can use more labor, take better care of their livestock and increase total farm profits. Table 15 shows marginal returns for capital inputs on livestock with labor "held constant" at the mean of the sample. Because the derived elasticity for capital is less TABLE 14. MARGINAL PRO DUCTIVITY OF LABOR IN LIVESTOCK PRODUCTION WITH CAPITAL INPUT "FIXED" AT THF MEAN. Inputs of labor in months Marginal return per month of labor with Input of capital at the arithmetic mean ($) TABLE 15. MARGINAL PRO DUCTIVITY OF CAPITAL IN LIVESTOCK PRODUCTION WITH LABOR INPUT "FIXED" AT THE MEAN. Input of capital m 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 12,000 13,000 14,000 18, Marginal return per dollar input of capital In livestock production ('$) While significance tests showed no significant differences In marginal capital productivity with labor input at the mean for both crops and live stock, significant differences can still exist for labor inputs greater than or smaller than the mean quantity.

25 1088 than 1.0, returns are relatively high for small inputs and decline quite rapidly as capital use increases and labor is held constant at the mean. In contrast to labor, however, returns on capital are low relative to the cost of the capital for inputs beyond the sample mean. This difference supports the earlier proposition that an increased investment in livestock capital, without an increase in labor to care for additional animals, gives a low return on the funds. Yet, the data suggest that farms evidently can use more labor for a given amount of livestock and increase returns through better care of the animals. INPUTS AND PRODUCTIVITY BY LABOR-CAPITAL STRATA The over-all sample also was broken down by.laborcapital strata for livestock. The manner of stratification was. the same as outlined earlier for crops. The average output, in value of livestock production, and the average inputs of labor and capital for each strata, are shown in table 16. The stratifications of farms for the crop and livestock analyses were done separately. Therefore, the same farms do not fall in parallel strata (i.e., the farms in the low laborlow capital stratum for crops are not necessarily the same as those in the same stratum for livestock). The top figure in each cell of table 16 is the value of livestock production, the second is the input of capital, the third is the months of labor, the fourth is the gross average productivity of labor, TABLE 16. PER FARM VALUE OF LIVESTOCK PRODUCTION. INPUT OF LABOR AND CAPITAL SERVICES ON LIVESTOCK AND GROSS LABOR AND CAP'ITAL PRODUCTIVITY. Capital service input group Low capital Medium capital High capital Labor input group Low labor I Medium labor I 3,818 I 6,964 I $ 3,535 $ 5, mo. 9.0 mo. $ 707 $ 773 $ 1.08 I $ 1.33 $ 7,329 II $ 9,044 I $ 6,356 $ 8, mo./ 9.6 mo. I $ 1,047! 942 I, 1.07 I y 1.09 $16,606 II $14,767 $14,519 $13,129 I 7.0 mo. 9.1 mo. $ 2,371 $ 1,623 $ 1.14 I $ 1.13 High labor $ 7,123 $ 5, mo. $ 620 $ 1.37 $10,613 $ 9, mo. ~ 68~.10 $19,288 $15, S mo. $ 1,084 $ 1.39 The figures In each cell are from top to bottom: value of livestock production per farm: value of capital inputs per farm; months labor inputs per farm; gross product for month of labor; gross product per $I Input of annual capital.

