A A ‘ AN momma COMPARISON or- DIFFERENT sxzas or BEEF- FEEDER CATTLE cpemnons on SELECTED MCI-{EGAN FARMS Thesis for the Degree of M. S. MICHIGAN STATE UNWERSITY George Wilkins Arnold 196:3 LIBRARY Michigan State University AN ECONOMIC COI-PARISOI‘I OF DIFFEiEE-IT SIZES OF BEEF FEEDER CATTLE OPERATlONS ON SEEECTED MICHIGAN FABES by George Wilkins Arnold A Thesis Submitted To Michigan State University in partial fulfillment of the requirements for the degree of Master of Science Department of Agricultural Economics 1963 (IT- 7- ' x r.‘ -’ u w ./ .1 II/ J. I! L" 5 ABSTRACT An Economic Comparison of Different Sizes of Beef Feeder Cattle Operations On Selected Michigan Farms by George'Wilkins Arnold The chief objective of this study was to determine if economies of scale could be found in beef cattle feeding operations, and if so, to determine the cause and.magnitude of such economies of scale. Another Objective was to determine how consistent individual beef feeders are in their efficiency and./br profitability during two consecutive years. Fifty-one Michigan beef cattle feeding farms with data available from.Mail-inéFarm.Accounts,'were selected, and.the 1961 and 1962 operations of these farms were carefully studied. The farms were arbitrarily classified into four size groups based on the average number of head fed per farm per year. Seventy to seventyafive percent of the total farm costs are made up of costs to which economies of scale do not apply. Such costs are made up primarily of variable costs, which vary almost directly with the number of head fed.and.these costs include feed costs, cattle investment and miscellaneous cash operating expenses. It was found that economies of scale were applicable to certain inputs, which.were characterized.by some degree of fixity to the farm business, namely labor, land and building investment and.machinery investment. ‘E’k George'Wilkins Arnold The cost of these inputs make up apprcximately twenty-five to thirty percent of the total farm costs. It was also found that the cost of these inputs per head fed decreased by about twenty-five percent between those farmers feeding an average of fifty head and those feeding an average of approximately hOO head per year. The total cost per head finished by large operators will only be six to eight percent less than that of small Operators. Such a reduction in total cost, however, could increase profits by as much as sixty percent. Economies of scale resulted chiefly from the increased labor efficiency of larger opera- tors made possible by a higher degree of automated feeding equipment on larger farms. It was also found in this study, that the chief economies of scale will have been realized whenthe size of a beef cattle feeding opera- tion has reached 200 head. Beyond.this level small economies of scale may still be realized but they accrue at a reduced rate. There was considerably more variability in profitability and efficiency on individual farms included in this study than would be expected. when farms were ranked according to their labor incomes only thirty-six percent remained within the same quartile from 1961 to 1962. In ranking the farms on the basis of an efficiency factor such as returns per hundred dollars feed fed, only twenty-seven percent of the farms remained in the same quartile over the two-year period. ACIQ‘IOZ‘ILED can-mus The author wishes to convey his sincere appreciation to Dr. K. T.'Nright of the Department of Agricultural Economics under whose direction this study was carried out. It has been a very rewarding experience working with Dr. wright. The author is also indebted to Dr. L. V} Nanderscheid for his suggestions and assistance dealing with the statistical aspects of the study. The author also appreciates the clerical and financial asSistance rendered by the Department of Agricultural Economics. Special thanks are due to Hrs. Cathyrn'west and.Nrs. Iynn Rooks who typed.most of the initial draft of this thesis. Finally the author wishes to convey his sincere appreication to those many Americans who were instrumental in making his sojourn in hichigan such a worthwhile and memorable experience. ii CHAP TER I II III IV TABLE OF CON TEE-J TS A GENERAL INTRODUCTIGN TO THE STUDY 0 o o o o o o o 0 Importance of Beef-Cattle Feeding in Michigan . . . ObjectivesoftheStudy.............. THEORETICAL CONSIDERATIONS OF SIZE OF BUSINESS AND ITS EFFECTS ON COSTOFPRODUCTION . . . . . . . . . . . . The Concept of Average Cost Curves . . . . . . . . Economies and Diseconomies of Scale . . . . . . . . The Concept of a Production Function . . . . . . . TABULAR ANALYSIS OF ECGIOI'LIES OF SCALE . . . . . . . Economies of Scale Within the Beef Feeding Ehter- prise Itself a o o o o o o o o o o o o o o o o o o Economies of Scale as Related to the Entire Farm . Price Conditions Affecting Profitability of Cattle Feeding in 1961 and 1962 o o o o o o o o o o o o o A Description of the Farms Under Study . . . . . . A Description of the Means by Which the Farms were DiVided into GTOUPS o o o o o o o o o o o o o o o o The Duplication of Size as Related to Efficiency Of Operation 0 o o o o o o o o o o o o o o o o o o Efficiency and Economies of Scale as Related to Cost Per Unit Of OUtpUt o o o o o o o o o o o o o o o 0 THE PRODUCTION FUNCTION ANALYSIS OF ECONOMIES OF SCALE 1961 RESUltS o o o o o o o o o o o o o o o o o o o 1962 RESUltS o o o o o o o o o o o o o o o o o o o A Comparison of the Production Function Results in 1961 and 1962 o o o o o o o o o o o o o o o o o o 0 iii Page Q 10 21 21 23 2h 26 28 32 39 SO 57 61 CHAPTER V VI VII Investment Per Han and Investment Per Head Consideration o o o o o o o o o o o o o o o o o o 67 BEEF FEEDING BUILDINGS, EQUIPMENT AND LABOR COSTS AS DERIVED FROMr THE SPECIAL QUESTIONNAIRE . . . . . . 70 Investment and Charges Per Head Fed.for Housing and Yard and.Feed.Storage, and Equipment . . . . . . 70 Capacity of the Feedlot and Average Number of Cattle Fed o o o o o o o o o o o o o o o o o o o o o o 0 7h Labor Requirements of the Beef Feeding Enterprise 75 Feeding Systems Used by the Farms Under Study . . 77 Future Plans of Farmers for their Beef Feeding Enterprise 0 o o o o o o o o o o o o o o o o o o 79 RETURNS TO SCALE AND SUGGESTED OPTIMUM SIZE OF BEEF me OPm-Anmls O O O O O O O O O O O O I O C O O 8’4 Relationship Between the Number of Head.Fed and GTOSS Farm.InCQme o o o o o o o o o o o o o o o o 8h Relationship Between the Number of Head.Fed and Labor Income 0 o o o o o o o o o o o o o o o o o 85 Relationship Between the Average Number of Head Fed Per Farm and the Average Total Farm Empenses Per Head.Fed. o o o o o o o o o o o o o o o o o o o o 8? Suggested Optimum Size of Beef Feeder Operations 90 CONSISTENCY OF SELECTED CAUSAL AND RESULTANT FACTORS OF PROFITABILITY ON SELECTED INDIVIDUAL FARMS . . . . 92 The Classification of Farms on the Basis of Consistent Causal Factors of Purchase'Weight and Sex . . . . 95 The Classification of Farms on the Basis of Consistent Resultant Factors of Returns Per $100 Feed.Fed. . 98 Distribution of Farms By Quartiles for 1961 and 1962 on the Basis of Decreasing Returns Per $100 Feed Fed and.Decreasing Labor Income . . . . . . . . . . . 101 iv CHAPTER Page VIII SUIMARY AND CONCLUSIONS . . . . . . . . . . . . . . . 108 Inputs Subject to Economies of Scale . . . . . . . 108 -Inputs that are Not Subject to Economies of Scale . 111 Magnitude of Economies of Scale . . . . . . . . . . 112 Suggested Optimum Size of Beef Feeder Operations . 113 BIBIJIOGPt—APH O O O O O O O O O O O O O O I O O O O O O O O O l22 TABLE 10 11 LIST OF TABLES Average Characteristics of the Farms Under Study . . . Average Physical Characteristics of Farms by Size 0f Beef Feeding Operations c o o o a a o c o o o o o 0 Gross Farm Income Per Unit of various Inputs . . . . . Analysis of variance Table . . . . . . . . . . . . . . A Comparison of Size of Cattle Feeding Operations with Respect to Investment or Cost of Selected Inputs Per $100 Gross Farm.Income o o o o o o o o o o o o o o o o The Intensification of Land and Labor Use by Groups . Average values for Dependent and Independent Variables by Groups for 1961 and 1962 o o o o o o o o o o o o 0 Regression Coefficients (bi's), Standard Error of Regression Coefficients (Sbi), Coefficient of Multiple Determination (R2), Multiple Correlation Coefficient (R) and Standard Error Estimate (Syx) for the Pro- duction FUIICtiOHS (1961.) o o o o o o o o o o o o o o‘ 0 Regression Coefficients (bo's), Standard Error of Regression Coefficients (Sbi), Coefficient of Multiple Determination (R2) Multiple Correlation Coefficient (R) and Standard Error of Estimate (Syk) for the Pro- duction Functions (1962) . . . . . . . . . . .. . . . A Comparison and Simple Average of the Regression Coefficients of the Production Functions for the Years 1961 and 1962 o o o o o o o o o o o o o o o o o o o c Total Investment Per Ran and Total Investment Per Head Fed, 1961-62 a o o o o o o o o o o o o o o o o 0 Housing and Yard, Feed.Storage and Equipment Invest- ments and Charges Per Head.Fed.. o o o o o o o o o o o A Comparison of Feedlot Capacity and Average Number of Head.Fed o o o o o o o o o o o o o o o o o o o o o o 0 Labor Charges for Regular and Irregular Chores and Buying and Selling 0 o o o o o o o o o o o o o o o o 0 Type Of Feeding System 0 o o o o o o o o o o o o o o 0 vi Page 27 3O 33 37 to A2 52 53 59 63 67 72 7h 76 78 TABLE 16 17 18 19 20 21 22 Future Plans of Farmers for Their Beef Feeding Enterprise.......o.....o...o... Two-Year Average Relationship Between the Average Number of Head.Fed.Per Farm and'the Tota1.Farm.Expenses PerHeadFed..........oo......'.. Correlation of Consistency of Results of Consistent and Inconsistent Groups'When Sorted on the Basis of weight andSex................o..... Correlation of Consistency of Results of Consistent and Inconsistent Groups‘When Sorted on the Basis of Returns Per$lOOFeedFed.o.....o......... Distribution of Farms by Quartiles for 1961 and 1962 Based.on Returns Per Hundred.Dollars Feed.Fed . . . Distribution of Farms by Quartiles for 1961 and'1962 BasedonLaborIncome............... A Comparison of Quartile Ranks of Farmers for Years 1961 and 1962 Based on Returns Per $100.Feed.Fed and LaborIncomeo00000900000000.0000 vii Page 79 89 97 99 102 103 10h FIGURES LIST OF FIGURES Short and Long Run Average Total Cost Curves . . . . . Figure Showing the Relationship Between Total Physical Product, Average Physical Product, Marginal Physical Product, Value of the Marginal Product, Average Value Product and.Price of Variable Input . . . . . . . . . = Calculated.Price Margin of Michigan Beef Cattle Feeders fortheYearsl9blandl962 900.000.0000. Percentage Change in Cost of Selected Inputs by Size of Beef Feeding Enterprises . . . . . . . . . . . . . Relationship of Two-Year Average Number of Head.Fed and Average Gl‘OSSFamInconle 00000000000000 Relationship of Two-Year Average Number of Head Fed and AverageLaborIncomeoo000.000.000.000 Relationship Between the Average Number of Head.Fed and the Average Total Farm Expenses Per Head.Fed.. . . . ._ viii Page 111 86 88 91 CHAPTER I A GENERAL INTRODUCTION TO THE STUDY Thefeeding of beef cattle is an important segnent of American Agriculture. In the year 1960-61 the sale of all cattle and calves accounted for 21.5 percent of the total cash receipts of farmers.1 This figure would have to be discounted to some extent since it includes the sale of discarded dairy animals. Therefore, a reasonable estimate of the percentage of total cash receipts of American farmers derived from the sale of beef animals would be in the range of sixteen to eighteen percent. It would appear that changes in technolog and size of cattle feeding operations have been somewhat slower than in other areas of livestock production. In some other areas of livestock production, such as poultry production, new technology and advances in agricultural science has led to larger and more efficient production units. In a recent Illinois study it was found that eighty percent of the beef farmers in that particular state handled fewer than fifty head.2 While many farmers throughout the north central areas of the United States 1U. S. Department of Agriculture, ERS, Farm Income State Esti- mates 19149-61, PIS-187 Supplement, August 1962. 2VanArsdall, Ray N., The Effects of Unit Size on Cattle-Feedin Profits, paper presented for Agricultural Indmtriesfirm, Vanuary 29530, I965, University of Illinois, Urbana, Illinois. 2 continue to feed small numbers of cattle, many other farmers have successfully established large cattle feeding operations. Farmers continue to feed small numbers of cattle largely as a means of market- ing farm produced roughage and feed which has little alternative value. In addition, small beef feeders experience some deg-es of asset fixity in which they find it profitable to use the existing equipment and buildings on farms for the feeding of beef cattle. This study is primarily concerned with the impacts of size of operation and its effects on profitability and efficiency in the feed- ing of beef cattle. Importance of Beef Cattle Feeding} Michifl While beef cattle feeding is not the most important segnent of the agricultural production of the State of Michigan, it is, neverthe- less, of considerable importance. According to the Michigan Agricultural Statistics Bulletins, the sale of cattle and calves in Michigan accounted for approximately thirteen percent of the total cash fam receipts in the year 1960 and twelve percent of the total cash farm receipts in the year 1961. Since this figure also includes discarded dairy animals, the sale of beef animals will account for somewhat less than the per- centages of total cash fem receipts quoted. Cattle on feed in the State of Michigan have increased by nearly fifty percent in the past decade, more than in any of the other east north central states, but less than in the west and fcr the nation as a whole. Since 1955, how- ever, the increases in cattle feeding in Michigan has accelerated to a 3 rate above the national average.3 It would appear then that the feeding of beef cattle in Michigan has becane more important during the past few years. The heaviest concentration of beef cattle feeding is located in the southern part of the State of Michigan. Soil and climatic conditions in this area of the State are particularly favorable for the growing of corn and other beef cattle feeds. Geogaphically this area is situated close to large urban centres and consequently close to the principal markets. This area in Michigan then is well adapted to the feeding of I beef cattle. Most of the farms that were included in this study were located in the southern portion of the state. waives of the Study The objectives of this thesis may be summarized as follows: (I) To determine if larger beef cattle feeding units are more efficient, than small. (2) To determine if economies of scale are inherent in beef cattle feeding operations, and the magnitude of such economies. (3) To determine possible reasons for such economies. (h) To determine if there is any degree of consistency in efficiency and/ or profitability of the enterprise during 3Ferris, J. N. and C. R. Hoglund, Implications of ChanELn' g Demand, Government Programs and Technolo on Cro and Livestock en , paper presznted at‘lfichiganTtate Universa. orage osium, March 22, 1962, p. 1 . h the two-year period among the famers in this study. Chapter II will deal with some of the theoretical aspects of economies of scale as well as the theoretical implications of the pro— duction function analysis, thereby laying the framework for the analysis in the following chapters. Chapter III will deal with the tabular analysis of economies of scale, while Chapter Iv will deal with.the production function analysis of economies of scale. CHAPTER ii THEORETICAL CONSIDERATIONS 0F SIZE OF BUSINESS AND ITS EFFECTS ON COST OF PRODUCTION General economists have long recognized.the effects of size of operation on cost of production. Early economists developed a theory centered around.per unit cost of production and later developed cost curves appropriate for each firm. They defined some costs as being fixed to the.firm in the short run, costs which cannot be avoided.as long as the firm chooses to remain in production. Such costs include insurance, property taxes and.costs associated with fixed.investments. Other costs they defined as being variable and.therefore dependent on output. Total variable costs and.total fixed.costs were drawn geo- metrically with.units of production being expressed on the horizontal axis and.units of cost of production being expressed on the vertical axis. Economists then related.these total cost functions to per unit cost functions and developed.average fixed cost curves and.average variable cost curves. Typically the average fixed cost curves appear geometrically as a rectangular hyperbole convex to the origin of the two axis. Average variable costs on the other hand.appear as "U shaped" curves convex to the horizontal.axis. An average total cost curve can . be drawn by summing average variable and average fixed costs and ’ _ 6 typically appears "U shaped" and concave to the horizontal axis and lying above and somewhat to the right of the average variable cost curve. In addition to the cost curves discussed.above, an additional cost curve was added.to the analysis, the marginal cost curve. The marginal cost of production may be defined very simply as the change in total cost incurred.per unit change in output. it too can‘be drawn geometrically and typically lies below the average variable cost curve and.the average total cost curve where each is declining and lies above each.when each is increasing. The marginal cost curve then intersects the average variable cost curve and.the average total cost curve at their lowest point. When using marginal analysis the optimum level of production is reached.where marginal cost is equal to marginal revenue, 'where marginal revenue is defined as the change in total revenue per unit change in output. later economists referred to the above cost curves as short-run cost curves representing cost structures facing the firm for a period of time in which some factors are fixed in quantity and.form. At the same time economists developed.a theory of long-run cost curves repre- senting a time period over which all factors were completely variable either in quantity or form. Such an assumption is reasonable, if one considers a long enough.time period during which all factors may be- come variable. 