A SHORT RUN SUPPLY CURVE ESTIMATE FOR FLUID MILK, DETROIT MILK sum, OCTOBER, 1951 - SEPTEMBER, 1952 by George Edward Schuh A THESIS Submitted.to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Econamics 199: ACiflQO‘uIEDGmEN TS Above all, the author wishes to express his sincere apprecia- tion for the guidance, inepiration, and unending patience of Dr. Glenn L. Johnson who supervised the study and to whom the results are herewith dedicated. He is also greatly indebted to Professor Raymorxi C. Hoglund, Professor Lauren H. Bram, and Professor Gerald G. Quackenbush for their aid and suggestions at various stages of the study and to other members of the Department of Agricultural Economics for their general criticims and suggestions. Thanks is due to Dr. Thomas K. Cowden, former head of the depart- ment, who provided funds in the form of an assistantship and scholar- ship that made graduate study possible. In addition the author wishes to express his grateful appmcis- tion to his parents whose periodic loans of money and continued inspira- tion have made his entire college education possible. To llrs. Norma Trent, Hrs. Faye Tingleson, and Mrs. Agnes Copus, the author extends his thanks for checking the computations and for typing the preliminary drafts of the manuscript. Special thanks is due to Hrs. Edna Kenworthy, Mrs. Jean Barley, and Hrs. Arlene Nelson for typing the thesis and to Mr. Robert Ken- Iorthy for cutting the stencils for the figures. Last, but certainly not least, the author wishes to thank the numbers of the Michigan Milk Producers' Association who cooperated by filling out and returning the questionnaires. 01' 4‘ ““4 (Via-,3 i 3 I l- A. B. 0. TABLE OF CONTENTS Chapter I INTRODUCTION Purpose and relevance of the study . . . . . . . . . . . . . 1. To guide the Michigan farmer . . . . . . . . . . . . . . 2. To augment consumer well being . . . . . . . . . . . . . 3. To illustrate the use of theory in analyzing a prdblem . Description of Michigan agriculture in relation to the Detmitmilkshed...................... 1. Importance of dairying as an enterprise in the state. . . 2. Feedproduction in the state . . . . . . . . . . . . . . Description of the Detroit [ilk Shed . . . . . . . . . . . . 1» Location . . . . . . . . . . . . . . . . . . . . . . . . 2. Productionconditions.................. 3.Kindofcattlefound................... h.Typeaoffeedfed............'........ Chapter II Resume of Technical Literature and Framework for the Preglan Resumeoftechnicalliterature .. . .. . . .. . . . . ... Conceptual framework for the problem . . . . . . . . . . . . l. Selectionofrelevant theory . . . . . . . . . . . . . . K 2. Assumptions needed to secure the selected system . . . . 3.Productionfunctiona.................. HHH N NNOUIWW \ c. \L. ‘~B. D. E. 14. 5e Derivationofthe costcurves. . . . . . . . . . . . Description of the length of run considered and the respective characteristics of the dairy enterprise . Weaknesses and advantages of the prOposed method . . . . 1. 2. Weaknesses of the proposed method . . . . . . . . . . Advantages of the proposed method . . . . . . . . . . Chapter III The Computation of the Cost Curves for the Representative Enterprises. eeeeeeeeeeeeeeeeeeeeee Datermining the Physical Input - Output Relationships . . 1. 2. 3. h. 5.. 6. Feed . . . . . . . . . . . . . . . . . . . . . . . . Labor........................ lilkcans...................... Electricity..................... Feedgrinding.................... Ianurecredit.................... Pricing of the factors of production . . . . . . . . . . 1. 2. 3. Inputs with little or no seasonal variation in use or price Inputs with seasonal variation in use and price . . . . . . Labor - an asset that is fixed for the farm but variable betweenenterpriaes....o............... cmmutiOHOItheCOStcur'VOSOOOQ eeeeeeeeeeoo Economic significance of these curves for purposes of aggrega- tingthesupplycurve.........o...o....... Selection of the relevant portions of the marginal cost curves 22 25 26 26 29 31 31 31 146 h? ha 50 50 SO 51 Sh 67 A. B. A. B. C. D. Chapter IV The Computation and Explanation of the Composite Supply Curve . Aggregating the micro-response into a.macro-response . Adjusting the composite supply curve 1. 2. 3. Adjusting the curve to present butterfat content . Shifting the curve to correct for bias Adjusting the composite supply curve for year to year changes in.number of cows, quality of cows, and input Chapter v Significance and Implications of the Material Presented Thesemi-macro—analysis................ 1. 2. 3. Controlling production for the operation of suppor‘bprogram.......... The Federal.milk marketing order . Interregional competition . . . . . The micro.ana1y318 e e o e e e e e e 0 Suggestions for additional research . . 1. 2. 3. h. 5. Input-output studies . . . . . . . Cost computations for other lengths Adjustments to risk and uncertainty of run How'do producers enter and leave the market Converting to an aggregate index . Uses of the data synthesized in this study . . Chapter VI Summary and Conclusions . . . . . . . . . . . . 9 price . 72 72 72 75 77 90 90 90 91 92 96 100 100 101 101 102 102 103 101. LIST OF TABLES Table Page I Value of Farm Sales, By Products, Michigan, 19h? . . . . . . 3 II Nmnber of Farms, by Type of Farm, Michigan, l9h9 . . . . . . L; III Cash Farm Receipts From Sales of Dairy Products Compared with Total Cash Receipts from Farm Marketings and Total State Income (Income Payments to Individuals), Michigan, 1951 0\ U1 IV Production and Distribution of Selected Crops, Michigan, 1952 V Herd Size, Type of Barn, and Average Production Per Cow, Percentage Occurance in the Detroit Milk Shed, October 1, 1951-September30,l952o................. 9 VI Gross Income, Labor Income, and Estimated Marginal Value hoductivity of Labor on Selected Hichigan Farms, 1952 . . . 53 VII Types of Herds and Estimsted Number of Producers of Each Type in the Detroit Milk Shed, October 1, 1951 - September 30, 19 2 O O O O O O O O O O O O O O O O O O O O O O O O O _. O 0 7h VIII Percentage Concentrate Cost is of Total Variable Cost at Three Points on the Marginal Cost Curves, Detroit Milk Shed, OctOber 1, 1951 ' September 30, 1952 e e e e e e e e e e e e 80 LIST OF FIGURES Figures 1e Location 0f the Detroit milk Shed, 1951 e e e e e e e e e e 2. Production surface for three variable analysis . . . . . . . 3. Marginal cost curve for the Firm in the Short Run . . . . . 1;. Grain - Total Digestible Nutrient Relationship for COWS With 3. Capacity Of 5,133 Pounds Of Milk 0 e e e e e e e 5. Grain — Total Digestible Nutrient Relationship for Cows with a Capacity of 7,332 Pounds of Milk . . . . . . . . .6. Grain - Total Digestible Nutrient Relationship for Cows with a Capacity of 8,350 Pounds of Milk . . . . . . . . 7. Grain -- Total Digestible Nutrient Relationship for COWS fith 3 Capacity Of 10,120 Pounds Of Milk 0 e e e e e O 8. Marginal Cost Curve, 8.3 Cow Herds, Producing 5,133 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 September30,l952.o................... 9. Marginal Cost Curve, 12.9 Cow Herds, Producing 5, 133 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 September30,l952....i................. 10. Marginal Cost Curve, 22.6 Cow Herds, Producing 5,133 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 Septelnber30,l952..................... 11. Marginal Cost Curve, 8.3 Cow Herds, Producing 7,332 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 September30,l952..................... 12. Marginal Cost Curve, 12.9 Cow Herds, Producing 7,332 Poxmds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 Baptmmr 30’ 1952 Q 0 O O .0 O O O O O O O O O O O O O O O C 1.3. Marginal Cost Curve, 22.6 Cow Herds, Producing 7,332 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 Septmber30,l9§2...o................. Page 20 23 36 37 38 39 S7 S8 59 60 61 62 15. 16. 17. 18. 19. 20. 21. 22. 23. 2h. Marginal Cost Curve, 16.1; Cow Herds, Producing 8 ,350 Pounds of Milk, Pen-type Barns, Detroit Milk Shed, October 1,1951 - September30,,l952...................... Marginal Cost Curve, 8.3 Cow Herds, Producing 10,120 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 September30,l9§2..............o....... Marginal Cost Curve, 12.9 Cow Herds, Producing 10,120 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1 1951 September30,l952..................,.... Marginal Cost Curve, 22.6 Cow Herds, Producing 10,183 Pounds of Milk, Stanchion Barns, Detroit Milk Shed, October 1, 1951 September30,l952...................... Production Surface for the Dairy Cow . . . . . . . . . . . . . Supply Curve for Milk, Based on Mail Questionnaire, Four Per- cent Fat-Corrected Milk, Detroit Milk Shed, October 1, 1951 - SeptenberD,19S2............’.......... Supply Curve for Milk, Based on Mail Questionnaire, Corrected to 3. 68 Percent Fat-Corrected Milk, Detroit Milk Shed, October 1’ 1951 " September 30,1952 e e e e e e e e e e e e 0 Supply Curve for Milk, 3.68 Percent Fat-Corrected Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952 . . . Supply Curves for Milk, 3.68 Percent Milk, Different Levels of Input Prices, Detroit Milk Shed, 1951 - 1953 . . . . Supply Curve for Milk, 3.68 Percent Fat-Corrected Milk, DetrOitMilkShed,1953................... Supply Curve for Milk, 3.68 Percent Fat-COrrected Milk, DetroitMilkShed,19Sl ................... 63 6h 65 68 73 76 79 83 88 LIST OF FORMS, APPENDIX A Fonm Page 1 First mail questionnaire 112 2 Enclosed card 113 3 Follow up questionnaire 11h Tattle II III VI VII VIII LIST OF TABLES, APPENDIX B Annual Feed Input and.Milk Production of Dairy Cows, Production Ability - 5133 Pounds of Milk, Fed at Different Levels, 305 Day Lactation Period, Predominantly Holstein Cows, Average Hay and Pasture for the area, 1200 Pound Cows, Four Percent Fat-Corrected Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952 Annual Feed Input and Milk Production of Dairy Cows, Production Ability - 7332 Pounds of Milk, Fed at Different Levels, 305 Day Lactation Period, Predominantly Holstein Cows, Four Percent Fat-Corrected.Milk, Detroit Milk Shed, OctOber 1, 1951 - September 30, 1952 Annual Feed Input and Milk Production of Dairy Cows, Pro— duction Ability - 8350 Pounds of Milk, Fed at Different Levels, 305 Day Lactation Period, Predominantly Holstein Cows, Average Hay and Pasture for the Area, 1200 Pound Cows, Four Percent Fat—Corrected Milk, Detroit Milk Shed, Catcher 1, 1951 - September 30, 1952 Annual Feed Inputs and Milk Production of Dairy Cows, Pro- duction Ability - 10,120 Pounds of Milk, Fed at Different Levels, 305 Day Lactation Period, Predominantly Holstein Cows, Average Hay and Pasture for the Area, 1200 Pound Cows, Four Percent Fat-Corrected.Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Salt used per Cow Annually at Different Feeding Levels, Four Qualities of Cows, Detroit Milk Shed, OctOOer 1, 1951 - September 30, 1952. Labor Requirements, Hours per Cow per Year, 8.3 Cow Herd, Stanchion.Barn, Averaging 5133 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Labor Requirements, Hours Per Cow Per Year, 8.3 Cow Herd, Stanchion Barn, Averaging 7332 Pounds of’Milk, Detroit Milk Shed, OctODer 1, 1951 - September 30, 1952. Labor Requirements, Hours Per Cow Per Year, 8.3 Cow Herd, Stanchion.Barn, Averaging 10,120 Pounds of’Milk, Detroit Milk Shed, Octdber 1, 1951 - September 30, 1952. Page 116 118 120 122 12h 125 126 127 4" II III XIII XIV XV XVI XVII XVIII XXI Labor Requirements, Hours per COW'per Year, 12.9 Cow Herd, Stanchion.Barn, Averaging 5133 Pounds Of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Labor Requirements, Hours per Cow per Year, 12.9 Cow Herd, Stanchion Barn, Averaging 7332 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Labor Requirements, Hours per Cow per Year, 12.9 Cow Herd, Stanchion Barn, Averaging 10,120 Pounds of Milk, Detroit Milk Shed, October 1, 1951 — September 30, 1952 Labor Requirements, Hours per Cow per Year, 22.6 Cow Herd, Stanchion Barn, Averaging 5331 Pounds of Milk, Detroit Milk Shed, OctOber 1, 1951 a September 30, 1952 labor Requirements, Hours per Cow per Year, 22.6 Cow Herd, Stanchion Barn, Averaging 7332 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952 Labor Requirements, Hours per Cow per Year, 22.6 Cow Herd, Stanchion Barn, Averaging 10,120 Pounds of'Milk, Detroit Milk Shed, Goteber 1, 1951 - September 30, 1952 Labor Requirements, Hours per Cow per Year, 16.h Cow Herd, Pen Type Barn, Averaging 8350 Pounds of Milk, Detroit Milk , Shed, October 1, 1951 - September 30, 1952 Some Labor Requirements for Jobs Varying with Feeding ILevel, Stanchion Barn, Hours per Cow per Year, Different Herd Sizes, Detroit Milk.Shed, OctOber l, 1951 - September 30, 1952. Electricity Inputs, Variable with Feeding Level, Various Types of Herds, Detroit Milk Shed, October 1, 1951 - September 30, 1952e Feed Grinding Charges, Variable with Feeding Level, Various Types of Herds, Detroit Milk Shed, October 1- 1951 - September 30, 1952. Fertilizer Elements Reaching Fields from Manure, Various Quality Cows, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Prices Used in this Thesis Variable Costs, Feed and Associated Inputs Variable, 8.3 Cow Herd, Stanchion Barn, Average 5133 Pounds of Milk, Detroithilk Shed, OctOber 1, 1951 - September 30, 1952. 128 129 130 131 132 133 13h 135 136 137 138 139 XXII XXIII XXV XXVI XXVII XXVIII Variable Costs, Feed and Associated Inputs Variable, 12.9 Cow Herd, Stanchion Barn, Average 5133 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Variable Costs, Feed and Associated Inputs Variable, 22.6 Cow Herd, Stanchion Barn, Average 5133 Pounds of Milk, Detroithilk Shed, October 1, 1951 - September 30, 1952. Variable Costs, Feed and Associated Inputs Variable, 8.3 Cow Herd, Stanchion Barn, Average 7332 Pounds of Milk, Detroit.Milk Shed, October 1, 1951 - September 30, 1952. Variable Costs, Feed and Associated Inputs Variable, 12.9 Cow Herd, Stanchion Barn, Average 7332 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952 Variable Costs, Feed and Associated Inputs Variable, 22.6 Cow Herd, Stanchion Barn, Average 7332 Pounds of Milk, Detroit Milk Shed, October 1, 1951 - September 30, 1952. Variable Costs, Feed and Associated Inputs Variable, 16.h Cow Herd, Pen Type Barn, Average 8350 Pounds of Milk Variable Costs, Feed and Associated Inputs Variable, 8.3 Cow Herd, Stanchion Barn, Average 10,120 Pounds of“Milk, Detroit Milk Shed, OctOber 1, 1951 - September 30, 1952 Variable Costs, Feed and Associated Inputs Variable, 12.9 Cow Herd, Stanchion Barn, Average 10,120 Pounds of‘Milk, Detroit Milk Shed, October 1, 1951 - Sept- ember 30, 1952 e Variable Costs, Feed and Associated Inputs Variable, 22.6 Cow Herd, Stanchion Barn, Average 10,120 Pounds of’Milk, Detroit Milk Shed, October 1, 1951 - Septem- ber 30, 1952. 1h2 1&3 lhh 1h5 1h6 1h? 1h8 1H9 150 CHAPTER I INTRODUCTION Purpose and Relevance of the SM T_o $512221: Michigan Law. This stuck was undertaken pri- marily as part of a research program designed to help farmers as they seek to adjust to a world whose dominant characteristic is change. More specifically, its purpose is to help the Michigan dairy farmer assess his cost position and ability to supply ndlk relative to produc- ers from neighboring states. Combined with other studies, this analysis enables the Michigan dairy farmer more adequately to size up his situa- tion with respect to the future. It can serve as a guide in adjusting present operations to meet changing conditions. 3'3 ament consmuer 1331.1 being. Beyond guidance to the individ- ual producer, the present study may serve indirectly to augment consumer fill-being. The channeling of milk from the farm to the consumer has ,eO‘.‘ ' become heavily burdened with more or less restrictive institutional mangenents in recent decades. Federal Milk Marketing Orders have Iltered the distribution of the right to produce milk within the t 930mm. If the administrators of these programs can have better in- m“milieu on hen! the amount of milk supplied will vary in response to Price changes, they can more competently recommend price adjustment, “Bitchy making both the consumer and producer better off. A price support program for dairy products has been instituted since World War II with an apparent malallocation of consumption and resources leading to large surpluses of butter in government ware- houses. This study, combined with others designed to appraise the demand side of the problem, and more fully the supply side, will en- able price support programs to be developed that are more efficient in their allocation of resources. 1'2 illustrate t_h_e_ _u_s_e_ 9.1:. 233931 in analyzigg _a problem. A third purpose of the study was to illustrate the use of theory in analyzing a problem. Experimental and other data compiled at this and other institutions are combined with the classical static theory developed and elaborated since the time of Adam Smith and with a technique de- veloped by James A. Wells1 at the University of Kentucky. Use of this technique produces marginal cost curves for several representative fine in the Detroit milk shed. These are then aggregated into a milk shed supply curve through the use of proportions derived from a mail survey conducted in the Spring of 19532. The result is an estimate of the supply curve for fluid milk in the area under study, assuming that the number of producers and size of herd does not increase, that the quality of cow remains constant and that prices of variable inputs re- main constant. 1 wells, J. A., "A Technique for Synthesizing Cost of Production Data - With Special Reference to Dairy Enterprises in Green and Taylor Counties of Kentucky," (unpublished Master's thesis, Departmnt of Farm Economics, University of Kentucky, 1951). 2 See specimens in Appendix A. Description of’Michigan Agriculture in Relation to the Detroit Milk Shed Importance g_f_ dai 53 pg enterprise in the State. Michigan, as a state, ranks ninth in the number of milk cows and heifers on hand as of January 1, 19533. Some form of dairying is the predominant type of’farming in the state, other alternatives being beef cattle, sheep, swine, specialized vegetable or fruit farms, and some crop farms. The relative importance of the different types is indicated by Table I. TABLE I VALUE OF FARM sum, BY PRODUCTS, MICHIGAN,19h9 ”I fl Thousands Product of dollars Crops Fruits and nuts 30,600 Vegetables 17,h97 Horticultural specialties 15,99h All other crops 120,578 Livestock and livestock products Dairy 1h3’115 Poultry and poultry products hl,215 All other livestock and livestock products 101,581 Forest products All forest products 3,031 Total value of products sold h73,612 SOURCE: Michigan Agricultural Statistics, KEV, 1953, Pa hge 3 Mflgm Agricultural statistics, Hay, 1953, p. S. For further information as to the importance of dairying in Hichigan, see Table II. TABLE II NUMBER OF FARMS, BY TYPE OF FARM, MICHIGAN, 19h9 Type of farm Number Percent Cash-grain 15,037 9-7 Other field crops 1,995 1.3 Vegetable 2 ,5h5 1.6 Muit and nut 11,710 3.0 Dairy h5,729 29.h POUltl'y 5, 268 30,4 Livestock other than dairy General, primarily crops 1,990 1.3 General, primarily livestock 5,993 3.8 General, crop and livestock 11,195 7.2 Miscellaneous and unclassified 50,350 3.2 SOURCE: Michigan Agricultural Statistics, Hay, 1953, p. e For the relative importance of cash receipts from dairying, see Table III. TABLE III CASH FARM RECEIPTS FROM SALES OF DAIRY PRODUCTS COMPARED WITH TOTAL CASH RECEIPTS FROM FARM MARKETINGS AND TOTAL STATE INCOME (INCOME PAYMENTS T0 INDIVIDUALS), MICHIGAN, 1951 Cash farm receipts from sales of dairy products 198,830,000 dollars Total cash receipts from farm marketings 725,272,000 dollars Income payments to individ- uals 11,352,ooo,ooo dollars Ratio of cash dairy receipts to total cash farm receipts 27.h percent Ratio of cash dairy receipts to total income payments 1.75 percent SOURCE: Michigan Agricultural Statistics, May, 1953, p. 11. Feed promotion in 31:13 state. Corn, winter wheat, oats, barley, and soybeans were the principal feed grains grown on Michigan farms in 1952. Production and disposition figures are given in Table IV for the feed grains and hay. Winter wheat. and soybeans are principally cash crops while corn, oats, barley and hay are produced for use as feed. 01‘ the 1,698,000 acres of corn grown in Michigan in 1952, 83.5 percent was utilized for grain; 12.14 percent for silage; and 3.11 percent for hogging down, grazing and forage.h Total corn silage production for the state was It Ibid, p. 19. TABLE IV PRODUCTION AND FARM DISPOSITION OF SELECTED CROPS-MICHIGAN, 1952 Produc- Crop tion Used on farm where grown Sold Farm house- Seed Feed hold Thousands Corn - bushels 83,200 -- 67,759 9 15,1132 Winter wheat 9 bushels 36,111.10 2,289 5,830 37 28,281; Cuts - bushels 50,786 - h3,168 -- 7,618 Barley - bushels 2,552 -- 1,991 -— 561 Soybeam - bushels 1,7118 105 52 - 1,591 All hay - tons 3,538 -- 3,131 - ho? At SwRCE: my“ Agricultural Statistics, May, 1953, p. 18. 