26 1089 and the bottom figure is the gross average productivity of capital. These figures show an increase in value of livestock production as capital is "increased" between strata within a labor stratum-or as labor is "increased" between strata within a capital stratum. Increases also take place for diagonal movements from northwest to southeast in the table for simultaneous increases in capital and labor. The diagonal "movements" show an increase in gross average returns for both labor and capital-a point which is consistent with the fact that the sum of elasticities in the livestock function is 1.08, even though probability tests do not allow us to say that this sum differs significantly from 1.0. There is more variation between cells for livestock than for crops. However, diminishing capital return is generally expressed, as capital is "increased" between capital strata within a labor stratum. Gross labor returns diminish consistently between labor strata within a capital stratum. These findings parallel those of the earlier sections indicatil).g that the productivity of either th~ labor or capital resource will be high or low depending upon the amount of the other resource with which it is combined. The figures in table 16 show certain tendencies for average labor and capital returns to change as the two resources are combined in different proportions. Since a definite mathematical relationship exists between average and marginal returns, they are suggestive of the nature of marginal resource returns for farms using different combinations of labor and capital in livestock production. 9 More precise information on incremental returns is given in table 17 which shows (1) the total product for each stratum predicted from the original production functions with resource inputs at the average levels of table 16 and (2) the marginal returns of labor and capital for strata average input. The marginal product is equal to the ea where e is the elasticity of production and A is the average productivity of the resource. This con dition is gpparent where we have a production function of the nature of that in (1) below, where R is the input of the particular resource, Y is total production and e is the elasticity of production: Y=aRe (1) are A=~==aRe-l ( 2) :i == eare-l == e A (3) The average output, A, is the total product (1) divided by the number of units of resources or are-l as shown in (2). Since the marginal product, the derivative of (1), is eare-l, as shown in (3), the marginal product is equal to the average product multiplied by the elasticity of production, or ea.

27 1090 TABLE 17. PREDICTED TOTAL PRODUCT AND MARGINAL RETURNS OF LABOR AND CAPITAL BY LABOR CAPITAL STRATA. Capital input group Lahor input group' I Low lahor Medium labor High labor ($) ($) I ($ ) I 3,536 Low capital 6,431 I 7, I ,248 ::IIedium 10,040 12,303 capital 220 I I 1.02 I 1.12 High capital 14,896 14,409 19, I I 0.96 I 1.10 Upper figure is predicted product, middle figure Is derived marginal reo turn to labor, and lower figure is derived marginal return to capital. All figures predicted from original function with mean input figures shown in table 16. When the predicted value of production of each stratum in table 17 is compared with the mean production of table 16, they again are quite similar, but less so than in the case of crops. Aside from the high labor-medium capital, low laborhigh capital and medium labor-medium capital groups, predicted and mean production are of similar magnitudes. Support again is given to the particular production function used and in marginal returns predicted from it. It appears to have logic even where predictions are not at the mean of resource inputs. The derived marginal returns figures lead to the same general conclusions as the gross productivity figures computed by arithmetic procedures in table 18. The derived marginal returns are consistent in "direction of change" for capital as well as labor, since the single function forces this condition (i.e., marginal productivity of capital declines through capital strata within a labor stratum in every case under the marginal figures derived from the function, while some variation exists for the gross average returns Of table 16). The marginal returns figures are consistent with the earlier findings: Marginal labor returns remain fairly high as labor is increased with capital relatively fixed; marginal capital returns decline rapidly with labor relatively fixed and as capital is increased through the several strata. These figures also indicate that the 160-acre farms can make a much greater investment in livestock than in crops and still maintain a high return on capital-if the necessary labor is used along with the capital.. Table 18, using quantities derived from the original functions, further illustrates this point: Capital services used on crops (i.e., crop services such as seed and fertilizer