7 It was at about this period in the development of economic theory that economists identified economies and diseconomies of scale. The fact that a firm's short-run total cost curve is "U shaped" gives some indication of the principle of economies of scale and diseconomies of scale. On the negatively sloping segnerrt of the average total cost curve, there is every indication that if production is expanded the average per unit cost of production will be reduced. Similarly on the upward sloping segnent of the average total cost curve there is every indication that if production is increased, the average per unit cost of production will be increased. However, this concept of economies and diseconomies of scale was brought out more dynamically when economists started relating short-run average cost curves to long-run average cost curves. The concept of a long-run average cost curve developed as economists realized that various firms having various scales of opera- tion were represented by different short-run average cost curves. They realized that a whole family of short-run average cost curves existed and that this family of short-run average cost curves was generated from the fact that each short-run average cost curve represented one particular scale of plant and that may scales of plant exist. The following diagram will aid in giving a more canprehensive understand- ing of the foregoing analysis. Figure 1 Short and Long RunfiAverage Total_Co_st Curves ' ' LAC _ 31107 Cost $591 l Per S} C Y1 Y2 Y3 Yb Y5 Y6 Output of Product In Figure l we have drawn five short-run average cost curves representing the short-run average cost curves facing five firms with different scales of plant. It will be noted that these five short-run average cost curves are only five taken fran a whole family of short- run average cost curves for various firms with various scales of plant. The long-run average cost curve can be defined as the curve which is just tangent to every short-run cost curve at sane point. It then is an envelope curve which is at every point along it, just tangent to one 9 particular short-run cost curve. This long-run average cost curve has a corresponding long-run marginal cost curve which bears the same relationship to it as does the short-run marginal cost curve to the short-run average cost move. In addition the long-run marginal cost curve intersects the short-run marginal cost curve at the optimum level of production for each scale of plant. It will be noted that in the production of Y1 the $19.01 is just tangent to the long-run average cost curve at that point. Lower per unit average cost can be experienced within this firm by producing Y2 as this represents a lower point on the short-run average cost curve and hence a lower per unit cost. However, it should be pointed out that Y1 is the most optimum level of production for this firm where its short-run average cost curve is Just tangent to the long-run average cost curve. At this level of production, the short-run marginal cost is equal to the long-run marginal cost, since it is at this level the two marginal cost curves intersect. In the long run if it is desirable to produce 12, a new plant could be constructed with a larger scale than firm 1 which had its short-run average cost curve just tangent to the long-run average cost curve vertically above 12 on the X axis. Hence, a lower per unit cost could be experienced than by producing 12 in firm 1. The SAC2 curve represents firm 2 having a larger scale of plant than firm 1 and having generally lower per unit costs. Its most optimum level of production will be I3. t? (5 10 SAC is the short-run average cost curve for firm 3 and its 3 optimum level of production is Yh. m closer examination one finds this firm has an exceptional relationship with regard to its short-run average cost curve and the long-run average cost curve. It is tangent at its lowest point to the lowest point of the long-run average cost curve. Then this particular plant is producing at the lowest per unit cost both in the short run and in the long run. Firms h and 5 re- presented by SACh and SAGE, on the other hand, have their short-run average cost curves tangent to the long-run average cost curve at a level beyond the lowest per unit cost on their short-run average cost curve. They produce Y5 and 16, respectively, in the most efficient way where their respective short-run cost curves are tangent to the long-run cost curve. It is obvious then that firm 3 has a distinct advantage over the other four firms in that it is producing at a level where its per unit costs are lowest and where its short-run average cost curve is, tangent at its lowest point to the lowest point on the long-run average cost curve. ' Returning to the concept of economies and diseconomies of scale, one may visualize the concept more readily if one imposes it on diagram 1. If one thinks of the long-run cost curve as being divided into two parts, that part of the long-run cost curve lying to the left of Yh, and that part lying to the right of In, it will facilitate the purpose of this discussion. In that segnent of the long-run cost curve lying 11 to the left of Yh economies of scale are operative. In other words, by increasing size of plant in this area, lower per unit costs are experienced. In that segnent of the long-run cost curve lying to the right of In diseconomies of scale are operative. In this case, if scale of plant is increased throughout this area of the long-run average cost curve, higher per unit costs are experienced. Economies and diseconomies of scale can each be further sub- divided. Heady subdivided economies and diseconomies into internal and external economies and diseconomies of scale.1 Economies of scale re- sult when further expansion adds more to total revenue than to total cost. Internal economies are those realized from size adjustments with- in the individual producing unit. Internal economies may be further subdivided into internal pecuniary economies and internal physical economies. For example, an internal pecuniary economy exists when a rim is sufficiently large to take advantage of quantity buying at reduced costs. An emanple of an internal physical economy is in existence where the firm is large enough to take advantage of division of labor and inherent work simplification techniques. External economies are those economies that are dependent on the general development of the industry. With the development of an industrial camnunity comes cheaper transportation rates to this particular commmity, therefore laeaav, Earl, Econanics of lglculmral Production and Resource EEE’ Prentice-Hall, Inc. , ewo sTNew—Jersey, p? 352. 12 this is an example of external economies ofscale. Diseconomies of scale result when fm'ther expansion adds more to total cost than to total revenue. Diseconomies of scale may be ex- ternal or internal. An external diseconcny results fran the expansion of an output of an industry when this expansion causes the price of in- put resources to rise. An example of external diseconomies is when all the firms in an industry bid labor away from competing industries. Thus, the price of labor rises to all industries. Internal diseconomies result when the management that the firm has, becomes the limiting factor. Thus, the operations of a firm may be too large for the limited management that the firm has and as a result efficiency decreases and profitability goes down. Thus, the economies of scale which are most important to the operator of any firm-are the internal economies, both plwsical and pecuniary. These are factors over which the manager of a firm has sane control since they are located within his firm. Internal economies of scale are indicative of increasing prysical returns to scale which cause declining per unit costs. Managers whose firms face diseconomies of scale experience difficulties when they attempt to expand their plant's output beyond the optimum level. ' Within this particular study, economies of scale could appear with respect to the greater utilization of fixed resources by further expansion. The beef cattle feeder has several fixed resources such as land, buildings, machinery and labor. If he is able to feed a larger number of cattle, using the same resources, he will therefore be able 13 to spread such fixed costs over a greater number of livestock and in so doing reduce the per unit cost of production. Therefore, one might expect to observe economies of scale in a beef cattle feeding operation through geater utilization of fixed resources. Diseconomies of scale could be observed in a beef cattle feeding operation when the limited management that is available is no longer capable of co-ordinating such resources of land, buildings, machinery and labor in the most efficient way. As a result, there is a decline in the efficient use of ary or all of these inputs and profitability may decline. One may deduce from the above discussion then that where economies of scale are apparent to a firm through further expansion, then con- siderable thought should be given to expanding the output of the firm. On the other hand, where further expansion may lead to diseconomies of scale, further expansion would add more to total costs than to total receipts and therefore, would not be advisable. Then managers of fims should attempt to take advantage of economies of scale that exist but at the same time they should guard against expansion which will lead to diseconomies of scale. For every firm there is a level of. optimum production both in the short run and in the long run, and this is the level that rational managers will attunpt to attain. 1h The Concept of a Eduction Funetion In a later section of this thesis, production functions will be developed for the farms under study. A theoretical conSideration of a production function together with a consideration of how the economiz- ing principle relates to production functions is appropriate at this point. Typically, production functions refer to input-output relation- ships. A production function may be defined as the relationship between variables. Production functions may be expressed in the form of an algebraic equation. The following is an example of a production func- tion expressed algebraically. Y "' f(X1, X2: X3) In the above equation, I is known as the dependent variable and represents output. X1, X2, and X3 are three independent variables going into the production of Y. The equation states that the amount of I produced is a function of the inputs X1, X2, and X3. As an example, assume that Y represents the quantity of corn produced per acre and X1 represents the amount of fertilizer used, X2 represents the amount of labor used and X3 represents the amount of seed used. The quantity of corn produced then is a function of the amounts of fertilizer, labor and seed used. Production functions may involve single variable inputs or multiple variable inputs. 15 Y - f(X) single variable input. I - f(X1, X2, X3, ..., Xn) multiple variable inputs. Multiple variable inputs are most common in the production of most commodities. Most commonly production functions involve some variable inputs and some fixed inputs. An equation representing such a condition appears as follows: 1’ -f(X1, X2 X3, ...,Xn) In other words, the above equation states that the production of I depends upon variable inputs X1 and X2 given the inputs X3 to Xn as fixed. In the following analysis, a single variable input will be con- sidered assuming that the other inputs are held fixed. This example may be represented by the following equation: I Y - £(x1| x2 Xn) Input-output relationships involving one variable input have been stu- died by numerous pmrsical scientiest. Almost without exception physical scientists have observed the law of diminishing returns to be operating within such a relationship. The law of diminishing returns states that the addition of a variable input to fixed inputs results first in total returns which increase at an increasing rate, second in total returns which increase at a decreasing rate and third in total returns which decrease with increases in the variable inputs.2 The law of A w — 2Bradford, L. A., and G. L. Jotmson, Farm Management Analysis, John Wiley and Sons, Inc., New York, p. 1.13. ' .43 9.8 l6 diminishing returns can best be explained by means of a graph showing the total physical product. In addition other relationships can be shown on the same graph. Marginal product, which is the addition to total production resulting from an increment in the variable input can also be shown on the gaph. Average product can also be shown and average product is defined as tint portion of total product produced by the variable input divided by the amount of the variable input used. Also in this graph other price relationships have been included for further analysis. By multiplying the average physical product times the price of the product, the average value product is determined. By multiplying the marginal physical product by the price of the pro- duct, the marginal value product is determined. The price of the variable input is also included and is indicated by the horizontal line le. All of these price relationships will be used in the analysis which follows. 17 Figure 2 Diagram showing the relationships between Total Pmsical Product, Average Physical Product, Marginal Physical Pro- duct, Value of the Marginal Product, Average Value Product and Price of Variable laput.3 Stage 1 :Stage 2 Stage 3 Total Physical Product Average Physical Product x Price of Pieduct fl 1 le (Price of Variable - (Average Value Input) Product) XllX2 ""Xn C Marginal Physical Product x Price of Product =(Value of the I-Iarginal Product) Figure 2 illustrates on the total plysical product curve the law of diminishing returns - first total returns increasing at an in- creasing rate, then at a decreasing rate and finally total returns decreasing with additions of the variable input. Economists developed __ iv— 3In Figure 2, the horizontal axis measures units of the X1 variable while the variables to Xn are held constant. The vertical axis measures physical product in its and after introducing price relationships, the vertical axis measures value product in dollars. 18 three stages of production by means of the above physical product curve relationships. In stage I the marginal physical product is greater than the average physical product. In stage II marginal physical pro- duct decreases continuously and is always less than average physical product. In stage II, however, marginal physical product is above zero. Within stage III, the marginal physical product is less than zero and the total physical product is declining. A consideration of where to Reduce within the three stages of production is now relevant. Within stage I, as long as the marginal physical product is greater than the average pmrsical product, and the average physical product pays for itself, it pays to add more units.h Then if it pays to produce at all, it pays to produce the maximum amount that can be produced in stage I. Within stage III, since marginal physical product is less than zero and the total physical product is declining, then additional input will reduce total output. Therefore, stages I and III are not desirable stages of production. Therefore, stage II is the relevant stage of production as determined by physical terms. In order to decide at what point within stage II to produce, one must introduce price relationships. In an earlier part of this chapter it was pointed out that the most optimum: level of production was that point at which marginal cost was equated to marginal revenue. Modifying that analysis to suit the current analysis one must equate the value of the marginal — —_ *1 thi-de, Po 115. 19 product with the cost of the increments of input. In this example the marginal value product of X1 must be equal to the price of X1. Stated in terms of an equation, it can be presented in either of the two ways as follows: RWPXI n - - S I-IVP le or 1 le These equiations imply (I) that if the last unit of X1 does not pay for itself, less of X1 should be used, (2) that if the last unit of X1 more than pays for itself, more of X1 should be used and (3) the use of X1 should.be stopped at that point at which X1 just pays for itself.6 This relationship is represented in the diagram at the point at which le intersects the marginal value product curve. The amount "on then is the optimum amount of X1 which should be used. This concept is known as the economizing principle. The example that has been used is for a production function involving a single variable input. The reason a single variable input was used.was to keep the analysis as simple as possible. In the case of a multiple variable input, the economizing principle still applies and the following equation holds for the optimum level of output: MVPX]. ' }IVPX2 '3 o c o 0 I‘mX-d - 1. le sz de 5In this equation MVP has been substituted.for VNP as the price of X1 is not considered.to be a function of the amount of X1 used. 61bid., p. 117. 