2,071,000 tons.S No specific figures were available on the breakdown of hay production into kinds, other than that 39.3 percent of the farms in Michigan reported some acreage of alfalfa cut for hay and 38.7 per- cent reported some acreage of clover-timothy cut for hay in 1950.6 Description of The Detroit Milk Shed This thesis is directly concerned with fluid milk production in the Detroit milk shed. Having described Michigan agriculture and the —__ S Md, P. 190 6 Ibid, P0 170 7 importance of dairying in the state as a setting or background, a more detailed description of the conditions under chh fluid milk is pro- duced for the Detroit market follows. Location. In 1952, the milk shed for the Detroit market en- compassed approximately Wo-thirds of the lower peninsula. Approximately 70 percent of the milk cows in the state were concentrated in this area.7 Within this geographic area, though, many producers shipped to local markets such as Lansing, Muskegon, Bay City, and Midland, rather than to Detroit. The approximate boundaries of these smaller milk sheds are indicated in Figure 1. Production conditions. In order to set up representative firms for purposes of deriving the marginal cost curves, information was needed as to herd size, type of barn, and quality of cow. Secondary sources of data did not supply information of this nature, So a mail survey was taken of producers in the Detroit uc‘le shed. Results of the questionnaire in describing conditions under Which fluid milk is produced for the Detroit market are summarized in Table V. The marginal cost curves which were constructed for each of these representative conditions of production were weighted according to the indicated percentages in aggregating the composite supply curve. (See Chapter IV). 7 Ibid, p. 8. W saroom‘r ‘ DICKINSON MACK/M46 4s M (MOM/fl ( $0034.“? . 075560 MONTMOR.‘ALP£NA 607L051“ (RA wr'o cooA mo MAY MAN/S. WEXFORD MISSAUKIE ROSCOM. GEMAW \ MASON ”(5 auto“ CLARE ‘aLAo'wm 6:32;. In Y) || 0(EA ‘ AYGO MtcasrA 3 MUSKE. . .1 : ::a!s's j OTTAWA u “w: 1:137: "cum I ~. 393* “" 55:33"? ' I . OAKLAND AIAc ALLEGAN MRI? ~33 ‘ “3 "1m.. 1’. 5m ‘ "71., .1. 2% "p 3 °‘ ' ' ' ' .\' .". ‘. ~ :1 °:‘\ ‘ . '54 It: L 0 MM A. u .. MW mm: ‘ ‘ Figure 1 Location of the M "W" . ,... * Detroit mm Fast: , 000' e : c ' p e 0 ; E— Bhed’ 1951. ‘t‘) Q.‘|.\" . :' ";:30000. ; 4 51.1055»! 3 ... ”a ,} (Shaded areas :mév', $.53.“ m“ .‘. a- are local $5353 33:52- 13:;- ' ...... .';:::.1 markets. ) ‘ “ “ SOURCE: nual Repoth and Proc dings, mchigai 1k Produc rs' Associ tion, Thirty- 13th ‘lbeting, ovember 6, 19520 65 ’ 04' 07' a" 83' 0-1219 .pun happen accused mo.m mo aspen nHa 000.00H w . . 0 whose n.0H wills m as n 2.8 23 season whom omens»: aspen camp com 888 08.4788 mao.om . Hmo.sm mom.~m mam.wm Hence . omens» «8.8 8?: 5.3 was Steamm .38 a“ m.mH omwho>< ONOomN HmJoOH mmweOH HmMom DIDO mHIHH m.m ommneh¢ Roam we? 03.: .32.: .300 add pseonmm eunuch ooo.HH amassed season ohm» omeno>< unused ommm owenopd shun moanoswpm H33 .33 e5 353 88 sensed mamwuoog season 8% have: ’1'! «m2 .on gum .. £3 .a mamoaoo . seam sax Eomfin was 2H segues moaazmofim .. too sum 28.5:qu mag: a? .23 so ME .33 use > mnm ‘ . p - .\ .l x . . I v), - . I . . . .. . ‘ V I 0' t y .0 .. . e O A . .l I,. . .' ,. , s e‘ ' ‘ . .-. ¢ ' ' l‘ ‘." ' — . . ' .. ,- e s “ . I. . a I \ . y a a I ' 'f .‘ , ’3 . 7. s s 19 12. Otherfactors - pasture, silage, and labor - which are fixed for the firm but variable between enterprises, are priced at their on-farm opportmnity costs. (A specific treatment of these is given later in the paper.) 13. The farmer buys and sells his factors free of coercion in a free or open market. The back of theory which is to serve as a conceptual framework has been selected and the assumptions necessary to assure an identified system have been spelled out. The conceptual framework can now be de- veloped, startim with an analysis of relevant production functions and carrying it through the derivation of the marginal cost curves to their aggregation into a supply curve for the area and farm under stucw. Production functions. Production can be conceived of as a functional relationship betwaen the factors of production and output. Synbolically this would be presented thusly: Y a ‘f(xl,X2,...,Xn), where I stands for output and X1,ooo-,X.n stands for the factors of production. The f signifies that output depends in some definite way on the fac- tors of production. The theory of the production function can be found in one of several college theory books, such as, Stigler13, Beadinglh a, Weintraub15, 13 Stigler c J The Theo of m , . ., __ ce The Hacnllian Company New Iork, New York, 1950, mail—9&0 - F“ ’ 1" Boulding x E Ec ‘ , . ., onondc W, Harper and Brothers New York, New York, 191:8, pp. 1393 - 309, l - 709. ’ 15 Veintraub s Pri 31, , ., ce Theo Pitnan Publishing Corporation law Iork, flew York, pp. 32 - 70. ’ .I9\ 20 and will. not be developed in detail here. The theory is most easily envisioned when output (I) is conceived to be a function of two vari- able inputs, :1 and x2, with 13,om,in fined. Plotting 11 on the ordinate axis of a Cartesian coordinate and 12 on the abscissae, out- put is conceived of as rising from the surface of the coordinate in a third dimension. Points 'of equal elevation can be indicated by contour lines much as is done on a regular surface map. These contour lines connecting points of equal height are called isoproduct lines, and are illustrated in Figure 2. I1 .. . K II. quadrant boundaries >isoproduct contours F— #— \ scale line L... - budget lines "2 v Figure 2. Production surface for three variable analy'SiSe 21 The significant portion of this diagram is the area within which a rational entrepreneur would operate. This area of rationality can be delineated by drawing in isoclines, which connect points on each isoproduct curve at which a tangent is parallel to either the ordinate or abscissa axis. Within these isoclines the MPP's of both X1 and 12 are positive. Two problems of economic choice exist within this area of ration- ality. The isoproduct contours indicate that a given output can be produced by alternative combinations of the two inputs. Which combina- tions to use becomes a problem of economic choice and the criteria emloyed in making the selection is the minimum cost combination. This is determined by superimposing budget lines on the isopro- duct map (Figure 2). These lines indicate the different combinations of the two inputs which can be purchased for a given outlay of funds. The optimum combination is indicated at the point of tangency between the isoproduct line and the budget line. (Proof that this is the mini-3 mm cost combination can be found in arm of the suggested references.) A line connecting these points of tangency will indicate the optim combinations as output is expanded, and is called the scale line or expansion path. This brings us to the second of our problems of economic choice; that is, the optimum output to produce. Further production is pro- fitable as long as the revenue from one further unit of production is mater than the cost of securing that greater output. Skipping the Production function where output is a function of x1 and 12 combined 22 according to the scale line and going direct to the related cost curves, maxim profits are secured when MC 8 P. Combining the inputs as dic- tated by the scale line, output is expanded until this point is reached. Dorivation 93 the cost curves. Of the traditional set of cost curves that is derived for the firm in the short run, only one is germane to the present analysis. Since in the short run it is to the producer's interest to carry production to the point where marginal cost equals price, his short run MC curve will also be his rational short- run supply curve relating price and quantity supplied. Thus, this cost curve is the fundamental curve for the present analysis. The ”short-run! is taken to be a period long enough to permit of am desired change of output technologically possible without al- tering the scale of plant, but which is not long enough to permit of an adjustment of scale of plant. For this problem, the relevant length of run is/ in which feed and its associated inputs are variable. (See Chapte or a further discussion of this.) All other inputs are fixed and are part of the “plant“. All costs to the firm can then arbitrarily be classified into “'0 groups - those which are necessarily fixed in amount and whose n‘lelltude delineate the scale of the plant, and those which are freely "liable and change with changes in output. This latter group are vari- ‘510 in their aggregate amount as output varies, as well as in their munt per unit of product. 23 Marginal cost is defined as the additional costs necessary to produce one additional unit of output. is total fixed costs remain constant, only variable costs enter into marginal costs. Total vari- able costs are defined as the sum.of the total variable costs necessary 'to secure a given output. Total variable costs divided by the respective output to give a per unit value is average variable costs. Marginal 'vsriahle and marginal costs are syncncmcus. Dollars MC Output Figure 3. Marginal cost curve for the firm in the short run. 2h The marginal cost curve for a firm is illustrated in Figure 3. It is typically U-shaped as a result of the law of diminishing returns.16 Theoretical presentations often indicate that only variable costs are imortant in decision making once the commitments for fixed costs have been made. Such presentations indicate that production can be maintained in the short run so long as average variable costs are covered, and further, that losses are minimized by this continued operation. However, if the price becomes so low that the earning power of the fixed asset becomes less than its salvage value, the fixed asset will be sold. This may well occur at a price that is still more than covering average variable costs. When this takes place, a longer length of run is entered into and the cost computations for the previous length of run are not applicable. The supply curve for the firm, then, consists of the marginal cost curve of the firm above the level of the average variable costs, unless the earning power of the fixed assets become less than their salvage value. In this case, the short run supply curve does not euc- tend down to the average variable cost curve, but stops at this point where the planning span involves a longer length of run. The supply curve for the industry in a given length of run is simply the sum of the abscissa of the individual marginal cost (a in- dividual supply) curves for that length of run. 15 Ibid, pp. 75 - 76 25 Discussion 2;; the m 93 £19; considered and the respective characteristics g_f_ the £1321 enteijarise. A large number of productive agents are used in the dairy enterprise. Various lengths of run17 or planning spans can be identified by dividing these inputs into a fixed and variable classification. Typically, three lengths of run can be identified with respect to the dairy enterprise. _'1_‘_h_e_ §_h_9_r_t_ 59;. The short run is that planning span in which most of the factors of production are fixed. The level at which the cows are fed and the combination in which roughage and concentrates are fed is variable, and in addition some other minor inputs and small per- tiom of other inputs associated with the feeding level are variable. The intermediate length 2f £95. In a somewhat longer length of run, the dairynan can vary some of the factors fixed in the short run. This planning span is called the intermdiate length of run, and with- in this spsn the dairyman may increase or decrease the size and quality of the herd by changing the breeding program or by purchasing and selling cows. Certain portions of equipment and labor associated with varying herd size and quality of cow are also variable. An upper limit on herd size is imposed by barn space. 