28 1091 and machine services such as fuel and repair) give extremely high returns for relatively small inputs. They tend to fall quite rapidly, however. This high return followed by diminishing returns results as the farm area is put into crops and the crop and machine services are fully used. Added machine and crop services then yield returns to added capital which fall off rapidly. Added funds can then be invested in livestock to add the greatest amount to income. TABLE 18. MARGINAL PRODUCT OF CROP CAPITAL AND MACHINE CAPITAL ON CROPS AND :\!ARGINAL PRODUCT OF CAPITAL ON LIVESTOCK. LABOR CONSTANT AT SAMPLE MEANS. - - ($) :.\Iarginal return per dollar of input of capital Capital input services Crop I Machine services I Livestock services ~6 I n; I I 1.99 I , [ , I 0.77 I ,000 I I ,000 I ,000 I I ,000 I I ,000 I I ,000 I I ,000 I ,000 I I 1.02 In other words, if a farmer in this area has extremely limited funds, he can realize the greatest return from his limited funds by using them for crops and cash grain sales. As he accumulates more capital, investment in livestock becomes profitable.lo Undoubtedly this situation explains why so many beginning farmers build their. farm organization around cash-cropping systems. PRODUCTIVITIES FOR 240-ACRE FARMS Production functions were also derived for a sample of 240-acre farms (all farms falling in the acreage range of 220 to 260 acres). The source of data was the same as for the 160-acre farms. Only 31 farms were available for this subsample, however. The statistics are given in table 19. Because the sample is so small and because the data are highly variable, it appears that predictional errors are too great to allow use of the statistics from the crop function; 10 The extreme figures of tahle 19 include computations for capital inputs which are at the extreme of the observations, and, in the case of livestock. are outside the range for small inputs found in the study. While errors of inference are undoubtedly greater at the extremes, they are employed as predictions from the hasic functions which correspond to the physical conditions of the production situations on the particular farms.

29 TABLE DERIVED COEFFICIENTS, t VALUES AND RELATED STATISTICS I?OR 240-ACRE FARMS. ltem Crops Livestock Value of cons tan t 0: Value of elasticities:' c m Sum of elasticities Value of t for elasticities:' t 1.83:1: c 2.28:1: m 2.38t The figures for c refer to crop services on crops and all capital services for livestock, m refers to machine services for crops while I is labor in hoth cases. t P> 50 ~ 10> P > 5 1>P>O the regression coefficient for labor is not significant at an acceptable level of probability, and its negative sign causes it to be meaningless. In the case of livestock, however, all coefficients are significant at the 10':'percent level. The mean quantities of resources and the mean product for livestock are shown in table 20. Production and inputs are measured in the same manner as for 160-acre farms. A greater proportion of 240-acre than 160-acre farms have large cashgrain sales. While the livestock output and total capital used are slightly greater and while labor use is slightly smaller on 240-acre farms than on 160-acre farms, these mean differences are not significant by analysis of variance tests. TABLE 20. MEAN PRODUCT, MEAN INPUTS AND :MARGINAL PRODUCTS MEASURED AT ARITHMETIC "leans FOR LIVESTOCK ON 240-ACRE FAR;\IS. Item Value Mean product ($) Mean resource inputs: Labor (mo.) Capital ($) Marginal products at geometric means: Labor ($/mo.) Capital ($/$) , When the livestock elasticity coefficients for 160-acre farms are compared with those for 240-acre farms, the differences are not significant. Also, as is indicated in table 21, the elasticity coefficients for 240-acre farms necessary

30 1093 to give marginal productivities equal to those for 160-acre farms are not significant.ll These findings are consistent with those of an earlier section: TABLE 21. TESTS OF SIGNIFICANCE BETWEEN COMPUTED ELASTICITIES Al\'T) ELASTICITIES NECESSARY TO GIVE EQUAL :MARGINAL RETURNS TO RESOURCES ON 160-ACRE AND 240-ACRE FARMS. Item Between elasticities computed in each sample Value of t Between elasticity for 240-acre farm to give same marginal return as on 160-acre farm Labor Capital In terms of probability tests, returns to resources in livestock production are constant; added quantities of resources, if increased in constant proportions from a 160-acre to a 240-acre farm, will add as much income per $1 of investment on the latter size of farm as on the former. PRICES FOR PRODUCTS AND RESOURCES The productivity coefficients presented in the body of this study are in value or dollar terms applying to the price situation of a particular year. However, they also can be viewed in the manner of physical coefficients-much in the same manner as similar statistics from a fertilizer experiment or animal nutrition investigation. Hence, they apply in one year as well as in another year when the production coefficient is the same as for the 2-year period but when only prices differ. Transformations can be made to other price situations, and the same functions might be used to express both physical and value quantities. For example, if crop prices dropped by one-half, the marginal return per month of labor in table 2 -<page 1074) would be $39 rather than $78. If crop prices dropped by one-half but the costs of crop services remained unchanged, the value productivity per $1 crop services would be $0.59 instead of $1.08, with a mean input of $334. If the cost of crop serv- U The t values between elasticities derived in the sample have been com- }luted as t = el- e2,vhere el is the elasticity for 160~acre \/(104)'S,2 + (27)2S,," farms, e2 is the elasticity fcr 240-ucre farms and S1 and S2 refer respectively to the standard error,; for the two sizes of farms. I;'or the test of the elasticity On 240-acre farms necessary to give marginal returns equal to those of 160 acre farms, the procedure outlined in a previous footnote (on page 1085) was us2d.