20 In the above equation the variable inputs X1 to Xd are combined in the proper proportion and when this equation is set equal to one, this equation represents the optimum amount of I to produce. The above equation indicates that the use of any input should be expanded as long as its marginal value product is greater than its cost, that the use of an input should be contracted it its marginal value product is less than its cost, and that all inputs are properly used when their respec- tive marginal value products are precisely equal to their costs.7 When a production function involves more than a 2 variable input a graphic presentation will involve more than three dimensions and it is im- possible to represent more than three dimensions graphically. Then in the case of more than a two variable input the economist must determine the amount of Y to be produced by an algebraic equation similar to that presented above and proceed with the analysis algebraically rather than geometrically or graphically. From the analysis throughout Chapter II, the successful manager should determine the optimum amount of production from the relationships that have been discussed. He should be familiar enough with cost conditions in order to take advantage of econanies of scale that may exist. He must also be aware of the production relationships in combin- ing the resources going into production if he is to achieve the Optimum level of production. 7Ibid., p. 133. CHAPTER III TABULAR ANALYSI§OF EQQNQEIES 0F SQéEE Before proceeding with tabular analysis of economies of scale, some consideration should be given to the implication of economies of scale to beef cattle feeding operations. ven Arsdall indicates that cost and income advantages can be gained with increases in size of operation both from factors within the feeding operation and from those related to but outside the actual feeding operation.1 Economies of Scale within the Beef Feeding‘Entegprise Itself In Chapter II the concept of economies of scale was developed in which increases in production led to lower per unit costs of pro- duction. Therefore, in considering economies of scale as related to the beef feeding enterprise itself, one must consider cost of production. The cost of producing beef could be broken down into two components, (I) feed costs and (2) nonfeed costs. Feed costs per hundred pounds of gain and.per animal vary widely among farmers. This is due to differences in purchase weight, sex, inherent ability of the animals to convert feed to gain in weight, length of feeding period and possibly to the skill and care with which —__—_‘ “ .— “— ii- lVan ArSdall, Re No, .920 SEE-LEO, p. 30 22 the farmer feeds the cattle. It does not necessarily follow that any or all of these differences are associated.with the size of the feeding operation. Nonfeed costs are those which are tied to investments in such facilities as buildings, machinery and equipment used only by the beef enterprise. Other nonfeed.costs include labor, veterinary, death losses, and.miscellaneous inputs, all of which apply only to the beef enterprise. It is more likely that these are related.to the scale of the operation than are feed costs. ven Arsdall also pOints out that by increasing the capacity of a beef feeding operation, the unit investment and costs for equipment and structures drop until a size is reached which requires duplication of the largest available unit.2 Such conditions can be related.to the declining longhrun average cost curve referred to in Chapter II. 'When duplication of the largest available unit has to be made, such a long. run average cost curve will begin to flatten out. Other cost advantages enjoyed by larger feeder cattle operators will be the spreading out of fixed overhead costs over a larger number of animals. This too, will tend to lower per unit costs. A California investigation showed per unit nonfeed costs declining continually from feed10ts of 1,000 head capacity to those designed for 50,000 head capacity.3 2Ibid., p. 3. 3Hopkin, John Am, Economics of Size in the CattleéFeedin Indust of California, Journal of Farm Economics, Vol. XL, No. 2, May, . 23 While the feedlots referred to above are much larger than those included within this study, it is expected that the same principle of reduced per unit nonfeed costs as size of operation increases, will apply within this study. There are also cost and income advantages to be gained with increases in size of operation from factors related to but outside of the actual feeding operation. Such advantages are related to the in- creasing size of the entire farm operations. Economies of Scale as Related to the Entire Farm All of the farms included in this study derive some income from secondary enterprises in addition to the beef feeding enterprise. It would be reasonable to assume that economies of scale may appear in secondary enterprises or the combined primary and secondary enterprises when enterprises are complimentary. On most of the farms included in this study, the feed fed to the beef cattle was largely home grown. If largeriaianers are able to feed more cattle per acre than mall, this would imply economies of scale with respect to crop production. When this is the case larger Operators would be getting better utilization of machinery and land in crop production than are small operators. There are certain costs fixed to the entire farm operations and such costs involve insurance on buildings as well as property taxes. By intensifying all operations on a farm these general overhead costs can be spread over more units of production thereby reducing per unit costs 2h of production. From the preceding discussion then, there are certain economies of scale which may be better attributed to the size of the entire farm business rather than to any one single enterprise. Price Conditions Affecting ProfitabilitLof Cattle Feeding in 1961 and 1962 Throughout this study many inter-year comparisons will be made for various factors which are of interest. While these inter-year com- parisons may indicate consistency or trends of profitability and efficiency, it should be noted that it is virtually impossible to have the very same price and weather conditions from one year to the next. For example, favorable weather conditions during the growing season one year, followed by unfavorable weather conditions the second year will. have a tendency to make the first years operations appear more profitable. Likewise cattle price conditions can add a bias to inter-year canparisons. Therefore, in making inter-year comparisons one should at least be aware of the external conditions involved over the two year period and modify his conclusions accordingly. It is generally agreed among cattle feeders that 1962 was a much more profitable year than was 1961. The main reason causing this con- dition was cattle prices. Feed prices did not vary significantly from 1961 to 1962. In a study by Dr. K. T. Wright involving sixty beef cattle feeding operations in Michigan, he found that the main difference between the years 1961 and 1962 was in the prices paid and received for n per th. Mar 25 cattle.1‘ While the data used in this study was calculated on a drove basis for many of the farms, he found that in 1961-62, the farmers paid .77¢ more per hundred weight but sold the cattle for $2.21; more, so they had a positive price margin of .63¢ per hundred as opposed-to an .80¢ negative margin for the year 1960-61. Thus, the returns over feed cost per head in 1962 averaged $118 as compared with $31 for the year before, and the return per $100 of feed fed was $166 and $139, respectively. On a per farm basis, the return above value of feed fed in 1962 averaged about $10,800 compared to approximately $6,500 the year before. The following figure presents the calculated price margin relationship between the years 1961 and 1962. Figure 3 Calculated Jrice margin for Michigan beef cattle feeders for the years 1551 and I962b ,1 Calculated Price Margin (If bought Good-Choice 300-50064 steers at Kansas 0 City 9 months earlier 8: cost $2.00 a cut. to deliver) -1 -2 m -3 . / ~ ~ ‘- ..h +- 2 ~ _19_6; / -5 b ~ ~ " V ’ -6 j 4 1 l 1 1 l l l l _p a Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. Month of Sale hwright, K. T. , 1961-1962 Cattle Feeding Costs and Returns, Agricultural Economics Bulletin' 5377, fiepartment of Igicmural Economics, Michigan State University, April 1963, p. 3. 51b1d., p. 21. 26 From the above graph one may conclude that the price margin as calculated from purchase and sale price relationships was much more favorable for the year 1962 than 1961. It is important then that this price advantage be considered in making comparisons on profitability between the years 1961 and 1962 in latter sections of this thesis. A Description of the farms under stuq Fifty-one farms were included in this study. All fifty-one farmers were enrolled in the Mail-In Accounting project that is carried on by the Department of Agricultural Economics at Michigan State University. The farms selected were 51 of the 60 cooperating farms with which Dr. K. T. Wright has been working in his special. beef study during both 1961 and 1962. The farms were also selected because of the relative importance of the beef feeding enterprise to the total farm program. The fifty-one fanns selected also provided a wide distribution of size of operation or number of head on feed and this size distribution is of considerable importance to this study. Since most of the farms included in the study had as their main enterprise the feeding of beef cattle, it should be acknowledged then that most of these farms were larger and more specialized than the typical beef farm in Michigan. Fifteen of the fifty-one farms under study were located in Lanawee and Monroe counties in southeastern Michigan, seventeen of the fauna were located in central Michigan and the remaining farms were located in eastern or southwestern Michigan. 27 Most of the data that have been used within the study were ob- tained from the mail-in records for the years 1961 and 1962. Identical farms were used in both years of the study. The records that were kept by all fifty-one farmers included information on invent cries together with itemized expenditures and receipts for each farm business. These farmers submitted monthly records of their purchases and sales of cattle indicating the number of head, the weight, and the dollars involved. In addition they provided records on the amounts of the different kinds of feed they fed their cattle. This included both home-gown feeds as well as purchased supplements and ether feeds. The following table will present some idea as to the average size of the farms under study. The figures quoted are averages for the same fifty-one fame for the years 1961 and 1962. Table 1 Average characteristics'cf the_fams; under stxg' 1961 1962 Number of beef cattle per farm6 1:81 , 215 Number of men'per farm 1.8 1.8 Number of tillable acres per farm 301; 295 Investment in land and buildings per farm - $7h,652 $8h,817 Investment in machinery per farm lid-193 15,539 Investment in cattle per farm 33,511 111,515 Value of feed fed per farm 21,681; 23,6514 , Gross income per farm $36,761; $115,770 Labor income per farm ' 2,986 . 6,886 Percentage of goss fam income from beef cattle per farm 62.9% 72.5% 6This figure is an average of the number of cattle per farm. The means by which the average number of cattle per farm was determined will be discussed in the following section. Actually this figure will represent somewhat less than the average total capacity per farm. 28 A.Descripticn of the Means by;whichfghe%§armsjwerg;Divided_into Groups Since this study was primarily concerned with the size of beef cattle feeding operations, a method of calculating the average number of head per farm per year was devised and the groups were developed on this basis. Records of the purchases and sales of cattle by months were used in calculating the average number of cattle per farm for the year. First of all the number of animal months were calculated. 'This was accanplished by multiplying the number of months a particular lot of cattle were on the farm by the number of cattle in the lot. Then the number of animal months for all lots of cattle on each farm were summed and divided by twelve in order to arrive at the average number of cattle per farm per year. The author would admit that the average number of cattle per farm per'year as calculated on this basis will vary from the actual number ofcattle on each.farm.per year. For example, in calculating the average number of cattle per fann per year, it was assumed.that if cattle were purchased during any particular month they were on the farm for the entire month. It is possible that they were purchased at the end of the month, in which case this method will give a higher. estimate than the actual. Similarly in the case of sales it was assumed.that cattle were on the farm for the entire month during which the sale was made. In reality the cattle may have been sold early in the month, in which case this method will give a higher esti- mate than the actual. 29 Also if one hundred head of cattle were on .a particular fam for nine months during the year, this method of determining the average number of cattle perfann per year would estimate the number to be 100 X 9 .. 75 head. Therefore, this method of determining the average 12 number of head per farm per year will underestimate the capacity of such a farm, since the capacity of this farm is one hundred head, whether it is full to capacity for nine months of the year or twelve. Even though there are discrepancies in this method of calculating the average number of cattle per farm between the actual and the calculated, in the opinion of the author it gives a better estimation of the actual number of cattle per farm per year than by averaging beginning and ending inventory numbers. . This is by virtue of the fact that many cattle feeders buy and sell cattle at several different times throughout the year. By using an animal month basis on which to calculate the average number of cattle per farm per year on all of the farms under study, this method will give a reasonable estimate of the size of the beef cattle feeding operation on a particular farm in relation to the size of beef cattle feeding operations on all other farms. Therefore, by using a consistent method of determining the size of operation for all farms, one can logically compare and group farms on the basis of size. In dividing the farms into groups, four arbitrary size levels were established. Group one included farms having up to an average of seventy-five head per year. Group two ranged from 76 to 150, group three ranged from 151 to 250, while group four included those farms 30 having an average of more than 250 head per year. The following table presents some of the average characteristics of the'farms by groups for the two year period. Table 2 Average Egsical characteristics of farms _y size e f eeding'operation Gro 1 Crox 2 ' up to '75 Head 76- ead 1961 1962 1961 1962 No. of farms in goup 6 6 19 17 Ave. no. of tillable acres 292 2314 230 217 Ave. no. of head 146 51; 110 111 Gross farm income $22,512 19,896 214,627 29,5145 Percent of goss farm income fran beef cattle 21.2 32.6 56.9 65.8 Gro 3 Gro 14 lfihead over 255 Head 1961 1962 1961 1962 No. of farms in goup 16 lb, 10 11.; Ave. no. of tillable acres 2914 281; 1:65 129 Ave. no. of head 187 192 w 388 1422 Gross farm incane 35,905 10,011.; 69,752 82,316 Percent of goss farm income from beef cattle 62.8 75.8 75.0 . 77.9 In examining the above table one finds that only 21.2 per cent of the goes income from goup one was attributable to beef cattle for the year 1961 and only 32.6 per cent for the year 1962. The sample in goup one only includes six farms for each of the two years. Because of the small sample size in goup one and because of the fact 31 that less than one third of the gross farm income for group one for bothyyears could be attributed to the feeding of beef cattle, group one was excluded.from.the analysis made in Chapters III and IV. This reduced.the total number of farms under study from.fiftyaone to fortyh five. By excluding group one from the analysis, all groups had con- siderably better than fifty percent of the gross farm income attribut- able to the feeding of beef cattle. Group four included all of those operations which involved.the feeding of more than an average of 250 cattle per farm.per'year. No upper limit was set for this group. Consequently this group had a wider range than that of group two or group three. In 1961 the range of this group extended.from an average of 258 cattle per farm to 659. In 1962 the range of group four extended.from 265 to 688 head.per farm. It should be born in mind.that the groups referred.to above have been developed on the basis of the number of cattle.fed. It will also be noted.that the larger the group size, the higher the percentage of gross farm income attributable to the feeding of beef cattle. Therefore, secondary'enterprises will account for a larger percentage of gross farm income in group two than in group three and.simi1arly secondary enterprises will account for a larger percentage of gross farm income in group three than in group four. In the analysis which.follows the various size groups of farms based on the number of cattle fed, will be compared with reapect to efficiency. 