17 A word of explanation relative to the concept of length of run is amropriate at this time. This is not strictly a time concept, but involves planning and the associated decisions with respect to varying the specified factors of production mentioned above. The length of run is determined by the planning span one is considering when comitmants are made. If a variation in feeding level is contemplated, it is a short run phenomenon. If a variation in barn size is being considered, it is a long run phenomenon. 26' 111: L129; 5'2. A still longer length of run can be conceived of in which all factors of production are variable. Buildings and land are variable in this length of run and conceivably management could be vari- able, for with the passing of time, the farmer could undergo a learning process and increase his managerial skill. Whether management could be increased in proportion to the other factors is debatable. These are only three examples of an infinite mmber of lengths of run possible. They are rather arbitrary, but somewhat meaningful in referring to lengths of run in which farmers usually plan. 259; 2}; run considered i2 this m. In this study, only the short run is selected for consideration. The level at which the cows are fed and the combination of roughage and concentrates is variable. That part of labor associated with the feeding level will be variable. Additional milk cans will be needed to handle the increased milk re- sulting from a higher level of feeding. A small amount of electricity will also be variable as the milking time increases and the volume of milk to cool is changed. All other factors of production are assumed fixed. The size of herd is constant, and land is fixed. For the milk shed, the number of herds is fixed at 12,223. Weaknesses and Advantages of the Proposed Method Weaknesses g}; the p_r_oposed method. The proposed method of analysis has several innate weaknesses. (he of these involves input prices and 27 the problem of partial equilibrium analysis. It is assumed for purposes of the study that the price for each of the inputs remains constant, although for am of the inputs in the econosw as a whole it is obvious that price is a function of the amount used. This problem is partially circumvented for items with a national market such as corn, oats, soy- bean oil Dal, milk cans and salt, by the fact that we are dealing with the production in only one of the areas in which the connodity is pro- duced in the total econcnv. The relationship between the price and the quantity used in the Detroit milk shed is probably slight, then, if it exists at all, because the use under consideration is only part of a such larger market. The problem is more acute for those inputs that are fixed in supply either locally or on an individual farm basis, but variable within the individual farm between enterprises, such as labor, hay, silage and pasturage. Here the price very definitely is a function of the quantity used. This problem is partially solved by holding the quantity of silage and pasture used constant at all of the feeding levels. Labor and hay cannot be held constant as the level of feeding changes, though, so they must be given special treatunt. A discussion of the method used is found in a later chapter. A second weakness of the study is that it makes no direct al- lowance for events of an episodic nature. It is assumed that there are a definite number of producers, and that they continue to produce throughout the period under consideration. In reality many events will occur to eliminate some producers from the market, such as fires, '4'. it 28 epidemic diseases, hail storms, were and crop failures. These occur- rences are of a random nature and are in no way connected with the market situation. Indirectly, events of this nature are taken into consideration when adjusting the final curve as discussed in Chapter IV. A third weakness is the inherent lack of accuracy implied by any sampling process, in addition to the bias resulting from sampling a special group of the total population with a mail questionnaire. It was impossible to secure a list of addresses of all the producers in the Detroit market to which to send the questionnaire. The Michigan Milk Producers' Association were very cooperative, however, in allowing the author access to their address list, from which two 10 percent random samles were drawn. Members of the Association make up approxi- mately 85 percent of the shippers in the shed, there probably being an mard bias in the sample toward the larger and more efficient pro- ducers as a result. This is indicated by the daily deliveries for ee'ch group in September of 1952. The members had an average daily delivery of 3214.8 pounds as compared to 292.2 pounds for the non-members and 319.7 pounds average for the total shippers. Another sample bias is the one that is indigenous to a. mail questionnaire. Again it is probably only the larger, more efficient producers that respond, although we have no estimate of the descrepancy in this case. A 50 percent response was secured after sending one re- minder letter. 29 A correction is made for these biases after the shape of the composite curve has been determined by shifting the entire curve later- ally to force it through the actual production for the period of time being considered. Advantages 2i; _thg ESE—532 m. An advantage of this study is that it is organized around a meaningful theoretical framework and is based on factual evidence derived from experiments, surveys, and time and motion studies. Theoretical and empirical procedures are teamed together for the attack on the problem. It considers the responses of the individual producer to price changes and aggregates them into the composite supply curve. Another advantage that stems directly from the consideration of the individual producer is the increased validity of the aggregation process. The supply curve will not be restricted to a straight line relationship, nor will it be burdened with the deficiencies associated with aggregating regression coefficients. It will be a lateral sum- mation of the individual supply responses, and as such, transcends many of the weaknesses of the traditional aggregation process. The historical-statistical procedure presupposes that producers will react in the future much in the same way that they have in the past. This precludes the possibility of a changing technology, chang- ing tastes, and changing alternative opportunities. The proposed method specifies that for the given cost structure, the supply response will be as indicated. Changing the cost structure will result in a different 30 supply response. There is not a projection over a time period for which there is not supporting evidence as is done in the historical-statistical method. Wold and Jureen have pointed out the lack of validity involved in predicting from a regression coefficient beyond the limits of the data.18 This method considerably increases the accuracy over that achieved by Highel and Black's process. Continuous responses are ascertained rather than Just the three or four alternatives proposed in their study. This results in increased validity over the range of the supply curve. Increased accuracy also comes from having ten representative enter- prises for each of which a marginal cost curve is computed. These curves are then weighted according to their respective occurrence in the lilk shed. This is considerably more accurate than setting up one typi- cal enterprise for which three or four alternative situations are bud- gated. 18 Hold H , ., and Jureen, L., Demand Analysis, John Wiley and Sons Inc., New York, New York, 1953, P. 31. , CHAPTER III THE C(MPUTATION OF THE COST CURVES FOR THE REPRESENTATIVE DAIRY ENTERPRISES As indicated in Chapter I and II, a marginal cost curve is required for each of ten representative dairy enterprises. This chapter describes (1) how the physical input-output data were secured and (2) the method of computing the marginal cost curves. Determining the Physical Input-Output Relationships £9951. For the length of run with which we are concerned, feed is the major variable factor of production. The input-output relation- ships used for deriving the cost figures in this study are based on a combination of secondary experimental data, survey data, and Judgement. Milk production in this length of run is generally conceived to be a function of varying quantities of roughage and concentrates and necessary changes in associated inputs such as labor, minor equipment, and electricity, combined with such fixed factors as the cow, the quality of her feed, the management ability of the farm Operator, and the climate. If one abstracts from the changes in the associated in- puts such as labor, minor equipment, electricity, the economic analysis for this length of run involves the traditional three-variable analysis referred to in Chapter II. The problems of choice involve the com- bination in which to feed the roughage and concentrates and the amount to feed the cow. 32 The range over which the total digestible nutrient intake of a particular cow can be varied has two limitations. Physically, the total digestible nutrients intake must be at least enough to satisfy the maintenance requirements of the cow. Economically it must be at least enough to equate the average physical product and the marginal physical product. As a maximum the total digestible nutrient intake is limited by the concentrate limit of the cow. In an economic sense this would be where the marginal physical product has decreased to zero. The economizing principle is rationally applied within this range. Cost curves are derived logically from the production function with the inputs combined as dictated by the scale line. The deter- mination of the optimum combination of the two inputs, roughage and concentrates, present