31 1094 ices dropped by one-half also, the marginal return per $1 of crop services would stili be $1.08, but the mean input, if representing the same physical inputs, would then be $167. LIMITATIONS OF METHOD The general method of analysis employed in this study needs to be extended to additional farm situations. Productivity coefficients of the nature derived in this study can be useful in guiding individual farmers into a more profitable use of their resources and in helping an efficient allocation of resources from the standpoint of the consuming society. Also, a great gap exists in the provision of marginal quantities upon which the logic of economics is based. One additional advantage of the particular anaylsis is that it draws resources into a single framework of the nature which must be considered by the farmer in his decisions-or the only way in which economic efficiency can be considered in an over-all sense. The particular function used in this study allows investigation of the interdependence of resources; the effect of the quantity and form in which resources are combined on the productivity of anyone resource can be examined. The method does have obvious limitations, as do most other particular research techniques in the physical and social sciences: The analysis can provide resource productivities and suggested directions for reorganization of resources only in terms of general categories of resources. It cannot express the productivity of resources representing particular techniques of production, nor can it predict how far investment should be extended in certain small practices -except as much greater funds are available for designing samples which are highly homogeneous. Budgeting methods, however, can be used effectively along with production function,analyses to determine the economy of both broad and small adjustments in resource use and production practices. This limitation of "broad analysis only" applies, nonetheless, equally to the traditional "cross classification" analysis of farm business data. Another limitation of this analysis is that it cannot give full consideration to functional relationships between products and resources which fall in the complementary and supplementary categories. Aside from certain budgeting techniques, this limitation also applies to most other empirical procedures. Perhaps the particular algebraic model used in this study allows complementarity as well as would any other algebraic form of function.

32 1095 Questions do arise, however, on the efficiency of the particular algebraic model as compared to others-particularly for estimation of resource productivities at points other than mean inputs; further study will be made of these alternatives. Like other data based on samples or farms selected from record groups, the analysis from the cross-section observations are used for intra-farm inferences. Complications of this nature may still be present, although they have been lessened through selection of farms homogeneous in the fact that all are on the Clarion-Webster soil association and are of similar size. While multicollinearity and related problems may also arise, they appear to be relatively unimportant in this study. Other statements on method and limitations can be made, but they are discussed elsewhere in the literature and need not be repeated here,12 "Cf. Heady, Earl 0., Productivity Coefficients from a Random Sample., Journal Farm Economics., Volume 21. Heady, Earl 0., Estimation and Use of Productivity Coefficients, Jour. Farm Econ., Vol. 34. Heady, Earl 0., Productivity and Returns of Resources on Marshall Silt Loam. Iowa Agr. Exp. Sta. Bul Tinbergen,.T., Econometrics. Blakiston, New York, pp Mendershausen, H. On the Significance of Professor Douglas Production Function. Econometrica, Vol. 6. };Iarshak,.T. and Andrews, 'V. H., Random Simultaneous Equations and the Theory of Production, Econometrica. Vol. 12. Also see references cited in these publications.