32 The Implication of Size_as Related to Efficiengy of_0perati22 Webster defines efficiency as an effective operation as measured by a comparison of production with cost in energy, time and money.7 Boulding defines efficiency as output per unit of input.8 In measuring efficiency with respect to the size of beef farms in this study, goss farm income will be used as the measure of output. Gross farm income is the output received for the use of various resources of the farm. Such resources include not only land, buildings, machinery, and cash operating expenses but also the skills and managerial ability of the farm operator. While a large proportion of goss farm income can be attributed to the feeding of beef cattle and a small proportion to secondary enterprises, crop production is of considerable importance to the beef feeding enterprise since most of the crops gown on the farms under study, were marketed through beef cattle. Gross farm in- come then encompasses the output from all inputs or resources used in the farm business. There are several different inputs going into the fam business including investments and charges for the use of land, buildings, machinery, labor, feed and other miscellaneous cash eXpenses. The following table relates goss farm income per unit of various inputs —— Mgbfier's New Collegiate” Dictionaq, G & C Merriam Co. , p. 262. 8Bou1ding, K. E., Economic Analysis, third edition, Harper & Brothers, New York, p. 717. W JHH mmo.mm rao.m paw Haae wee oaa eaa.am oes.mm mam.m eem.~ oer rem «mae omaa mead Homfl use: m am>o 11 mos; moa em~.au mme.m we: anew mad mm mam.em eao.- Haa.~ mam.m mm; mm: 3.8 «m3 8% mam. cmo NIH H wimmmmw ooa emw.wa emm.m as: «New wOH mm eaa.au mam.mfl mme.m mH~.N mm; or: emaa pear mama emmmmmmmmww meow oHQeHHHp I hoe momceaxe fleece ooaa yea I ems you I pnoEpmo>nH knocflnoms oooaw mom I semapmmsea maaeaasn s_eera oooaa are I newcomer Hence ooaw mom memenemw,aonIose ems non I p:o€pmo>nfi humefinoms oooaa mom I surefire: wage a area 80.8 are .. ‘mgmmdd mmmmnsMLmd pwmmrnomlmeoonalenwm.macho mmmmaohavmwmee< sopH m manna = c msooeH among once edemadap I you I mEoonH mmoao 33 3h for each group for the two‘year period, in an effort to measure the efficient use of inputs among groups. TWO year averages for each input are also included. In reference to the above table in which the farms have been grouped on the basis of number of head of cattle per farm, if gross income per unit of input is higher for one size group than for another, one could conclude that the size group with.the higher gross income per unit of input is more efficient in the use of that particular input than is the other. If a larger feeding operation attains a higher gross income than a smaller feeding operation for the same unit of input then it would.appear that economies of scale are implied with respect to the use of that particular input, since the larger feeding operation is producing more efficiently than the smaller feeding operation. In reference to Table three and on the basis of two;year averages, _.. o.” a“!!! _9_ cm. o-r thousa d .. .- .v- ‘11-. '9_ 7.... ._.. ._ . .3.- decreased.by less than one percent from group two to group three, but it increased.by'thirtyefour percent from group three to group four. Therefore, on the basis of simple averages one could conclude that there was very little difference with.respect to efficiency'in the use of investment in land and buildings for those feeding between approxi- mately 110 head and 190 head, but that there was greater efficiency in the use of land and building investment for those feeding 190 head on up to approximately hOO head. 35 Cross Farm_Income per $1000 mphmemmvestment increased by 15.5 percent from goup two to goup three and increased by lh.8 percent from group three to goup four, on the basis of two year averages. Therefore, on the basis of simple averages one would conclude that geater machinery efficiency resulted as the size of the cattle feeding operation increased. Using. two year averages, gross income Jar man increased by 28.7 percent from goup two to goup three and increased by 18.9 percent from goup three to goup four. Therefore, on the basis of simple averages it would appear that as the Size of the cattle feeding operation in- creased, greater efficiency of labor was achieved. 0n the basis of two year averages, goss fa£m__inc_ome_per $1009 tgtal expensgs increased by 14.9 percent from goup two to goup three and increased by 8.1 percent from goup three to group four. Therefore, from simple averages it would appear that the larger operations were somewhat more efficient than smaller groups in reapect to goss farm income per hundred dollars total expenses. It should be born in mind that the importance of the beef feeding enterprise to the total farm business increased in proceeding from goup two to goup three to goup four since the percentage of goss farm income from beef cattle increased throughout the three groups. In order to get a more accurate estimate of the reliability of the indicated increasing efficiency over the three groups an analysis of variance was run on individual farms for several variables for the two year period. 36 The independent variable was considered as the average number of head of cattle per farm per year and was denoted.by X2. Each of the dependent variables in turn were tested for analysis of variance with X2. The dependent variables were; X1 - gross farm income per $100 total expenses, X3 - gross farm income per man, Xh - gross farm income per $1000 investment in land.and buildings, and.X5 - feed cost per 100 pounds gain. It should be noted that feed cost per hundred pound gain is a.measure of feeding efficienqy. It was included as a variable in the analysis of variance to determine whether larger groups have lower feed costs per 100 pounds gain. It should be born in mind that the results in the following analysis of variance table indicate the entire farm response. From this table there was a significant difference in gaggs farm income_per $1000 invested in land.and buildings between groups with respect to average number of cattle per farm for the years 1961 and 1962 at the .05 level. On the basis of simple averages in the earlier discussion it was concluded there was little difference in efficiency between groups two and three, however, there was a definite increase in efficiency between groups three and four. Therefore, from the results of the analysis of variance it may be concluded that the larger beef cattle feeding farms were more efficient than smaller farms with respect to land and building investments. It follows then that there are economies of scale with respect to land and building investment. .Hmrma e mo. one an peaoaaaamam I r. .Hmpoa mace. one pa peaoaeaawam I ** osp_ens museum eons» .mcowpw>aomeo m: mcabaoeca . .m o haopapooemmn mm nee.:M .mm . an3.mM no macadamb no mfimhawne weakens oases aom.a tea *mom.: ems.a 05Hm> m Noma ma.oae mm.mmma maa.oma n:.NHH mama Hwnocoo mead mam.H N0.~H seem menace 00H non pmoo room I mm ramm.m ea.emee scrapersea maaeaase a1eeea oooae nee ascend swam emcee I 4% *aowm.HH wwaqdma one team esooca seem mmono I M am~.a mm.ooaw someones Hero» ooaa no osoonH sham macaw I osamb m can: Hmaonoo on use: as access .obw I NM mefl HomH moararaeuwo mammarea s oases 37 38 There was a significant difference in gross farm incomegper;man between groups with.respect to the average number of cattle per farm for the year 1961 at the .001 percent level and.for the year 1962 at the .05 percent level. It was correctly concluded in the discussion of gross farm income per man, using simple averages, that as the size of the group increased, greater efficiency of labor was achieved. Therefore, economies of scale are implied.with respect to labor. 0n the basis of the analysis of variance table there was no significant difference in_g£gss farm income per $100 total expensgg or overall farm efficiency between groups with respect to the average number of cattle per farm for the years 1961 or 1962. Even though simple averages indicated that larger groups were getting a higher return per $100 total expenses, the test for significance did not confirm such a conclusion. Therefore, it could be concluded that there are no definite economies of scale with respect to the relationship between gross farm income and total farm.expenses. It may also be concluded.from the analysis of variance that there was no significant difference in feed costgper hundred pounds gain between groups with respect to the average number of cattle per farm for the years 1961 or 1962. Then on the basis of this study it may be concluded.that economies of scale do not apply to feed costs per hundred pounds gain. In the following section efficiency and economies of scale as they apply to the factors considered in this analysis will be related to cost per unit of output. 39 Efficiency and Economies of Scale as Related to Cost per Unit of Output In the preceding section efficiency was defined as output per unit of input, the highest efficiency being achieved when the maximum output is attained per unit of input. When increasing sizes of opera- tion lead to increased efficiency, economies of scale are implied. This results in geater output per unit of input for larger sizes of operation. Efficiency also can be measured by input per unit of output. If highest efficiency is achieved when maximmn output in attained per unit of input, then input per 1mit of output is at a minimum. If cost per unit of output decreases as the size of the operation increases, economies of scale are implied. This results in lower costs per unit of output for larger sizes of operation. In Chapter II the concept of economies. of scale was developed on this basis as indicated by a decreasing long- run cost curve as output or size of operation increased. In relating efficiency and economies of scale as determined by reduced costs per unit of output to the factors considered in the pre- ceding section, the factors will now be considered in terms of cost per unit of output. Output will be measured in terms of hundred dollars of goss farm income. In the following table the investment or cost of selected inputs per $100 goss farm income are listed for each goup size for each of the two years. The average investment or cost of the input per $100 goss farm income for the two year period is listed as well as the average goss fem income for each goup for the two year period. Another column relates the average investment or cost of input per $100 average goss farm income for groups three and four as a percentage of that of goup two. ed ascend anew macaw manooonnmn anew Hensouanes one .enuadee ea neeeeeeee odds: anew Heoapnep one so wounoaexe ea oseon«_snuu anon» cede hem enema one no pnoo he phospuepqa esp ma ensues owupnoonen one once: mama Rosa mood mam mam uooa Ree are mace um» mam uooa Rue mooa mead Nimuoac “mum! emcee 83m omonm ma.mm a~.mm 4:.mm mw.oa No.ma ew.ma o:.~m mm.~n om.m: «ea sum same mammw saooa Emma om.;o m«.em mm.~m mm.m eo.HH as.sa sw.om ma.mm ma.oa 54H mom meme .nne N nee urea .Nema mmwmw mommm wuoam . m:.mm mN.JCH mm.:oa oo.~a ma.~H Hm.~a pm.mm me.aa sa.ms sea mmm «sue Head hHHeodnaenw connouonn one canes shone osp.eonm unannon 02¢.nadnw weanoHHon_onp nH asoonH_snuh scone ascend anon anon» DDHE nee muse gonna canoe and neon» nee encapmoan nauaasm s.eeen mmoonH pace no pnesvmobed on to hi FIGURE h Percentage Change in Cost of Selected Inputs by Size of Beef Feeding Enterprises 100T K“ \ “‘ ‘~- _ Total Farm Ebcpenses Percent \ \ -- ~“~~_ \ ~ ~ ‘ ~ - ~ 90+ \ Land & Building ‘ Investment Change \\ in \ \ \ Cost of \\ 80" . Machinery \ . Investment lhiput Q \~ Per \ ~ \ ‘\ $100 70" Labor Charge "\ - GI'OSS \ 60-- Farm Income 5 a b c l n l a l l L l l r" I ' I I I l' 25 35 us 55 65 75 Thousand Dollars of Gross Farm Income a - Average Gross Farm Income for Group 2 for 1961 and 1962. b - Average Gross Farm Income for Group 3 for 1961 and 1962. c - Average Gross Farm Income for Group h for 1961 and 1962. h2 The preceding graph presents four cost curves similar to those discussed in Chapter II. The time period under consideration will re- present the short-run since the size of the beef cattle operation is relatively fixed.for a time period as short as that considered within this study. As the size of the cattle feeding operation increased.from group two to group three and from group three to group four the cost curves of various factors are typically downward sloping to the right. This would indicate that economies of scale may'be operative. From the analysis of variance conducted in the preceding section it was concluded that economies of scale were apparent with respect to land and building investment and labor. In the preceding graph land and building investment per $100 gross farm income did not decrease between groups two and three but there was a 28 percent decrease in land and building investment per $100 gross farm income between groups three and.four. ‘With larger operations, there was greater intensifica- tion of the use of land and buildings as well as labor. The following table will illustrate the above statement. Table 6 .The intensification of land and lgbor use hy groups Group 2 Group 3 Group h 1961 1962 1961 1962 1961 1962 Ave.no. of tillable acres per head 2.1 2.0 1.6 1.5 1.2 1.0 Aye.no. of cattle per farm worker 69.0 75.h 113.2 121.9 137.7 160.1 In reference to table 3, it will also be noted that gross farm D3 income per tillable acre increased consistently over groups two, three, and four during both.years of the study. Greater intensification of use of buildings will spread invest- ment costs of buildings over a larger number of cattle, thereby reducing per head investments and introducing economies of scale. It should again be born in mind that the larger the size of operation within this study, the higher the percentage of gross farm income attributable to the feeding of beef cattle. Therefore, there will be greater intensifi- cation of livestock within the overallfarm business in the larger groups. Since economies of scale are implied with reSpect to land.and building investments, the farm Operators having large beef cattle feeding Operations will have lower opportunity costs with respect to land and buildings than will farm operators having smaller beef cattle feeding operations. According to the results of the analysis of variance, economies of scale were implied with respect to labor use. 'When labor charge per hundred dollars gross farm.income was diagrammed.there was a 2h percent decrease in the cost of labor per hundred dollars gross farm income between groups twO and three and.a 9 percent decrease between groups three and four. Therefore, the largest economy of scale resulting from feeding larger numbers of cattle occurred because of the better utiliza- tion of labor. The cost curve for labor on the preceding figure lies considerably below that of any of the other inputs indicating that as the size of the cattle feeding operation increases, the percent decrease in the cost of labor will be of greater magnitude than the percent decrease 141; in the cost of any other input considered. In a Minnesota study involv- ing labor use in cattle feeding, results indicated that larger lots required less labor per head than smaller lots, even though similar equipment and procedures were used.9 This is because a certain amount of time is required for each task regardless of the number of cattle in the lot. With larger lots, this fixed time is spread over a greater number of cattle, and as a result less labor is used per head. In this same study it was found that even using hand-feeding methods, large numbers of cattle were more efficient in use of labor than smaller numbers. Increasing the size of small lots, however, gave greater in- crease in efficiency than that obtained by increasing the size of the large lots.10 It is also noted in Table 6 that the average number of cattle per farm worker increased from goup two through goup four over both years of the study. Therefore, it can be concluded that as the average number of cattle per farm was increased, the average number of cattle per farm worker increased or in other words, increasing efficiency of labor was achieved in larger feeder cattle operations. The cost curve for machinery also sloped downward to the right as the size of the operation increased in Figure h. This may indicate 9Johnson‘R. G. , and T. R. Nodland, Labor Used in Cattle Feeding, University of Minnesota, Agicultural Experiment a on, a on Bulletin h51, p. h. loIbid., p. 11. 