a special problem in the case of the dairy cow. Current thought among dairy specialists is that it is economical to fill a cow's stomach either with roughages or with roughages and concentrates} Under the normal range of price relationships the price 1 In a rather new textbook, the renewing statement was found in a section discussing balancing rations: "The cows should be fed all the roughage that they will clean up" H. G. Henderson, Carl W. Larson, and Fred S. Putney, Dairy Cattle Feeding and Man ement (third edition, New York, John Wiley and Sons, Inc., 1957;, p. 123. Professor Morrison gives the following paragraph related to this subject, "Good milk production cannot be secured unless cows have an abundance of feed. When concentrates are so high in price in com- parison with roughage that it is wise to feed less concentrates than normal, special care must be taken to keep the cows filled up with high- quality roughage. Otherwise, production will be seriously reduced.” Frank B. Morrison, Feed and Feedi (let edition, Ithaca, New York, The Morrison Publishing Company, rl19h8), p. 678. This only refers to 33 of total digestible nutrients from roughage is such that fine farmer can buy three pounds at an outlay which would buy only two pounds or less total digestible nutrients from concentrates. Under these conditions the price line probably touches its highest product contour at the roughage base line. A consideration of the current thought of fine dairy specialists combined with the normal range of price relationships seems to imply'that the scale line should go out the roughage axis until it reaches the stomach limit line. Thereafter, total digestible nutrient intake can be expanded only by substituting, at varying rates, high valued digestible nutrients from concentrates for low valued digestible nutrients from roughage. It was originally decided that a ration consisting of 100 per- cent roughage should be the lowest level of feeding to consider in the study. Although this assumption is later dropped for the higher quality cows, the assumption is used here for the sake of logical de- velopment. Conceptually, it would seem that additional milk production could be secured from this point on only at a higher marginal cost per unit, because a high cost feed, concentration, would be substituted for a low cost feed, hay. Cost computations are to be made for six levels of feeding ranging from 100 percent of the total digestible nutrients good quality roughage, but he indicates that if a cow is worth keeping at all, she is more profitable if fed liberally. The United States Department of Agriculture Technical Bulletin Number 815 on.input-output relationships in milk production also utilizes this idea. In this ex- tensive study, one of'the two series of feeding experiments was made by feeding grain at specified rates in addition to all the roughage the cows would consume. 3h from roughage to one supplying 50 percent of the total digestible nutrients fro. roudlage and 50 percent from concentrates. The method of arriving at the physical quantities and the implications of the results follow. Feed input-output relationships were wanted for four quality cows. m converting the milk produced per cow as ascertained by the survey in- to four-percent fat-corrected-milk, it was observed that the amount of milk produced by each quality of cow compared quite closely at the 12!; level of grain feeding with the four qualities of cows for which input- eutput relationships were plotted in United States Department of Agri- culture Technical Bulletin 815.2 (The average annual production per cow figures that we acquired from the mil survey were assumed to be the result of a 12!; rate of feeding - a usual rate recommended and fol- lowed over much of the state of Michigan.) These input-output re— lations were therefore taken as the basic data for this cost study. Cows in the Detroit ndlk shed get their total digestible nutrients from a combination of concentrates, hay, pasture, and silage. To avoid the problem of pricing the inputs silage and pasture which are fixed for the farm, it was decided to hold these factors constant over the range of the feeding variations.3 The level of feeding is raised by 2 Jensen, 3., et al, I -Out 1'. Relationships .12 Milk Pro- duction Technical Bulletin Num r nited States Department—Sf m, waflhington, DOCO’ May, 1952, p. 1‘2. 3 For most Detroit milk shed dairy farms, the dairy cow is the main forage consuming animal on the farm. Silage and pasture are often find assets for the dairy enterprise, the farmer being moti- vated neither to buy more nor sell any of his present supply. ‘\ 35 adjusting the amounts of hay downward and increasing the consumption of grain from the level at which the ration consists of 100 percent roughage. The total digestible nutrient intake can be increased only by increasing the amount of concentrates fed and reducing the quantity of hay fed.under the conditions of the problem. Experimental data were available to indicate approximately the proportions in which.hay and grain substitute for each other along the stomach limit line. Such information is indicated by the manner in which total digestible nutrient intake increased as the level of grain feeding was raised in the experiments reported in United States De- partment of Agriculture Technical Bulletin 815.h In order to estimate this increase in total digestible nutrient intake as grain is substituted fer hay along the stomach limit line, a smooth curve was fitted to the, data in Bulletin 8155 relating grain consumption and total digestible nutrients consumed per year for each quality of cow. These curves were then adjusted up or down for the difference in quality between the cows in this study and those in Bulletin 815.6 See Figures h, 5, 6 and 7. As an example, using that quality of cow which had an annual average production of 5,133 pounds of milk at the 12h level of feeding h Ibid, p. h3. 5 Ibid, p. us. 6 Ibid, p. be. . has no erase nnaqm no gauges e 5.“: who can 3:30.339» 0:335: 3333»? 33:5ch 1.” who: . name» we gem : Sac; bBTH Ember one; b i . _ W . and: no 335a noon 3. finch» no 350A 23 e8 can: can accosted new £8989 use.“ no 396A Rims i e i once soon .. 3033s no." son a 33 oflsgeflfiss Illv .. I.\\|\\ i. one. eased 21m sausage Ail. 280 you 050 3932.4 as .1. Clean ‘0‘ Benet-tam amusefiw 1840'; 30 Banned 7 3 {ads co mosses «mm.» co huaoecmo m nefiz.msoo new annmcoapmaoa scrapes: odpwpmowfio deco» u cameo .m agenda dawn» mo apnoea o8.o ooo.m 083 ooo.m o8.m 08; t _ a . _ a. guru .I 8m; can. no messed .38 or swam no ,. \‘\ canon one no.“ can: MAE oopooaaoo . \\ l 8m.m pom scooped anon mo menace mmm.>*. \\ 4 some mace ooow a axaas messed uncowpeum 30H new menu aaw\V «mmqw wcfiwwao>m mace one. o... seesaw areas all... 4.2.... 8a chase ooeaanoa i 83. coma squetaqnu atqtqsestp Ieioi JO Spun0d 38 some. he messed omm .m Mo fiwomdoo m news mace so.“ agmnowpmaoa pacified manwpmmwwo H33 I macaw .0 mafia cams» mo mocnom coo; 80.0 ooo.m 083 ooo.m oood 8.3 o d u u a . fl HI. m .. emu: «an: mo moaned .58 3 cums» no a. ..\_ I omn .m mason one can con: 3.35 ooeoohhoo .. an.“ scooped how no cocoon owns? I. OWN.\@ ounce Hood I 305 uses a»? com 3% one 3 seesaw ease liar 35.... 5 cgwm nsonmon new fitness crosses ea odoamv dull ids co nosed own; J om»; 33985 960 no.“ ego poemsfié J 036 squsquu emu 9981p “[2401 $0 spunod 39 .EE No «page 813 He seasoned a 5n. 2.8 see afloaoaeaaoa assesses teaspoons. H33 .. date 4. 25mg 5.2» we 858a 08¢. 086 89m 803 8o.m 80$ 8o; 0 a . l _ 4 A . 4 H— ”In. .312 .ao sensed 813 mangoes mace oboe ooow .. 33.. no“ 950 $534 :lllv TIIII Judas AME you oven .2 05 op v0.5.3 go 80$ . ems em squat-um: Gunman) I940: JO Banned ho to correspond with the low stations poor cows,7 was estimated that 1,283 pounds of grain would result in a total digestible nutrient intake of h,977 pounds. This is found by reading from.the input-output curve for low stations - poor cows, the total digestible nutrients necessary to produce 5,133 Pounds of milk and adding to it the maintenance re- quirement for a 1,200 pound cow - of 3,39h pounds of total digestible nutrients.8 This rate of total digestible nutrient intake was plotted against its respective grain intake on the graph for that quality of cow. This point was found to be above the line fitted to the data reported in Technical Bulletin 815, so a second line was drawn through the point parallel to the first line. ThiS‘WaS the curve from which the total digestible nutrient intake was estimated as grain is substituted for hay in the ration. This was done for each of the quality of cows. (The slaps of the curve for the high quality cow was decreased slightly in order to keep from increasing the consumption of grain and hay simultaneously to secure sufficient total digestible nutrients.) At this stage the curve represented the range covered in the experiment. An extension of the curve was needed to carry the re- lationship down to the level of feeding at which 100 percent of the nutrients are being supplied by roughage -- this tentatively being the 7 Ibid, pp. he - h3. 