145 economies of scale with respect to machinery investment. As shown by Table 5, machinery investment per $100 gross farm income decreased by 13 percent between groups two and.three, and by 12 percent between groups three and four. Since gross farm income per $1000 machinery investment was not tested.for analysis of variance with the number of cattle fed in the preceding section, no definite conclusions will be drawn with respect to economies of scale in machinery investment, how- ever, the cost curve for machinery in Figure h, would suggest that economies of scale may be applicable to machinery investment. It was concluded that economies of scale did.not exist in respect to gross income per hundred dollars total expenditures in the preceding section. In Table 5, total farm expenses per $100 gross farm income decreased by 3 percent fran goup two to goup three and decreased by 6 percent from group three to group four. However, in the analysis of variance test on gross farm income per hundred dollars expenditure with number of cattle fed.there was no significant difference between groups. Even though the cost curve for tota1.farm expenses in Figure My does appear to be slightly downwand sloping to the right there were no 1 significant economies of scale for this factor. Feed costs make up a high proportion of total farm expenses and.feed costs prObably will increase almost proportionately with increases in the number of head fed. Since economies of scale were not significant in gross farm income per hundred dollars total expenses, this would indicate that economies of scale were not significant to the total farm business. It he is of interest to determine what percentage of total fam expenses is made up by those factors to which economies of scale may apply. The percentage of total farm expenses made up by land, building and machinery investment as well as labor charge was calculated. A 5 percent charge on investment was used in calculating the charges for land, buildings and machinery while labor was evaluated as the charge for all labor. In 1961 these costs amounted to 25 percent of total farm expenses, while in 1962 these costs accounted for 26 percent of total farm ex- penses, Therefore, such factors as land, buildings, labor and machinery, all of which have at least scme degee of fixity to the farm business, are responsible for 25 to 30 percent of total farm expenses. Therefore, economies of scale will be observed in only those factors which go to make up 25 to 30 percent of total costs. It may be concluded that the Other 70 to 75 percent of the total farm costs overshadow these factors in which economies of scale may exist and therefore, make economies of scale to the overall fem business insignificant on the basis of goes farm income per $100 total farm expenses. It was concluded that economies of scale did not apply with respect to feed costs per hundred pounds gain. Even though feed costs per hundred pounds gain in 1961 ranged from $11.19 for a particular farm in goup three" to a high of $21I.52 for a farm in goup four and in 1962 the range of feed costs per 100 pounds gain was from $12.97 to $20.78 with both farms being in goup two, on the basis of this study feed costs per hundred pounds gain did not appear to be influenced by the number of head fed. 147 On the basis of the analysis in Chapter III economies of scale in beef cattle feeding operations were apparent so far as labor and land and building investments were concerned. Economies of scale may also apply with reSpect to machinery investment. The cost of the above factors make up approximately 25 to 30 percent of the total farm ex- penses. There was no evidence to indicate that larger cattle feeders enjoyed economies in feed costs which were unavailable to smaller operators. The main advantage occuring with larger operations was due to more efficient utilization of certain factors involving fixed costs to the farm business, namely labor, land and building investment, and possibly machinery investment. CHAPTER IV THE PRODUCTION FUNCTION ANALYSIS OF ECONOMIES OF SCALE A theoretical consideration of the production function was made in Chapter II. In the analysis used in this chapter, a production function of the following type is used. I - f(X1, X2, X3, Xh’ X5, X6) + U In the above equation I was considered as the dependent variable representing dollars gross farm income for the farms under study. The dependent variable Y was considered to be a function of the following independent variables: X1 dollar investment in land and buildings X2 dollar value of all feed.fed X3 dollar charge for all labor Xh dollar investment in machinery and equipment X5 dollar charge for miscellaneous cash operating expenses X6 dollar investment in cattle U represents random elements nOt taken into consideration .All of the data making up the dependent and independent variables were taken from the summary sheets of the mail-in-farm accounts for the farms under study. As discussed.ear1ier in Chapter III, data for farms in group one :for both years were not used because of the small sample size and because 19 of the low percentage of farm income within group one attributable to the feeding of beef cattle. Data for the remaining forty-five farms in groups two, three and.four were used in calculating the production functions. 1 A further consideration of what each of the independent vari- ables included is now in order. X1 - the dollar investment in land and buildings was calculated from the summation of average inventory values of land and farm improve- ments.1 X2 - the dollar value of feed fed was taken directly from the summary sheet. X3 - the charge for all labor included the summation of the total values for hired.labor, family labor and.the operator's labor. In the 1961 records, the operator's labor was valued at $225 per month 'while in 1962 the operator's labor was valued at $2h5 per month. The ‘value of family labor was also calculated on the same basis per month namely $225 and $2h5 per month for 1961 and 1962, respectively. Xh - the dollar investment in machinery and.aquipment was calculated at average inventory values. X5 - the dollar charge for miscellaneous cash operating expenses 'was a summation for the following items: (1) custom work, (2) property — — 1The average inventory value for the components of this independent ‘variable was calculated by summing beginning inventory values with ending inventory values and dividing by 2. The same procedure was used in calcu- lating the average inventory values of independent variables Xh and X6. 50 taxes, (3) farm share of electricity and telephone, and other miscellaneous expenses, (1;) livestock expenses such as purchasing or marketing expenses, veterinary fees, etc. , (5) gasoline, fuel and oil, (6) insurance on property and (7) improvements repair and maintenance expenses. X6 - the dollar investment in livestock was calculated as the average livestock inventory values. The above independent and dependent variables were recorded for each farm for the two years and this information appears in Appendix A. The following table presents average figures for each of the dependent and independent variables for each goup over the two-year period. The table also includes average values of the dependent and in- dependent variables for all forty-five farms for 1961 and 1962 (Table 7). Production functions were fitted to the data for each goup of fence for each of the two years and for all forty-five farms (for each of the two years), using the regression method. Estimates of a, bi, R2, R, Sync: were calculated for each of the three goups of farms and all forty-five farms for 1961 and appear in Table 8 o 1961 Results Considering the regession equation for all forty-five farms for the year 1961, it would appear as follows: I - 4200.9 + .1988X1 + .3962X2 + 3.57h8x3; .0105Xh - 1.1226X5 It .11I7SX6 ‘ The a and bi values have been substituted into the above equation. The Sl bi coefficients or the partial regression coefficients of the linear production function on the observed variables are the marginal pro- ductivities of the productive factors with respect to output. They in- dicate the additional product that would be produced on the average, other factors held constant, if a particular input is increased by one unit.2 I If for example, an additional dollar is invested in land and buildings (X1), and all other inputs are held constant, an increase in 1' (gross farm income) of approximately .20¢ would be expected. If an additional dollar's worth of feed is fed (X2), and all other inputs are held constant, Y would be expected to increase by approximately .1095. If an additional dollar is expended in labor, and other inputs are held constant, gross income would be expected to increase by $3.57. If an additional dollar is invested in machinery, while other inputs are held constant, gross fann income would be expected to decrease by .0195. If an additional dollar is spent on miscellaneous cash operating expenses, while other factors are held constant, gross farm income will be expected to decrease by approximately $1.12. If an additional dollar is invested in livestock when all other inputs are held constant, gross income would be expected to increase by approximately .15¢. 2Hover, C. B., "Economic Interpretation of Production Function Estimstes," Resource Productivity, Returns to Scale and Farm Size, (edited by Heachr, Johnson, and Hardin, limes, W Towa State College Press, 1956) p. lh8. 52 Rafi: Ream amass aims 3me 33.8 «SJm Seam 338 5 paospmoEH .. ox 39m :26 mmmfi 8N3 mam 8m; Sim sou; .sa mfipepodo ammo Somaaflmomaz .. ma 08.3 mama 0R8” mmoJH Sum.” 98.8 8?: SHJH dang s E02232 5 22385 .. as 83 $5 on} 3.0.3 Sum 8.3 H83 :83 .333 H9 to this .. me warm 08:3 33H 0%.? 08.3 08.3 madam moan“ use same no Sag .. «a 8me seams mama 06.8 +3.8 gamma 23m Siam passpmmpfi @533 a 33 .. Ha Sums” mame a 48.03 mamas” 30.3% gums a momfima 593$ oaoofi 5am 395 u mMMwmmmr all! m P m Mfimmmmwi a F m I N! .02 $6.8 83 BE. 139” one .62” now masonwlho, moanwaawb pomvcomolmmw. unswpnmwmbmou now 33”.? $3653. N canoe)! u ‘y I N “ I l L I mama..eam asap..mnm aagw..:nm asap..mpm oeaa..~pm mamo..apm c.00mw mmnm. Homw. m~aa.+ wNNH.H: moao.u wapm.m+ Noam.+ mmmfl.+ m.oommu m: proa mean..enm maaa.m.mnm eHaa..:nm aaom.«.mnm amae..mnm swam..apm m.emmma Jams. swam. momm.a doom.+ awoa.u Hmmm.m+ momm.+ omau.+ m.omomu 0H : mama..onm maaw.umnm womm..spm amma.anmnm oasm..~nm oooo.-Hnm H.3aam oaam. moms. ammm.+ aofiw.g mqmfl.u ammo.o+ o:m~.u mooa.+ H.Hmaa+ ma m mmam..epm mmem.N-mnm waom..snm seao.m.mpm awpe..~nm maoa..anw H.Hpm~ om:~.+ oaom.+ moma.+ moo~.u memo.+ mmmm.m+ wmmw.+ Nowa.+ m.mmwas ma N I I II I III) I ll r ‘mdona ”dz saw m mm wp mp an mp up Hp a nwmsnmm @5090 .1. In. I. In. I, .L. .uur, .. me .oz f .Aaomav maoapocsm aoapuseond one no“ Axawv opmsapmo mo honno shutdown one Amv powwoammooo cowpaaonhoo omofipdss «Away cowpwnwsnopoo oHofipHss Ho pcoaowmmooo .A nmv upcoaoammmoo :oaumonwcn Mo guano oncogene «Am. nv mpcoaofimmooo scammonwom w manna 53 St .A consideration of the various inputs will be made based on the order of the magnitude of their respective b coefficients.3 The highest returns in the year 1961 is to labor input. Throughout all three groups the b values for labor is equal to or exceeds 3.29. On this basis it could be argued that since there is a high return to labor, the amount of labor should be increased. An opposing argument, however, ‘would be to consider labor as fixed.to the individual farm. The average number of men per farm.for the forty-five farms for 1961 was 1.9. The biggest share of the labor on these farms will be made up of the operator's and.family labor. Assuming that this labor has little opportunity cost, it is reasonable to assume it is fixed. The farm operator's labor will have a low opportunity cost since he will most likely leek the skill and.knowledge to make a reasonable living in off the farm employment. Even if off the farm.opportunities are an alter- native the operator is still faced with a heavy'investment in land, buildings andumachinery'which he cannot afford to allow to remain idle. Most of the other labor on the farm in addition to the operator's will be family labor. Alternative opportunities to unskilled.family labor are likely'to'be few. Therefore, the assumption that labor is fixed to the farm.is reasonable. Since returns to labor are high and since 3If expenditure items such as feed and miscellaneous expenses are to be profitable, the returns from additional expenditures in such items mmst be greater than their cost. Investment items will be profitable if the returns from additional investments is greater than the cost of the interest, repairs, and depreciation on the additional investment. SS labor is considered to be a fixed.factor, perhaps existing labor is not being utilized as efficiently as it might be. Such a conclusion would further substantiate the conclusions drawn in Chapter III. In that chapter it was concluded that economies of scale do exist with respect to labor. Farmers in the larger size groups were getting better labor efficiency in which case less labor was required per head.fed. In considering all forty-five farms, the second highest returns per additional dollar invested went to feed. ‘While this statement is generally true it does not apply to group three which has a negative b value for feed fed. Land and building investment over all fortyhfive farms give the third highest returns. The b values for each individual group for this variable were all positive and the greatest return was noted in group four. Using a similar argument to that used for labor and considering land and building investment as fixed to the farm, it could be argued that the b value for land and buildings should be driven down to a value that would give a reasonable return to investment)"L In this case the MVP of land and buildings would be closer to being equal to the marginal.factor cost of the investment, assuming that a 20 percent re- turn on investment is too high. Since returns to land and building investment are high this could indicate that existing land and buildings ——-—v hAllowances have been made for maintenance and depreciation. Maintenance and repairs are included in the X variable while depreciation is accounted.for by using the average invento value of land and.build~ ings. 56 are not being utilized as efficiently as possible and.this conclusion is compatible also with those drawn on land.and.bui1ding investment within Chapter III. On an overall basis the fourth highest returns went to livestock investment. The b values for livestock investment in groups two and three were positive, however, the b value for group four was negative. This could imply that those farmers in groups two and.three should invest in more cattle while those farmers in group four should.not. In considering all fortyafive farms, the b value for machinery investment was negative (-.OlOS). It does not appear, however, that there was a serious overinvestment in machinery for all forty-five fans because of the low negative value of bu. In considering b values for individual groups, the only group with a positive b value for machinery investment was group two. Group three had.a b value of -.12h3 while group four had a b value of -.7087. The problem of intercorrelation of the variables may'be appearing here, in which case high returns to land.and.buildings, for example, could.drive the returns to machinery down. The investment in miscellaneous cash operating expenses gave the lowest returns over the fortyhfive farms. The b5 value for all fortyafive farms was -l.1226. The b5 values in groups two and three were negative while the b5 value for group four was +.306l. It'would appear that groups two and.three have not reached sufficient size of business on the average to avoid negative returns to miscellaneous 57 cash operating expenses. On the other hand, group four has a positive return to these costs, indicating that the size of business in group four is at least large enough to avoid negative returns to such costs. The multiple correlation coefficient (R) for the production function involving all forty-five farms was found to be .914 indicating a high degree of association between the dependent and independent variables. The coefficient of mfltiple'detennination (a?) of .89 indicates that 89 percent of the variance in gross fam incomes was associated with the independent variables. The standard error of estimate (Sync) in this case was canputed to be $7807. Production functions were also filled to the data for each goup of fame and for all forty-five fame for the year 1962, using the regression analysis. The regression coefficients for 1962 appear in Table 9 o 1262_B_gsults Considering the regression equation for all forty-five fans for the year 1962, it would appear as follows: 1 - 41766.1; 4- .1552X1 + .7563x2 + .8h87x3 + .3806Xh + 3.1;7901:S .. .osuox6 As was noted earlier the regression coefficients (bi's) indicate the additional product that would be produced on the average, other factors held constant, if a particular input is increased by one unit. On the basis of all forty-five farms, the highest returns is to 58 15 or cash Operating expenses. Breaking it down by groups, all groups had positive b coefficients for miscellaneous cash operating expenses. This variable gave the lowest returns in 1961. In referr- ing to Table 1, it is obvious that average gross income increased significantly from 1961 to 1962. On an average over the forty-five fams gross farm incane increased by 27.3 percent. This increase in goss farm income will have a significant impact on retm'ns to ex- penditures in miscellaneous cash operating expenses. Indications are that in 1962, the average size of fam business was at least large enough to have positive returns for miscellaneous cash operat- ing expenses in each of the groups. The significance of such high. returns to miscellaneous cash operating expenses is somewhat reduced due to the fact that the standard error of b5 is larger than the stan- dard error of any of the other regression coefficients when consider- ing all forty-five farms. Since miscellaneous cash operating expenses include several fixed costs such as property taxes and insurance, it would not be rational to suggest increased expenditures for this variable. The second highest returns in 1962 was to labor charge. ‘C'troups two and three had positive b coefficients while group four had a negative coefficient. Using a similar argument as that used for labor in 1961, on the basis of all forty-five fams, there are indications that the labor fixed to the farm is not being utilized as efficiently as possible. 