8 Morrison F B Feeds and Feedi The MOrri , . ., son Publishing Company, Ithaca, New'York, I935, p. llfi7. hl lowest level of feeding in the study. EJCperinental data indicate that can fed no grain will produce approximately 80 percent as much milk as when fed at a 1:6 grain-milk ratio.9 The curve was extended to the left until a level of grain feeding of 1:6 was reached. The total digestible nutrient needed to produce 80 percent as much milk and main- tdn the cow was ascertained, and the intersection point on the ordinate axis was then located. The curve from this point to the 1:6 point was dram so that total digestible nutrients would be increasing at an increasing rate with beginning increments of grain. A smdy by Badman'indicates a similar awareness of an extremely high rate of substitution of grain for hay for these initial increments of grain to a 100 percent roughage ration.10 9 Mosely, 1'. w., Stuart, Duncan, and Graves, R. 11., M work at the Bantu, Montana Field Stations, Huntly, Montana, 1918-lg27, Film 3 ates Depar ment of Agriculture Technical Bulletin 116, 1329; Sherwood, D. H., and Dean, H. K., Feedigg Alfalfa _Iiay Alone and With Concentrates to Bad Cows Oregon Agricultural Experiment Station Ballet-in 580,1:950; Hea ey, F. B., The Economics of Feedigg Alfalfa %and Grain to Holstein Cowg, Nevada Agricultural- Experiment Station EEK-EC: I739; Graves, R. R., Bateman, George Q., Shephard, J. B., and Cains, George B. , Milk and Butterfat Production by Dai Cows a3 93 Four Different Planes of Feedin United States Dep ment of Agri—Ei'o t"""ur.,"""EnTec Tic afieti—fi 2' 'E, 19th. 10 Redman, J. C., "Ecommic Consideration of Grain-Roughage Substitution in Feeding for Milk Production”, unpublished Ph.D. thesis, University of Kentucky, 1951, p. 103. Published as a Journal Article nEconomic Aspects of Feeding for Milk Production", Journal 23 Farm Economics, Volume XXXIV, August, 1952, pp. 333 - 31:5. [I (1 1:2 These relationships between concentrates and total digestible nutrient intake were then used to determine the amount of grain in the ration at each of the feeding levels for each of the four quality of cows. Hay was adjusted dowmrard accordingly while pasture and silage were held constant. Input (feed) - output (milk) tables are given for each of the four quality of cows in Appendix B, Tables I, II, III, and IV. The rate of substitution of grain for hay is quite variable over the range considered. For the initial increments from the 100 percent roughage ration, there was the aforementioned high rate of substitution of grain for hay. Then as additional grain is added, the rate of sub- stitution of grain for hay approaches zero as grain consumption is in- creased with very little decrease in hay consumption, indicating an almost vertical stomach limit line. Still more grain added to the ration begins again to substitute for hay at successively higher rates until the stomach limit line becomes almost horizontal. This appears contrary to findings of Hoglund,11 Horrison,12 and Wells,13 but it is 11 Hoglund, C. R. and Wright, K. T., Reducing 93:151.... Costs en Mchi an Farms Michigan Agricultural Experiment S ation, East ,man and United States Dopartment of Agriculture, Washington 1952, p. 17. 12 31. £22., Morrison, p. 676. 13 Wells, J. A. , "A Technique for Synthesizing Cost of Production Data- With Special Reference to Dairy Enterprises in Green and Taylor Counties of Kentucky", unpublished Master's thesis, Department of Farm Economics, University of Kentucky, 1951, p. 38. h3 consistent with work done by Redman;h at the University of Kentucky and part of the data presented in Technical Bulletin 815.15 Hoglund in his work at Michigan State College has used a cone stantly increasing rate of substitution along the stomach limit line ranging from..15 for the first increments of grain up to .99 for the last increments. This appears to be an inadequate allowance for the rate of substitution for the first increment of grain. Further, it does not reflect the low rate of substitution existing where the stomach limit line is almost vertical. Morrison assumes a changing rate from between .6 to .8 while ‘Wells uses a rate from'between .5 and .7. Redman, though, in deline- sting the stomach limit line, found them.to be shaped as suggested by this study. The data in Technical Bulletin 815 for different quality cows reflect the substitution rates ascertained earlier in this study. Hewever, when.lumping all the data together, the authors of Technical Bulletin 815 arrived at an "average" rate of substitution of between .5 and .7. The results of this study are based.on the experimental data presented in Technical Bulletin 815 for the different quality cows. 'When.lumping all the cows together to getan "average" rate of sub- stitution Jensen, et. al., no longer'were dealing with a single 11‘ pg. 939., pp 100, 122. 15 E. 23:53, P0 1430 14h production function, but were combining segments of functions for a number of cows into an inter-cow function. The fallacious results that arise from combining points from unlike functions have been pointed out by Bronfenbrennerlb and Radar.“ Other feed inputs must be considered also. Investigation showed that vitamins and minerals supplied in the ration were sufficient at all levels with the exception of salt. It became an associated variable with the feeding level, and the amount needed to be supplied at each feeding level for each or the quality cows is given in Appendix B, Table V. These amounts are based on recorrmendations of Morrison18 of a dnim requirement of .75 ounce daily per 1000 pounds live weight, plus .3 ounce in addition for each 10 pounds of milk produced. £3333. Certain portions of labor are associated with the level of feeding and hence must be included in the variable and marginal costs for this length of run. In computing these inputs, data were taken from cost studies conducted in the Detroit milk shedl9 and in addition from work simplification studies made at this and other institution»?0 1‘5 Bronfenbrenner, 11., ”Production Functions Cobb-Douglas, Inter- fin, Intrafirn", Econometricg, Volume 12, January, 19“.» PP 35 - M. 17 Reder, H. 3., “An Alternative Interpretation of the Cobb- Doug§as fixation", Econometrics, Voltme 12, July-October, 191:3, H) 2 9 " 2 e 18 go 21...!" p. $3e 19 Unpublished data, Agricultural Elqmriment Station, Michigan State College, 1952. ' . . 20 Brown, 1.. 3., "A Comparative Analysis of Stanchion and mm Parlor Barns", Work S lification News Letter, Purdue Work Simplification Laboratory, Issue fie. I; (Quota, Inaana: Agricultural Hall Annex), 15 From the cost study, base quantities were determined at the 1:1; level of grain feeding for each of the quality of cows under the given conditions of herd size and type of barn. These figures which were given in terms of hours required per cow per year, were then broken down into Jobs for each of the rospective herds according to the relative importance of each Job as ascertained in work siwlification studies. mly certain portions of the labor are variable with the level of feeding. As a result the 'jobs were divided into those that vary with the level of feeding and those that do not vary with the level of feeding. Olly those portions that are variable for this specific length of run are included in the computation of the cost curves. Rates of doing the several jobs that vary with the feeding level were estimated for each of the sizes of herd and the different types of barns. These rates were based on a per hundred pounds of feed fed or per hundred pounds of milk handled - whichever operation the job entailed. For the pen-type barn with an average herd size of 16.1; July, 191:8, pp. 9 - 18; Lowry, B. 11., "Labor, Equipment and Building Costs in Dairy Farming with Special Reference to Work Methodsfl (Un- published Master's thesis, Department of Fare: Economics, University of Kentucky, 1919), pp. h9 - 59, and 75 - 9h; Wells, J. 1., "a Technique for Synthesising Cost of Production Data - With Special Reference to Dairy Enterprises in Green and Taylor Counties of Kentucky", (Un- published Haster's Thesis, Department of Farm Economics, University of Kentucky, 1951), p. 673 Brown, L. 3., Cargill, B. F., and Bookhout, B. R., 229- e Dai B . Michigan Agricultural Experiment Station Special e n 35;, $1). 28 - 29. 146 cows, the rates of doing the jobs were quite similar to the rates for doing the same jobs in the stanchion barns for a herd size of 22.6 cows. The same rates were therefore used in each instance. Using these rates, the labor input was estimated for each of the levels of feeding for each of the qualities of cow. The results are pre- sented in Appendix Tables VI and IV along with the rates of doing the respective jobs for each of the herd sizes, presented in Appendix Table IVI. These inputs are only estimates of the labor used on Detroit milk shed dairy farms. Labor used varies quite widely among farms and pro- bably on the same farm in different seasons of the year. The results are thought to be fairly accurate, though, because the base quantities are determined by actmal data taken from the Detroit milk shed farms. ELLE fig. As the level of feeding is raised and more milk is produced on an annual basis, additional ndlk cans are needed to handle the daily deliveries. Average daily deliveries were estimated at the various feeding levels for each of the representative enterprises and the additional cans needed was determined. This number was multiplied by two to follow practices in Michigan where the milk hauler makes only one stop at a farm per day. An annual charge was estimated on the basis of a five year life for the cans. This charge was evenly distributed over the various feeding levels. Electricijz. As the level of feeding is raised and more milk is produced, additional electricity is used. This results from increased militia machine operation and milk cooling. h? Electrical appliances on several typical dairy enterprises were metered by the Michigan State Agricultural Engineering Department as part of a demonstration in 1952. Although the rate varied considerably between different farms, these studies showed that additional milk could be cooled at the rate ’of .98 kilowatt hours per hundred pounds of milk. The electrical power used by the milking machine in milking an addition- a1 hundred pounds of milk could be done at the rate of .0836 kilowatt hours. The results of applying these rates to the additional milk produced at the higher levels of feeding is presented in Appendix Table XVII. These averages may not be representative as power requirements vary considerably betwaen conditions. The data do indicate, hatever, something of the magnitude of electricity costs, and as such costs make up such a small part of the total variable costs, rather large proportional errors would not significantly influence the marginal cost couputations and the supply curve. Feed grim. As the level of feeding is raised another as- sociated variable is the cost of grinding the additional concentrates. A large preportion of the producers in the Detroit milk shed have their feed ground either by taking it to a local elevator or by having it custom ground at the farm. Consequently, it seemed reasonable to use custom rates in establishing the charge. MB A study on custom work in Michigan made by Vary21 indicated that the nost conon charge for grinding feed was ten cents per bag. It is estinated that a bag holds approximately eighty pounds. The cost, based on this charge, at each feeding level for each of the different herds is presented in Appendix Table XVIII. m M. The manure of the dairy animal has value to the farmer and as such is a credit for the dairy enterprise. It acts to lower both the variable and marginal cost of producing milk as it is associated with the feeding level. The amount of fertilizer elenents returned to the soil is detemined partially by the composition of the feed fed to the animals and partially by the manner in which the mm is handled. The composition of the hay used in this stub was such that a hundred pounds of it contained 1.8115 pounds of nitrogen, .24 pounds of phosphorus, and 1.9697 pounds of potassium. A hundred pounds of the grain lixturs contained 2.58 pounds of nitrogen, .3h6 pounds of phosphorus, and .61; pounds of potassium These figures are based on the average composition of feed as indicated in Morrison's Feeds and Feeding.22 Because of the richness of milk in nitrogen and phosphorus, when dairy cows producing a good yield of silk are fed the usual types 21 Very, x. 11., Rates for C_____uston work in me ”am , 1 2am 1 Extsmion Folder-m, Hichigan State College COOpera vs nsion Service. 22 Morrison, m. 933., pp 1086 - 1131. 139 of rations, they will excrete in feces and urine only about 70 percent of the nitrogen in their ration and 63 percent of the phosphorus. The proportion of potassium is considerably higher, being about 86 percent.23 8 Morrison indicates that under proper management not over 25 to 30 percent of the nitrogen and practically none of the phosphorus and potassium are lost.2h In this study, a 30 percent loss was assumed for nitrogen and a five percent loss for the phosphorus and potassiun under the conditions of the stanchion barns. As somewhat more nitrogen can be saved with a pen-type barn, it was assumed that eighty percent of the nitrogen excreted could be returned to the fields. In comuting the manurial credit to the dairy enterprise, the amount of the fertilizer elements fed to the cows at each feeding level was sstinated on the basis of the aforementioned data on feed comed- tion. The amount excreted by the animal was estimated and from this the anount reaching the fields. Results are presented in Appendix Table :11. In addition to the amounts of plant food it furnishes, farm manure also has other beneficial effects, including the addition of organic matter to the soil, the presence of certain acids that help to dissolve othezwise insoluble plant foods, and the great number of various Ends of bacteria that it contains. While the value of these 23 Ibid, p. 6&1. 2h ma, p. 61.8. So latter mentioned qualities is not measurable, it is assumed sufficient to offset the cost of spreading and hauling the manure. The total value of the fertilizer elements reaching the fields was therefore credited to the dairy enterprise. Pricing of the Factors of Production The inputs were valued at their on-farm prices. we to their heterogeneous uses, differences in marketability, and different sources, prices were arrived at in several ways. A description of the method of pricing for each input follows. M w_i_._t_h_ little 9}; £13 seasonal variation in 231.5; 95 23:. Milk cans, stock salt, nitrogen, phosphorus, potassium, electricity, and soybean oil meal have little or no seasonal variation in price, Consequently, a straight average of the average quarterly prices as secured from the Michigan Agricultural Statisticians office is used. These are at-fam quotations. m with seasonal variations in; 2323.2 a_n_d_ use. Both the use" - and value of feed grains and hay vary seasonally. In arriving at the : annual average price, an allowance for this was made by taking averagei monthly prices and weighting them by months according to their estimated use in the dairy enterprise. For corn and eats, a nine percent weight;- ing was used for October through April and a 7.14 percent weighting was used for Hay threugh September. For the shelled corn, seven cents per bushel was charged for shelling. 51 The average monthly prices for hay were weighted at 15 percent for November through March and 12.5 percent for October and April. It was assumed that little or no hay was fed through the remainder of the year. Labor - an asset that is often fixed for the farm but variable between enterprises. The pricing of labor, as earlier mentioned, pre- sents one of the more diffith problems of the study. For the in- dividual Michigan farm, labor is often considered to be a fixed asset, which ilplies its earning power is less than opportunity cost and greater than its off-farm disposable Value.2S Under these conditions, the farm manager is motivated neither to buy more of it nor to market some of it in an off-farm alternative opportunity. For the dairy enterprise, however, labor often has to be charged at its on-farm opportunity cost or its marginal value product in al- ternative uses on the farm. is the intensity of feeding is changed and the amount of milk produced changes, the amount of labor varies and must be priced. However, as an asset that is often fixed for the farm as a whole, it can be priced at its earning power in dairy or in an alternative enterprise. If a firm is in a state of equilibrium, the labor input is allocated among enterprises so that MIC = MVP for each enterprise and its MFC in one enterprise will be its MVP in an alterna- tive use. In order for one more unit of labor to be used in the dairy 25 Bradford 1. a and Johnson a L r , . ., , . ., arm Mangement m, John Viley and Sons, Inc., New Iork, 1953, p. El. C (m . C '3 4 o O O s 52 enterprise, it must be paid at least the on-fam opportunity cost which is the MVP sacrificed by diverting it from an alternative enterprise. If there are no on-farm alternatives other than the dairy enterprise, an additional unit of labor applied to it can not be valued higher than the MVP of labor so long as labor‘ is a fixed asset as previously defined. Comutations for dairy farms in Ingham County as made by Uagleyzé and modified tw Johnson estimate the MVP of labor at 67 cents per day. As this stuck has been criticized for underestimating the earning power of labor, a comarison was made with data presented in the Farm Busi- ness Analysis report for Area 527 by Michigan State College and also with data from a study made by Paul Wilkes.28 The results are indicated in Table VI. Due to the nature of the computations it is impossible to esti- mate the earning power of labor at the margin by methods used in pre- parirg the Area 5 report and the stuck made by Wilkes. There is, however, a high degree of consistency among the dif- ferent studies for gross income per PMVU and labor income per PMVU, the evidence suggesting that the Johnson-Wagley estimate of the MVP is not too low. 2‘5 Raglsy, a. v., “Marginal Productivities of Investments and n:- penditures, Selected Ingham County Fame, 1952", unpublished lbstar's Thesis, Department of Agricultural Economics, Michigan State College, 1953. 27.22? m M 322913 £2: snag, Agricultural ncperiuent Station, Michigan State College, 1952. 28 Wilkes, P. , unpublished computations, Michigan State College, 1953. .\ 53 TABLE VI GRGS INCCHE, LABOR INCOME, AND ESTIMATED MARGINAL VALUE PRODUCTIVITY OF LABOR ON SELECTED MICHIGAN FARMS, 1952 Wagley Area 5 Wilkes (Dallars ) (DOllars) (Dollars) .._ .A.__-__..-_. -._-_.-—._r_-.--4———-.’ --W——~----_— — Gross them/Pm 26.86am 22.18 25.h7 Estimated MVP/day .67 -—-- .— Labor insane/Pm 7.295‘ 5.56 6.22 .-._._ SOURCE: Refer to footnotes 26, 27 and 28 this Chapter. {Productive m Work Unit. “Gross income/day, actually d ross income fillfiri N flabor income per day, actually d( as income .. £1. p“ 31f?» a where the 1's are inputs other than labor. For purposes of this study, however, we would not be Justified in pricing labor at a value of 67 cents per day. The dairy enterprise competes directly throughout the year with other farm enterprises. During the height of the planting season or during the height of the haying season the cows still have to be milked. it these times the MVP of labor is probably significantly higher than its MVP for the year as a whole. This would seem to justify our placing a higher value on it than the evidence would seem toindicate. Sh An estinate of fifty cents per hour is used, it being realised that there is little or no empirical evidence to substantiate such a value. It is considerably below the going wage rate, this being Justi- fied by the fixed natm‘e of the labor asset and its low estimated earnim power. It is above the value at the margin for the above given reason. The prices used in computing the cost curves are found in Table XI, Appendix B. Computation of the Cost Curves The physical quantities of each of the inputs associated with that length of run in which feed is variable have been computed. Prices for each of these inputs to the farmer have been established fron vari- ous sources. is pointed out in Chapter II, marginal costs are determined by the cost of the imuts which can be varied within a specific length of run. Variable costs” are found by multiplying the input quantities by their respective prices at each feeding level. This gives the total cost of each input at each feeding level. These costs are then sumsd at each feeding level to determine the total variable coats” associated with the length of run in which feed and associated inputs are variable. 29 Less than total variable costs in some instances, but the difference is a constant and does not influence marginal costs for this length of run. 55 It was pointed out in an earlier section that the fertiliser elemnts returned to the fern in the form of manure were a credit to the dairy enterprise. The physical quantities of these nutrients at each feeding level are multiplied by their respective prices to de- termine weir credit to the farm. The value of this credit is then subtracted from the total costs at each feeding level and the total veriable costs chargeable to the dairy enterprise are determined. The problen is to determine the marginal cost of producing an addtionsl 100 pounds of 1111:. As the feeding level is raised changes occur in two factors. Total variable costs are increasing, and at the sale tine, 1111: production is increasing. Dividing the increase in total variable costs from one level of feeding to the next higher level by the increase in milk production, in hundreds of pounds, that resulted fron those additional costs, gave the mrginal cost per 1m pounds of milk. The resulting figure is an average marginal cost per hmdred pounds of milk for going from one level of feeding to the next higher level. The variable and narginsl costs at each level of feeding for each of the typical herds are presented in Appendix B, Tables XII - m. In drawing the curves, the milk production at each level of feediu was plotted on the horizontal axis. may between the quantity produced at each feeding level the average narginsl cost of going fron one level of feeding to the next higher level was plotted. 