32.1.8... Sashes ensure Sat-mam amiss cameras 3.8%.. 3?. 43m. osmo... 83.? 8mm... 53... moms... «m3... 4.82.? m: .9309 mosh. 33.7an 53.? seesaw salsa Raise 44.85.. 8mm. $3. 3%... ommmi 334 $93.. 3%... flaw: was? .3 a mature 38.7QO Qantas Reeves Ensues...” «mats... Sana. ems. 82.. mam... an... ode... a8... «33. non... 0.3mm- a m 3.33. seem. as. Banter anew-mam flatten seeks... manure shows... clam... 841? $8.. .68.? 32.? $3.. manna- S N i. :11. I. Imsonw .02 a me as me up as e a sense 995 .333 meanness 833.5% one he Army onsets no no.5 sausage e5 so passionate. Sandstone. massage 85 Sapefietsoe oHnApHns no pnouoaumooo .Aaomv opposedmmooo :oamuonwon no means oneness: .A .an nanoaoaumooo coaumonwom m canes 59 60 On an individual group basis, group two has the highest b coefficient for labor, followed by group three and group four in that order. Group four appears to be getting negative returns to labor. It would appear that goup two is getting the highest returns to labor and on the basis of previous arguments is using labor least efficiently of any of the three groups. 12 or feed fed had the third highest returns to investment as determined by the regession coefficients. All three groups had positive b coefficients, however, groups two and three were the only two groups which received higher returns than the cost of an additional dollar's worth of feed. ‘ihe fourth highest returns went to machinery investment. Go the basis of groups the only group having negative returns to machinery investment was goup three. On the average of all forty-five farms, the fifth highest returns went to land and building investment as indicated by the b coefficients for land and buildings. On an individual group basis the b coefficients were positive for all three size goups. It is also interesting to note that the standard error of the regression coefficient for land and build- ing investment is the lowest standard error of any of the regession co- efficients for all three groups. Since land and building investment is fixed to the farm business, positive returns of .1552 on the average suggests that the land and building investments is not being utilized as fully as it should be. Similar conclusions were suggested in regard to land and building investment for the year 1961. 61 The lowest return for any input category for the year 1962 went to livestock investment. The b6 coefficient for all forty-five farms was -.OShO. The only group having a positive b6 value was group three. Uhfle negative returns to livestock investment over the forty-five farms is difficult to rationalize, the magnitude of the negative b6 value is not great. High cattle prices during the year 1962 could be responsible for a negative return to cattle investment. Since it is virtually im- possible to increase the size of the cattle feeding operation and at the same time reduce the investment in livestock, then it would appear that the average size of operation in 1962 was close to Optimum. The multiple correlation coefficient (R) for the production function involving all forty-five farms was found to be .95 indicating a high degree of association between the dependent and independent vari- ables. The coefficient of multiple determination (R2) of .91 indicates that 91 percent of the variance in gross farm income was associated with the independent variables. The standard error of estimate 5y): was canputed to be. 8861. A Carperison of the Production Functionjesults in lgél and 1962 At this point it is of interest to compare the results of the production function analysis for the years 1961 and 1962, and to estimate a simple average for the a and b values for the separate pmduction functions for all forty-five farms for the two years. Table 10 lists the regression coefficients of the production functions for 1961 and for 1962 along with the simple average of the regression coefficients for 62 investment inputs and expenditure inputs, for the two year period. The table also ranks inputs according to decreasing returns to: (1) investment inputs, and (2) expenditure inputs, for each of the three regression equations. The standard errors of the regression coefficients is also included along with their rank of magiitude of error. In the table the inputs have been divided into two categories and ranked according to decreasing returns for each category in order to more accurately analyze the productivity of investment inputs and ex- penditure inputs. In considering investment inputs, _m_a_chinery_investment had the highest return of the three investment inputs for the two-year period as indicated by the simple average of the bl; coefficients. Returns to machinery investment ranked first in the year 1962 and ranked third in the year 1961. The magnitude of the standard error of bk was the third highest of all 5131's over the two-year period. It is interesting to note that the standard errors of the b coefficients were remarkedly consistent in order of magnitude over the two-year period. The investment input having the second highest returns over the two-year period based on the simple average of the b1 coefficients was land and buildings. Returns to land and building investment ranked second in 1962 and first in 1961; The standard error of the bl coefficient was the lowest of all Shim. The investment input having the lowest returns over the two-year period as indicated by a simple average of the b6 coefficients was H NHew. H 8%. H 4H3. N N emee. N .83.. N News. H : NNON. : meN. : oomH. m memeH.H + mfiHHNN + NxNeNm. H N m $83.... + mags. . Nessa. m H N mHeNNHH u meanem.m + NHNomm. .emHz no on mum NN upemnH 09mmcefl m HNNH. m 69. m wHNH. m + mango. m + oxozmo. N been xoo paces ox m mEN. m mmmN. m mSN. H + :MommH. H I JNBQ M. m : n H . em me .n« eHdEHm He beneHemez we seem o ono. 0 came. 0 mHmo. N . H85. + as .. N + HmemH. + eeNHHu H + numeeH. + eNmOHo. a wammH. + HONm . fines}: .weHm a 33 HH 35 CH Psenmwmoan mfinm Ho emanated mHaaHm AmomHv nzunm .Ho «condemns no ream aNemHv e.Hm No sense enneneem AHemHv e.Hnm Ne eeseHnmez we seem PHm Ne totem eteeeem 33.5 359: op mgpmm no xcum - M .ba eHeaHm Bean.“ on ngpom we scam I H Nme mean." ea 3.53 as near I H meH NemH ens HomH 23» one .8.... 3385“ 8333a one we 3:33:30 SHmmoumon as» no omega; 3956 one Sago 4 OH e32. 63 6h livestock investment. Returns to livestock investment ranked third in 1962 and second in 1961. The standard error of the b6 coefficient was the second lowest of all Sb 1.8. On the basis of simple averages land and building investment and machinery investment appear to be getting substantially higher rettu'ns than is livestock investment. This con- curs with the discussion in Chapter III of economies of scale for land, bm’lding and machinery investment. In considering the emendiiwe inputs, Labor had the highest re- turns of the three expenditure inputs over the two-year period based on the simple average of b3 coefficients. Returns to labor ranked second in 1962 and first in 1961. The reliability of this estimte is discounted to some extent, since the standard error of the b3 coefficient was the second largest of all Sbi's' . Miscellaneous cash expenditures had the second highest returns of the three expenditure inputs over the two-year period based on the simple average of the b5 coefficients. During the, year 1962, returns to miscellaneous cash operating expenses were highest among returns to expenditure inputs while in the year 1961 they were the lowest. Because of the fact that the standard error of the b5 coefficient was the largest of all Sbi's the accuracy of this estimate should be discounted accordingly. The expenditure input having the lowest returns over the two- year period based on the simple average of b2 coefficients was feed. Returns to feed in 1962 ranked lowest among returns to the three 65 expenditure inputs, while in the year 1961 returns to feed ranked second. The standard error of b2 was the fourth largest of all Save. On the average returns to labor and miscellaneous cash expenses were at least greater than their cost, however, returns to feed did not cover cost on the average nor in either year according to the pro- duction function estimates. Since labor had the highest returns of the three expenditure items over the two-year period, this analysis I will also cmcur with suggested economies of scale with respect to labor in Chapter III. It is expected that the increase in gross fam income of 27.3 percent from 1961 to 1962 has been responsible for many of the changes in returns to inputs that were noted to have occurred between 1961 and 1962. A simple average of the regression coefficients for production functions for 1961 and 1962 would be expected to give a better estimate of returns to inputs, than would the regression coefficients for in- dividual years. In the foregoing analysis reg-ession coefficients, have been used as a means of marginal productivity in measuring the marginal productivity of the various input factors. Changes in price relation- ships from 1961 to 1962 had significant impacts on the values of the regression coefficients for the two years. It would be reasonable to assume that it is virtually impossible for any farmer to have all of these inputs combined and arranged in a state of equilibrium. Farm operators are continually rearranging the structure of their business 66 to meet new and changing technological and economic conditions. Drake points outthat a study involving many farms is useful to operators in planning their business.5 He suggests that a study can- bining the emerience of many farmers will estimate average marginal value productivity for factors with reasonable accuracy. Drake also intimates that while a marginal productivity analysis is generally useful, it is not always interpersonally comparable. He suggests that farmers seek to maximize particular personal or family net utility functions. This means that farmers have different attitudes towards risk of capital, and the expenditure of labor. Part of these differences will depend upon unmeasured resources which the farmer has at his command. Then too, farmers are not likely to make the same estimate of the relationship between gross income and input factors.6 Therefore, a word of caution is in order in applying conclusions from the general to the specific. While many general conclusions are implied with respect to input relationships within the chapter, individual farmers should view these relationships in the light of their own particular business and their own personal objectives. 5Drake, Louis S. , Problems and Results in the Use of Fan: Account Records to Derive Cobb-Doug as ue o uc 1v1 unctions, unp Ph.D. Thesis, Michigan—State University, 1932, p. I7. 6Ibid., p. 18. 67 Investment Per Han and Investment Per Head Considerations Since Chapter IV in dealing with production functions, has been concerned partly with investments of various inputs as determinants of goss farm income, a consideration of investment per man or investment per head fed is appropriate at this point. Table 11 shows these calculations by groups for the years 1961 and 1962. Table ll Total inveshuent per man and total investment per head fed 1961-62 — 1961 1 1962 ‘ _ "‘ Total Invfi . Total Invest. Total livest. Total Invest.— __Group No. _Jer man per head fed_ Er man i N_head fed * 2 $63,658 $922 $71,8h7 $953 3 86,6114 765 89,518 73h h 81: 027 610 9h h72 590 Av. '55 farms $77,535 $735 $ , $39? The total investment figure used in the table above included land and buildings, machinery, cattle and feed.7 From the above table total investment per man increased from group two to group three and decreased in group four for the year 1961. Therefore, farmers in the larger size groups had more resources to work with. The intensity of the beef cattle 7Feed investment represents one-half of the value of feed fed. This adjustment was made in order to have feed investment represented ’ as an average inventory value comparable with those used for each of the other investment factors. 68 feeding operation or the number of cattle per acre, increased from group two to group four. As a result total investment per head de- creased substantially as size of operation increased in both 1961 and 1962. Most of the components making up total investment are of a fixed nature. Land and building investment is fixed to the business. Machinery investment, while not entirely a fixed cost to the business, still has some degree of fixity. Feed investment may be considered either as a fixed or variable cost. It is considered as fixed if it has little or no alternative value. It may be considered as a variable, if it has an alternate value. It would be considered a variable cost, if it is not grown on the farm and has to be purchased. Cattle in- vestment would be considered as a variable cost. While total investment includes both fixed and variable costs the larger percentage of the investment will be of a fixed nature. Therefore, as the number of cattle fed increases, the same investment in land, buildings and machinery can be spread over a larger number of cattle and, consequently, the investment per head decreases. The results in Table 11 would indicate that economies of scale do exist with'respect to fixed investments. Heady and Jensen hypothesize the following as possible cost reductions for livestock enterprises as size is increased: (1) less labor per animal, (2) less building and equipment capital per animal, (3) less feed, including pasture land per animal and (1;) less capital in the animals themselves.8 They go on to point out that the main -— 8Heady, E. 0. and H. R. Jensen, Farm Management Economics, Prentice- Hall Publishing Co., Englewood Cliffs, NewTerseSrT p. 157. 69 savings must cane from labor and building investment. They further state that there is little chance for economies or diseconomies in feeding, aside from.those due to good or poor management. The results and conclusions drawn within Chapters III and.IV are consistent with those mentioned above. mm v BEE FEEDJNG BUILDINGS, EQUIPI-IEIIT AND LABOR COSTS AS DERIVED FROM THE SPECIAL QUESTIONI‘IAEE It was concluded in Chapters III and IV the economies of scale were apparent in the beef feeding operations under study with respect to land and building investment and labor costs. In order to more accurately analyze such costs, additional information was requested from the farmers by means of a questionnaire, a copy of which appears in Appendix B. Information was requested on investment and depreciation in buildings, equipment and feed storage facilities for the beef cattle feeding enterprise, along with the type of feeding system used. Estimated labor requirements were requested and the cooperators were questioned as to whether they were going to expand their operation, continue to feed about the same number or reduce the number of cattle fed, along with their reason for doing so. All fifty-one farmers in the original four size goups were sent a copy of the questionnaire and forty-one farmers responded to the questionnaire. According to the 1962 classification of farms by size groups, based on the average number of cattle fed per farm, five of the six farmers in group one replied, sixteen of seventeen in group two; ten of fourteen in group three and ten of the fourteen farmers in group four. Replies to the questionnaire provided a good representative size distribution. 71 In order to get a.more accurate breakdown on building and equip- ment costs allocated.to the beef feeding enterprise, the cooperating farmerS‘were asked to give 1962 beginning inventories for the following cattle buildings and equipment (1) barns, (2) sheds, (3) concrete yards, (h) silos, (S) silo unloaders and (6) any other feeding equipment such as angers, bunks, etc. The first three items above were classified as housing and yard investments while the last three items were classi- fied.as feed storage and.feeding equipment investments. In addition, the farmers were asked to give the depreciation rate and the age of each item. Current investment in barns, yard.and.in storage facilities and feeding equipment per head were calculated, as well as the total investment for the four size groups, (Table 12). Annual charges per head fed.for housing and.yard.and feed storage and equipment have also been calculated. These charges include the yearly depreciation as well as charge of six percent of the calcu- lated new value, estimated.to cover interest, repairs, taxes and insurance. Table 12 lists these investments and annual charges, along with the total charge per head fed.to housing and.yard.and.feed storage and equipment for all four size groups. Table 12 indicates a ten percent decrease in housing and yard investment between those farms feeding an average of fifty-one head of cattle per year and those farms feeding an average of h35 head per year. However, feed storage and equipment investment increased'hy sixteen perb cent. Therefore, any economies of scale with.respect to housing and 72 Table 12 Housing and yard, feed storage and equipment investments and charges per head fed. __¥ u wr— — ———— ii ' Investment per Head Fed Annual Charge _per Head Fed AvTNomf—Cat- Housing Feed Storage Housing Feedfiorage Group tle per farm and for and for \ No. fed in group Yard Equipment Total Yard Equipment Total 1 51 $h8.b3 $117.98 $96.141 $7.09 $6.37 $13.h6 2 H2 h7.98 148.33 96.31 7.35 7.119 1h.8h 3 182 16.66 50.30 95.96 6.13 7.80 1h.23 h h35 16.31: 55.h6 98.80 5.98 8.55 111.53 __ AV. for fi' '— — 1; Clips 201 $m.9o_ $52.38 @3738 $339 $8.06 tilt-1:5 yard investment are more than offset by increased investment in feed storage and equipment as size of operation is increased. This is illustrated in that total investment in housing, yard, feed storages and feeding equipment increased by two percent as the average size of feeding operation increased from fifty-one to 1:35 head. Therefore, while housing and yard investment per head may decrease as size of operation increases, the investment in feed storage and feeding equipment increases, probably due to a higher degree of mechanization in larger operations, therefore making economies of scale non-existent with respect to hous- ing, feed storage and feeding equipment investment.1 0 A #- fi 1 1In a latter section in this chapter labor requirements as re- lated to size of operation will be considered, and it would be expected that less labor per head fed will be required in larger feeding opera- tions which have larger more mechanized feeding equipment. 73 The annual charge per head fed for housing and yard decreased by $1.11 or sixteen percent between those farms feeding an average of fifty-one head and 1:35 head. The charge per head fed for feed storage and feeding equipment, however, increased by $2.18 or thirty-four per- cent between those farms feeding an average of fifty-one head and 1:35 head. The total annual charge for housing, yard, feed storage and feeding equipment increased by $1.07 or eight percent between those farms feeding an average of fifty-one head and those farms feeding an average of 135 head. Group one had the lowest charge for housing, yard, feed storage and feeding equipment and goup two had the highest charge while groups three and four had charges in between. Therefore, any econanies of scale that may exist with respect to charge for hous- ing and yard investment are more than offset by increases in charge for feed storage and feeding equipment as size of operation increases. Therefore, any economies of scale that may exist with respect to charge for housing and yard investment are more than offset by increases in charge for feed storage and feeding equipment as size of operation in- creases. Therefore, one may conclude on the basis of this special study that economics of scale are non-existent with respect to charges for housing, yard, feed storage facilities, and feeding equipment. In Chapter III economies of scale in beef cattle feeding opera- tions were implied with respect to the total farm business investment in land and buildings in relation to goss farm income, but in Chapter V it was concluded that economies of scale did mt exist with respect to 7h housing and feeding facilities used by the beef feeding enterprise. Therefore, any economies of scale that were found in Chapter III with respect to land and building investment might be attributed to better utilization of land than to better utilization of buildings or feeding equipment. Capacity_of the Feedlot and Average N_u_mpep of Cattle Fed The farmers were also asked to report the capacity of their feedlot. Since most of the farmers in the study fed calves, they were asked to report the capacity of their feedlot in terms of number of head when feeding calves. The following table conpares the average feeding capacity of the feedlot with the average number of cattle fed, on a l2-month basis, by size groups. Table 13 A comparison of feedlot capacity and average number of head fed. Size Group No. Average Capacity Average Numper of Head 3; of Capacity 1 75 51 68% 2 1th . 112 78 3 229 182 79 h A98 ABS 87 —_ From the above table it is evident that the larger operations are utilizing their feedlots to a greater percentage of capacity than are the smaller operations. It should be pointed out , however, if farmers are feeding yearling cattle rather than calves, the above figures 75 will not apply. Likewise if the feedlot is in use only nine months of the year, the above figures underestimate the percentage of capacity. Since the farmers feeding more cattle are utilizing their feedlots to a higher percentage of capacity than those feeding less cattle, this will explain decreased investment in barns and yard and decreased charges to barns and yard as the size of the operation increases. Laborfiggguirements of the_§_eef Feeding_Er1terpr_i._s§ In Chapter III economies of scale in beef feeding operations were indicated with respect to labor. The special questionnaire also asked the cooperating farmers to estimate the amount of labor required by the beef feeding enterprise. They were asked to estimate the number of hours required in regular daily feeding operations, as well as the number of hours‘required to do irregular chores such as cleaning out sheds and yards, and the number of hours required to buy and sell the cattle. Labor was valued at $1.00 per hour. The following table lists the labor charges per head fed for each of the above chores for each of the four size groups. The table also shows the total charges per head fed including housing, feed storage and feeding equipment as well as all labor required by the beef feeding enterprise. In Table 11;, charges to regular daily chores per head fed de- creased as the size of the operation increased. The charge for regular chores per head fed decreased by $3.20 or sixty-seven percent between those farms feeding an average of fifty-one head and those feeding an average of 135 head. Charges to irregular chores per head fed decreased 76 Table 11; Labor char-es for re- . and irre ar chores and b v a ; and sellin. _ -.or ieper "-ea 0-‘ I- 893 Av.No.of w Buying for Housing, Group Cattle Fed Regular Irregular and Feeding Equipment 8: No. in Group Chores Chores Selling TotaLLaborfi per head_Fed 1 51 $h.78 $2.08 $ .65 $7.51 $20.97 2 112 3.70 1.29 .51 5.50 20.3h 3 182 1.91 .99 .59 3.h9 17.72 h 1135 1.58 .h6 .36 2.110 16.93 AV. 201' at — T “- — — — ‘ ___Croups 201 $2.21,__ $ .80 8 .h__, $3,h3 $17.88 by $1.62 or seventy-three percent while charges for buying and selling per head fed decreased by $.29 or forty-five percent between those farms feeding an average of fifty-one head and those farms feeding an average of h35 head. It will be noted, however, that the charges to buying and selling per head fed did increase between group two and group three. The total charge for labor per head fed decreased consistently as the size of the operation increased. Total labor charge per head fed de- creased by $5.11 or seventy-two percent between those farms feeding an average of fifty-one head and those fanns feeding an average of {135 head. The above analysis will further substantiate the conclusion drawn earlier that the greatest economy;r of scale to be derived from increas- ing the size of a beef feeding operation, can be attributed to more efficient labor utilization. While economies of scale are not apparent with respect to barns, feed storage and feeding equipment, larger operators are in a position to use a greater degree of mechanization resulting in much more efficient use of their labor. 77 The column on the extreme right of Table 1h lists the combined charges for labor and housing and equipment per head fed. The total charge for labor, housing and equipment decreased by $.63 or three per- cent between those farmers feeding an average of fifty-one head and these feeding an average of ll2 head and it decreased by $2.62 or by thirteen percent between those feeding an average of 112 head and those feeding an average of 182 head and decreased by $.79 or four percent between those farmers feeding an average of 182 head and 135 head. In other words, as the average size of operation increased from fifty-one to 135 head, the charges to labor, housing and feeding equipment de- creased by $h.0h or nineteen percent. The greatest economy of scale appears to occur between those farmers feeding an average of 112 and those feeding an average of 182 head. Since there are no economies of scale with reapect to housing and feeding equipment investment, the entire reduction of the charges for labor, housing and feeding equip- ment can be attributed to the more efficient use of labor. Feeding Systems Used by the Farms UndeLStudy The cooperators indicated that a wide variety of feeding systems were being used on the forty-one farms. Some farmers were feeding pri- marily by hand and consequently had a small investment in feeding equipment while others had completely automated feeding systems using either augers or fence line bunks with self-unloading wagons. The feeding systems reported were grouped into the following three categories: (1) hand feeding system, (2) auger feeding system and (3) fence line 78 feeding system. Table 15 lists the percentage of each type of feeding system used for those farmers who reported. Table 15 Type of feeding system. ' 1v. No. Fad Wand linger FEnce‘Line‘ ‘— Groyg No. per Grog) Feeding Feeding Feeding 1 51 10% 110% 20% 2 112 56 31 13 Av.for Groups 1 8c 2 98 52 353 I; 3 182 0 80 20 h 1:35 20 50 30 Av.for Groups 3 & 1: W .10- ‘6'3- ‘2';- Table 15 indicates that the larger size operations were using more automated feeding equipment than were the smaller size.groups. Fifty-two percent of the farmers in groups one and two were hand feeding, while forty-eight percent had automated feeding equipment, either auger systems or fence-line feeding systans. Only ten percent of those farmers in groups three and four were hand feeding while ninety ,per- cent had automated feeding equipment. Since a higher percentage of the larger, operators had more automated feeding equipment than the smaller operators this will help explain why economies of scale were not apparent with respect to charges for feed storages and feeding equipment per head fed but were for labor. The auger feeding systems or fence-line feeding systems will require a much higher investment per head fed than will the equipment used in . 79‘ a hand feeding system. The use of auger feeding systems or fence-line feeding systems on the other hand can substantially reduce the labor requirements per head fed in every day feeding operations. The usepof more mechanized equipment on the partof larger operators then will in part be responsible for apparent economies of scale with respect to labor. In the case of many small beef feeding operations the cost of mechanized feeding equipment is prohibitive thereby making the most efficient labor utilization impossible to the small cattle feeders. The final question that was asked of the cooperating farmers dealt with their future plans with respect to the size of their beef feeding enterprise. The following table indicates the future plans of the forty-one farmers reporting. Table 16 Future plans of farmers for their beef feeding enterprise. ETmp Size—3? — mxpand ‘ U‘ontinue to Weduce No. Group Considerably Feed Same No. ansiderably 1 0- 75 head 20% 80% -- 2 76-150 head 31 63 6% 3 151-250 head to 50 10 h over-250 head 30 70 -— Av.of all famers reporting 32 63 5 From the above table twenty percent of those farmers reporting who fed up to seventy-five head planned to expand while eighty percent planned to continue feeding approximately the same number of cattle. 80 Of those farmers reporting who fed between 75 and 150 head, thirty-one percent had plans for expansion while sixty-three percent planned to continue feeding the same number and six percent planned to reduce the numbers fed. Of those farmers feeding between 151 and 250 head, forty percent planned to expand the beef feeding enterprise, fifty percent planned to continue feeding approximately the same number while ten percent planned to reduce their size of operation. Of those farmers reporting who fed more than 250 head per year, thirty percent planned to expand their feeding operation, while seventy percent planned to continue to operate at their present size level. If one combines the two smaller size groups, sixty-seven percent were planning to continue to feed the same number, twenty-nine percent had plans for expansion and four percent planned to reduce their operations. If the two larger groups are combined, sixty percent were planning to feed the same number in the future, thirty-five percent had plans for expansion and five percent planned to reduce their size of operation. In total thirty- two percent of those farmers reporting planned to expand, sixty-three percent planned to continue feeding the same number of cattle, while five percent planned to reduce the number of cattle fed in the future. The cooperating farmers were also asked to indicate their reasons for their plans to expand or not to expand their operations. Most of those who planned to expand in the future indicated that they would do so in order to make more efficient use of the farm machinery, buildings, feeding equipment and feed supply. Quite a number of farmers who had 81 plans for expansion listed the main reason for expansion as a method of increasing labor efficiency. Table 16 indicates that sixty-three percent of the farmers re- porting planned to continue feeding about the same number of cattle in the future. The main reason given for continuing to feed about the same number was that they are now feeding as many cattle as their land and feed supply will carry. A small number listed buildings and equip- ment or lack of capital as the limiting factors. One farmer summed up his thoughts by stating that the present is not a time for the expansion of a beef feeding enterprise. A few other farmers indicated that their plans for future expansion depended a great deal on cattle prices. Only two farmers of those reporting planned to reduce the size of their operation, and they listed age of the operator or a shortage of feed as their reasons for doing so. Fran the above analysis it would appear that the majority of the farmers replying to the questionnaire feel that their present size of operation is about optimum with respect to the feed supply that they have, hence they do notfhave plans for sizeableexpansions. Those who do plan to expand will do so in order to make more efficient use of their buildings and equipment, labor and feed supply. In Chapter v, a more accurate estimate of building and feeding equipment investments and charges was obtained by means of a questionnaire 82 received.from.fortybone of the original.fiftyaone farms under study. The questionnaire also provided information on labor requirements for specific tasks involved with the beef cattle feeding enterprise, as well as a description of the feeding system used on each.farm. In addition, it provided information with respect to whether farmers planned to expand.their size of operation or not, along with their reason for doing so. . Investment in housing and.yards per head.fed decreased slightly as the size of operation increased. 0n the other hand, investment in feed storage facilities and feeding equipment per head.fed increased as the size of the operation increased.more than offsetting any economies of scale in housing and yard investment. The charges per head fed to each of the two building and equipment categories followed approximately the same Order as investment per head fed in the two building and equipment categories as size increased. Labor charges per head.fed.for (1) regular daily chores, (2) irregular chores and.(3) buying and selling cattle, decreased substantially over the four size groups and total labor charges per head.fed decreased by $5.11 or seventyhtwo percent between those.farms feeding an average of fiftyaone head and.those farms feeding an average of hBS head. The combined charges for buildings, equipment, and labor per head fed decreased.by $h.0h or nineteen percent between those farms feeding an average of fifty-one head and hBS head. It was concluded that the above economies of scale could be attributed almost entirely to the 83 more efficient use of labor in larger operations. It was also noted that larger operators had.more mechanical feeding equipment than smaller operators and.this will be partly responsible for more efficient labor utilization by larger operators than by small operators. When the farmers were asked whether they planned to expand.the size of their feeding operation or not, thirtyatwo percent of those reporting indicated that they intended to expand in order to make more efficient use of buildings, equipment, labor and.feed supply. Sixtyh three percent indicated.the present size of their operation was optimum with respect to the amount of land, buildings, equipment, labor, capital and.feed that was available on their farms. Five percent of the farmers reporting intended to reduce their size of operation on account of labor or feed shortages. In conclusion, the analysis in Chapter V would indicate that the most important economy of scale with reSpect to larger beef feeder operations will be derived.from more efficient labor utilization made possible by the use of a higher degree of mechanization on larger cattle feeding farms. CHAPTER VI RETURNS T0 SCALE AND SUGGESTED OPTIMUM SIZE OF BEEF FEEDER CPERATIONS In order to consider returns to scale, the average number of cattle fed and.the average gross farm income was determined for each farm for the twoeyear period 1961 and 1962. All fiftybone farms have been plotted.in.Figure S on the basis of the average number of cattle fed, and the average gross farm income. A simple regression analysis of the form I - a +‘hx was run, in which I, the dependent variable, represented average gross farm income from all sources while X, the independent variable, represented.the average number of cattle fed. The results of the regression analysis on the fifty-one farms are listed in the following equation in which the calculated values have been substituted.for a and.b. Y - 410,683 + 155x The above equation implies that as the average number of cattle fed per year? increased by one head, the average gross farm income from all sources increased.by $155. The multiple correlation coefficient (R) was found to be .91 indicating a high degree of association between the dependent and independent variables. The coefficient of multiple deter- mination (R2) of .82 indicated that eighty-two percent of the variance in average gross farm income was associated with the average number of cattle fed. The standard error of estimate was computed to be $10,102 which is 211.5 percent of the mean. 85 In Figure 5 a linear regression line has been drawn based on the regression analysis. A linear regression line automatically im- plies constant returns to scale. T‘w0 parallel broken lines have been drawn in on either side of the regression line showing the standard error of estimete of the regression line. The area between the two broken lines will normally contain approximately two-thirds of the observations. Since the area in which two-thirds of the observations fall in Figure 5 is not widely dispersed, it would appear that a linear function fits the data reasonably well. Therefore, returns to scale in a beef feeding operation could be assumed to be almost constant on the basis of this study. Relationship Between the Number: of Head Fed and Labor Income A similar analysis was used in relating the average. number of head fed on the fifty-one farms during 1961 and 1962 to the average labor income. In this case the regression equation was as follows: I - -283 + 31X The above equation indicates that as the average number of cattle fed increased by one head, labor income increased by approximately $31. The multiple correlation coefficient (R) was found to be .61, indicating a lower degree of association between the dependent and independent variables than with gross farm income. The coefficient of multiple determination (R2) of .38 indicate that thirty-eight percent of the variance in labor income was associated with the average number of cattle fed. The 86 FIG-UPF 5' Relationship of Two Year Average Number of Head Fed and Average Gross Farm Income 1201? / 112-- . , $1000 I 10h" / Gross , / x 965 _ / o / Farm ’ / 88" / Income ' / / 80' . / / 72" . / ' / 6Ui" / / 55- I l ’48- ° I o / .A O I I I I I j I I j I I I I 4 ‘ = J 50 100 150 200 250 300 350 too 1450 5’00 5’50 600 65'0 Average No. of Head of Cattle Fed 87 standard error of estimate was computed to be $5,521 which is 96.0 percent of the mean. In Figure 6, a linear regression line has been drawn based on the regression analysis. Once again, two parallel broken lines have been drawn on either side of the regression line in order to account for the standard error of estimate. It will be noted the observations in Figure 6 are much more widely dispersed than are the observations in Figure 5. The standard error of estimate in Figure 6 was 96.0 percent of the mean while in Figure 5 it was 217.5 percent of the mean. It should also be noted that the correlation between the average number of head fed and average labor income is much lower than the correlation of average gross farm income and the average number of head fed. Since there is proportionately greater variation in labor in- come than there is in goss farm income, and labor income is a better measure of the success of a beef cattle feeder than is gross farm income, and since returns to scale are almost linear, therefore it could be concluded that the success of a beef cattle feeder will not depend as much on the size of his operation as on his managerial ability . Relationshi Between the Average Number of Head Fed Per Farm and the Average; T091 Farmfipenses :6 r Head F§_d ' _ In the preceeding chapter, those inputs which were responsible for economies of scale in beef feeding operations were considered. In FIGURE 6 26‘ $1000 217‘ Labor 22' Income 20‘ 18' 16‘ 12' 10‘ 84 -6 88 Relationship of Two Year Average Number of Head.Fed and.Average Labor Income 1 1 1A_ 1, I 1 l 1 I l 1 150 200 250 300 350 hOO h50 500 550 600 650 Average No. of Head of Cattle Fed 89 an effort to determine the optimum size of a beef feeding operation the above relationship was examined. The average total farm expenses per head per farm during the two-year period were calculated as well as the average number of cattle fed per farm during the two-year period. All fifty-one farms were included in this analysis and the following table summarizes the above information by size groups. Table 17 Two-Year Average Relationships between the average number of Head fed per farm and the Total farm expenses per Head fed. —— _~ — 1 —~ Group No. of Head Fed Per Farm Total Farm Expenses Per Head Fed 1 53 $ h60 2 110 21:0 3 199 197 h 1735 159 The above table indicates that as the average number of head fed is increased by fifty-seven head from group one to group two, the average total expenses per head fed decreased by forty-eight percent. It also indicates that as the average number of head fed increased by eighty- nine head from group two to group three, average total expenses per head fed decreased by eighteen percent. Similarly as size increased by 236 head from group three to group four, the average total expenses per head fed decreased by 19.3 percent. 90 It should be recalled that secondary enterprises contribute a higher percentage of gross farm incane in the smaller groups, than in the larger groups. Therefore, secondary enterprises will be responsible for a higher percentage of the total farm expenses in the smaller groups than in the larger groups, and will bias the total cost per head figure for groups one and two upward. Therefore, the observed economies bet- ween groups one and two and between two and three will not be as great as the figures would indicate. In Figure 7 all fifty-one farms have been plotted on the basis of the average number of cattle fed and the average total farm expenses. Straight lines connect the average values of all four size groups. On the basis of the total expenses per head fed, the following figures would indicate that after the size of a beef feeding operation has reached 200 head, the main economies of scale will have been realized. The reduction in total farm expenses per head fed will not be as large between groups one and two and groups two and three as the following figure might indicate because of the effect of secondary enterprises contributing considerably to the total fam expenses per head fed in groups one and two. However, the following figure does indicate that the average total cost curve flattens out considerably beyond the 200 head size level. In the analysis of Chapter V it was found that the g'eatest economy of scale appeared between those farmers feeding an average of 112 and those feeding an average of 182 head. Therefore, the analysis in Chapter V would further substantiate the conclusion that most economies of scale will have been realized at approximately the 200 head level. 91 Figure 7 THE RELATIOI‘ISTIP BETWEEN THE AVERAGE NIHL’IBEIR OF PEAD FED PER FAME AND THE AVERAGE TOTAL EHEI‘JSES PER HEAD FED I «‘37 00'1 $600- $5001- $1100-b 8300* $2 00-7 r $100- 1 I i l I I I I I g I l 1 50 100 150 200 250 300 350 1100 h50 500 550 600 650 Average No. of Head Fed Per Farm CHAPTER VII _ COHSISTENCY 0F SEIECTED CAUSAL AND RESULTANT FACTORS 0F PROFITABILITI ON SELECTED lliDIVIDUAL FARMS Since this study is concerned with the profitability of cattle feeding farms and since the data are on fiftyeone identical farms for a twoqyear period, it provides an opportunity to select farms which were consistent or inconsistent in methods or results during the two years and to make further study of them in order to learn more about the successful management of cattle feeding farms. This is based on the assumption that there is a certain amount of consistency in the methods or results of a.farm manager from one year to the next and that one can learn more about successful management by studying opera- tions that are consistently profitable over a two-year period than by a study of operations for one particular year. In making the analysis for this particular part of the study, the data from the original fifty-one farms were again used. Six of the farms had incomplete data for one or both years and therefore, ' had to be excluded, so fortyafive farms were included in this part of the study. Complete feeding costs and returns data were available for both 1961 and 1962 for each farm. These data included.the following: (1) purchase weights, (2) sale weights, (3) price margin, (h) number and sex of cattle fed, (5) feed costs per hundred pounds gain, (6) returns per $100 feed fed and (7) labor income on the entire farm. 93 A.brief discussion of feeding efficiency was presented in Chapter III and needs to be further elaborated on at this point. Efficiency may be defined as the ratio of output to input. The animal scientist may measure feeding efficiency as the ratio of pounds gained by the animal to pounds of feed consumed by the animal or pounds of feed required for a specified gain. Poultry and swine nutritionists have long measured feeding efficiency in terms of pounds of feed per pound of gain. In considering feeding efficiency from an economic point of view, it might be considered the ratio of the value of the weight gained by the animal to the value of the feed fed used in producing that gain. This then is a measure of economic feeding efficiency as well as a.measure of profitability. One measure of feeding efficiency is feed cost per hundred pounds of gain. This efficiency calculation is partly physical and partly economic. In this calculation feed cost is in the numerator and is expressed in dollars, while the denominator is expressed in physical terms of hundred pounds gain. Another measure of economic feeding efficiency that will be used.within this chapter is returns per hundred dollars feed fed. This measure of feeding efficiency, however, includes other components in addition to.feeding skill. For example, the sale price Obtained on a lot of cattle will have an influence on the returns obtained. Therefore, this measure of feeding efficienqy would not be considered.a.measure of feeding efficiency only, by the animal scientist since it does include 9h the price of the product. However, if a beef cattle feeder is to have a profitable enterprise he must have the ability to by and sell cattle at the best prices and at the most opportune time. Therefore, the price margin which he is able to attain will determine to a considerable extent his success as a cattle feeder. In considering whether farmers were consistent or inconsistent in terms of production and profitability during the two-year period, consistency or inconsistency in profitability could be measured in terms of causal factors or resultant factors. Considering first causal factors, such would include: (1) the purchase weight of the cattle fed, (2) the sex of the cattle fed, (3) the quality of the cattle fed, (1;) feed cost per hundred pounds gain and (5) market margin. Each of the above factors will be a determinant of profitability and therefore, are listed as causal factors. The results of profitability in the feeding enterprise could be measured in (terms of returns per hundred dollars feed fed. Since the farms under study have the feed- ing of beef cattle as their main enterprise, labor income could also be used as a measure of profitability. Three methods of determining consistency were used in this chapter. They were as follows: (A) Farms were classified as consistent or in- consistent on the basis of causal factors and in this analysis the causal factors used were the purchase weight and sex of the cattle fed. (B) Farms were classified as consistent or inconsistent on the basis of a resultant factor which was returns per $100 feed fed. In each of 95 (A) and.(B) above a correlation of other causal and.resultant factors for 1961 and 1962 was run including all.fortyafive farms. (C) The third.method of determining consistency was to group all farms into quartiles for each of the two years (i) in order of their returns per $100 feed fed, and (ii) in order of their labor incomes and then compare the position of individual farms by quartiles for each of the two years for each factor. The following is a discussion of the results obtained in each of the above analysis. A. The Classification of Farms on the Basis of Consistent Causal.Facto£sw urc se ‘31 ‘_an ex. In this analysis the fortyqfive farms were divided into two groups: (1) those on which cattle were fed of approximately the same 'weight, and of the same sex, or of the same sex ratio in 1962 as in 1961 and (2) those on which cattle were fed of a different'weight or a different sex or sex ratio in 1962 as compared to 1961. Those farmers being placed in the first group were consistent over the two years in their pattern of production since they fed cattle of approxi- mately the same weight and sex in 1962 as in 1961. For this group the weight at which the cattle were purchased was not allowed.to vary by more than one-hundred pounds from one year to the next. All farmers being placed in this group fed either all heifers both.years, all steers both years or approximately the same ratio of heifers to steers for the two years. The second group were inconsistent in their feeding pattern fromil96l to 1962 with respect to purchase weight or 96 sex, 'since either the purchase weight of the cattle varied by more than one-hundred pounds from 1961 to 1962 or they fed steers one year and heifers the second year or they fed a different ratio of both heifers and steers from one year to the other. Following the described classification, twenty farmers were classified as consistent while twenty-five farmers were classified as inconsistent. The number fed in either year was not considered in making the above classification. A correlation analysis was run f on m Kind Barns for cattle (sq. ft. ) Sheds for cattle (sq. ft. ) Concrete yard. (sq. ft. ) Silo for cattle Silo for cattle Silo unloaders Feeding Equipment HIHIHHH' Type of feeding equipment set-up _- _...— ‘— w w— ‘r I r 3. Labor_igfgare of Feeder Cattle (make best estimate you can) 121 Hours per__day Days on feed T331 hrs. Regular daily chores ............. Irregular work - cleaning yards, etc. X X Buying and selling X X )4. With respect to future size of feeding operation are you planning to: a) continue feeding about the same number , b) expand considerably , or c) reduce the number considerably . Why? i ‘_ wt P.S. If you are interested in the results of this study when they are available, please check . 122 BIBLIOGRAPHY Boulding, K. E"-§E°“°TEE Analysis, Third.Edition, Harper &.Bros., New Ybrk. Bradford, L..A., and Johnson, G. L., Egrmgmanaggment Analysis, John Wiley & Sons ,Inc. , New York. 7" Drake, L. S., Pgoblems and Regsults in the Use of Farm Account Records to Derive Gash—Douglas Value Prodfictivitfg—Functions, unFuin—s'hed PE. D: Dissertatfon, De aftment offiiculturalfifilconomics, Michi- gan State College, 1952 . Ferris, J. N. and.Hoglund, C. R., Implications of Changed.D§mand, Government Programs and Techndlo ca Crop and Live§§§ckéT§end§, (paper presented at"NiEhigan“Sta e Ufiiversity“ForagE symposium; {arch 22, 1962). Haver, C. B., "Economic Interpretation of Production Function Estimates," Resource Productivity, Returns to Scale and.Farm Size, (edited by Héédyj'Ubhnson, and.Hardin, Iowa State COIIege Press, Ames, Iowa, 1956). Heady, E. 0., Economics of A icultural.Production and;Resource Use. Prentice REIT Inc., EngIewood CIiffE: New Jerséy:‘— ‘r' , and Jensen, H. R.,‘§arm.Managem§nt Economics, Prentice Hall, 0., Englewood Cliffs, New Jerseyl_fi— ‘— Hopkin, J. A., "Economics of Size in the Cattle-Feeding Industry of California," Journal of_§3£quconomics, volume XL, No. 2, Nay, 1958. Johnson, R. G. and.Nodland, T. R., Labor Used in Cattle Eegding, UniverSity of Minnesota, Agricultural Experiment Station,"(StatioEIBfilletin hSl). United States Department of Agriculture, E.R.S., Farm Income State Bgtimatgg l9b9-l9él, Farm Income Situation F.I.S. SuppIement, August,l962. ___ ,__, "Feedlots: Beef for America," The :" *Farm‘IndEx., E.R.S., July, 1963. van Arsdall, R. N., The Effects of Unit Size on CattleefieedingLProfits, (paper presented for Agricultural Industfies“Forum,'J§nE§ry, 29:30, 1963, University of Illinois, Urbana, Illinois). 123 BIBLIOGPalPM Webster's New Collegiate Dictionary, G. & C. I~Ierriam 00., Publishers, Springfield 2, Mass. Wright, K. T., 1961-1962 Cattle Feedinggosts and Returns, Ag. Econ. Bull. 907, Dept. of—Agr. Econ” RICH. St. Unvi., April 1963. .3 m