56 A snooth curve was fitted to these points for each of the typical herds. The results are presented in Figures 8 through 17. For the lowest quality cows, the marginal cost curve is contin- ually rising over the range plotted. For the other three quality of can the marginal costs first decrease with heavier feeding levels and then increase. The significance of this is discussed in the next section. For all the curves there is a considerable range over which the curves are only gradually rising. Beyond a certain level, however, the larginal cost of producing milk rapidly rises. For the higher quality cows, this range of rapidly rising marginal costs is not reached, even at the highest level of feeding. It was desired to know the marginal costs of producing milk up to a cost of six dollars per hundred, so the curves for these high quality of cows was extended up to this amount. As the extension was not very large in either of the three cases, it detracts little from the accuracy of the pre- diction curve. It is significant to point out that for the length of run in which only feed and associated inputs are variable, herd size has very little imact on the marginal costs of producing milk. A discussion of the reasons for this is given in Chapter V. 5 08 .Nmea .8 consooaom- flea .H aoooooo ooao ads season 7 «meson. nonhuman a. can no unused mmaem mnwosbona awoken soc new gosh—.8 woos Henge: .m shaman cameos accuse 0mm 8m om: 8: fl . — .1 scanned and: mo men—5m .30.“ some 3. each so ounce one eon eoea ads co cocoon «mime a 00...” 1 oo.m .. 8.: Loofi - coo .. 8.» - 86 c ooem 00eOH 9191:1300 .mmma .om consoeaom .. amma .H Lncacaoo .ooao one: escapee no, pawns cocoon: amass deflogn trade He cocoon mmaem 95260.3 £20: 300 momH ego shoe .3ng 08 0mm 08 Gus 02. 0mm cow 0mm 00m o _ _ a _ a a . . a xii?ll J |IIlllilllllillilillilllll kl. 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Had A afiofio 62» fig. b 36.58 .383 5.305% #352 «0 358a 8.13” 3328.5 66.5: zoo m6 .mgo swoo H.335: . .3 983...” 6 £93: 8.65: SH; 804 08; 0mm com 0mm 8» cm» o2. owe on» a a A fi fi . _ ~ _ l_|| 4 . m _ w . m .1 8A , nofioonobm ; 00.: § \ _ a Loo.m 4 86 4 00¢. 6388“ 3.5.2. mo 356m .33 3 awn» mo wagon one 8.“ :2: ads mo wagon 812* L 83 < 00.0..” 9‘9 112°C! . .«mfi .om umngfigom a fin .H 3938 63” nae a £938 £53 5323: *3de .8 883 85: 38329 5.8g :8 m.~a .258 $8 33.3: .3 95mg 233 885: 83” 08; 8m; 8.} com; 084 8a; 804 » 3.--I.IJ-:.-!-!.:.---....1._llx-.....l2!. iilé- ._ $22. wialii: _ _ Ezalilt, 1 OOoH .‘l. W - aofioonoum . \ 4. 8.: \\ 4.09m . ~ \ q.._...___.. ant-[ca 4*. co.» IJ 8.0 .2268.“ ad: no $53 .53 3 53.5 no canon 93 can :2? 5H: no 3559 Guano? J 00$ -1- - . - OOoOH am 0QO .a2 .8 nmfisgom .. HRH .H .338 .85 id: 3938 guano: downunmam_*qxaaa no nausea ONH.QH mqaoavoua .mvuon zoo wowm .mpnao anon Hmawmnmz .NH onsmwm £32., 3.65: a m 7 4 \Il“ cl“ \ kwfl—a-“ ‘- \ 3:2 .8 85cm .58 3 .82» :8 Egon 28 8m :2: ad: no 356m 813* 8.3. om?” o8.~ o3.“ 8m.~ RH.“ o8.~. Axuo d a _ _ A II Good OOoN oo.m 8.; OOom L COCO 00.5 I 80$ oo.m OOoOH . BJBIIOQ 67 Economic Siggificance of TheEeYCurvfieg for Purposes of éggregatfng the Supply Curve As was nentioned earlier, it was originally thought that the 100 percent roughage level of feeding would secure the lowest cost per hundred weight of producing the milk. Wells, in computing marginal cost curves for milk production over this same length of run in certain areas of Kentucky found this to be the case, and the feeding recon- nendations of the dairy specialists, as earlier mentioned, also seen to 1|le this. In cowuting the curves this was found not to be the case for high quality cows. For the three high quality cows in this study, the marginal cost of producing additional milk actually decreased as the initial increments of grain were added along the stomach limit level to the 100 percent roughage ration. This indicates that for these quali- ties of core, the scale line does not go out the roughage axis and up the stonach limit line, but actually leaves the roughage axis before reaching the stomach limit line for all roughage and mets the stomach lint line at sons combination of grain and roughage. See Figure 18. In searching the literature it was found that Badman achieved sililar results in his studies at Kentucky.30 The explanation for the phenomenon appears to be that the marginal plysical product of total digestible nutrients is very high as the initial increments of grain replace large quantities of roughage. 3° 93. 31., p. 100, 122. Grain Figure 180 68 Kstomach limit line scale line under ' normal price re- : lationships ’ roughage Production surface for the dairy cow. 69 Though the marginal factor cost at this time is increasing too, because as pointed out previously, a high cost source of digestible nutrients is being substituted for a low cost source, total digestible nutrients nay increase very little. If marginal costs are found by dividing marginal factor cost by marginal physical product, the lower marginal cost, than results from a high marginal physical product of total digestible nutrients along the initial segment of the stomach limit line. However, marginal cost rises with further additions of grain to the ration because of the dininishing marginal physical pro- ductivity of total digestible nutrients as grain loses its ability to replace large quantities or roughage. This ability to utilize grain in producing milk at a lower marginal cost appears to be related to the quality of the cow. For the laest quality of cows in this smchr, the marginal cost was lowest at the 100 percent roughage level of feeding. Wells, in his study at Ksntucky in which his marginal costs were lowest at the 100 percent roughage level of feeding had even lower quality cows, so this work is consistent with his results. Selection of the Relevant Portions of the Marginal Cost Curves Te reiterate what has been written previously, the relevant por- tions of the marginal cost curves for each of the typical herds are the firms' rational short—run supply curves, indicating the quantity of milk they will supply at alternative prices. As the firm attempts to maximize 70 profit it will adjust its output toward the point where marginal cost is equal to the price of the product. For each producer, changing prices call forth changing quantities of output, then and the firm's marginal cost curve indicates this relation between price and the quantity supplied by each firm - given the cost structure and.input prices. Determining the relevant portion of the marginal cost curve pre- sents a special problem due to the unique shape of these curves identi- fied with.the three high qualities of cows. Static nee-marshallian theory commonly indicates that the portion of the marginal cost curve above its intersection.with the average variable cost curve is the supply curve of the firm.in the short run. This appears to be logical and straight forward from an abstract theoretical standpoint but has to be further developed when applying theory to cost problems. in ex- tension ef theory has to be made in determining what portion of the marginal cost curve is the dairyman's rational supply curve and to cover conversion of fixed assets to variable assets. For the three highest qualities of cows the marginal cost curve first drops and then rises, even though the data indicate that average variable costs are rising. As was pointed out in the previous section this is because the inputs were not combined according to the scale line over this lower range. If the curves had been recomputed with the in- puts combined as dictated by the scale line, the marginal cost curve ‘would have increased continually over the range of the computations along with the average variable costs. 71 Preliminary work by Denio Caul3l here at Michigan.State College indicates that if the price of milk drops below a minimum level on the marginal cost curve corresponding roughly to the point of difficulty on the stomach limit line, the cow's earning power becomes so low that she will be disposed of at salvage value.32 The length of run in which herd size is variable is beyond the scope of this thesis. is stated previously, this is an analysis for that length of run in which feed is variable. Thus, to compute the supply response below this minimum price level would entail consideration of a longer length of run. Therefore, the composite supply curve will be computed only from that portion of the marginal cost curves of the firm that is to the right of the minimum level. The minimum price for which a supply response can be ascertained for all of the ten herds is two dollars and forty cents. The composite supply curve will therefore be estimated over the range from two dollars and.forty cents up to and including six dollars per hundredneight of milk. 31 Gaul, Denio, a tentative Master's thesis on estimating the value of various quality of cows. 32 This is based on a definition of a fixed asset as presented by Bradford.and.Johnson. Bradford, L..A. and Johnson, G. L., Farm Management AnalyEris, John Wiley and Sons, Inc., New York, p. 321. They state that ma e conditions ordinarily impose upper and.lower limits on variations in the worth of a fixed.asset. If the earning power, (marginal value pro- duct) of an asset becomes greater than its opportunity cost, it becomes advantageous to add more of it. If this earning power drops below the salvage value of the asset, it becomes advantageous to sell it. If the marginal value product of any asset is not within these limits, it is no longer fixed for the firm and becomes a variable asset. CHAPTER IV THE COMPUTATION AND EXPLnNATICN OF THE COMPOSITE SUPPLY CURVE Aggregating Micro Into Macro-Responses An.average of 12,223 producers shipped milk to the Detroitvmar- ket in the fiscal year under consideration. The number of these producers estimated to be represented by each of the ten typical enter- prises is given in Table'VII. This breakdown is based on the results of the mail questionnaire sent to the members of the Michigan Milk Producers' Association. The estimated response of each of the ten.typical enterprises at prices of two dollars and forty cents, two dollars and fifty cents and upward by fifty cent intervals to the six dollar level was multi- plied by the number of similar enterprises in the milk shed. These results were then summed at each price level to get the composite response for the entire market area. The resultant supply curve is presented in Figure 19. Adjusting the Composite Supply Curve The shape of this supply curve, being based on the experimental production functions from the four qualities of cows and.the relative importance of each quality of cow in the market, should be quite*valid .mmmfl .om tenseenem n amma .H nepoeeo .eeee gees phoneme .eaee 9.191106 .2!) ompoohnoo 9mm admouon neon .mawmgofimodu Hams do comma exam: you ego madman .mH shaman M52 «o mogom mo 303 coded oomea ooe.H ooe.H oom.H oo:.H . _ _ la l l 8% OLTOOOM 1 00.... \ I; 000m .. 00.0 [9.131 .3 I ,..l. 1.. 80F 7h II. 1' ..| l"| -nl. .‘ I" "I |.. ‘I ' II II I. ‘l' I‘lllvll'l'l 'l'l -.|||l .Ii‘ltlilll! r H 00.00..” oxawz oopogmoo new #:00an .30."? H3 on. mmm.m em: eme.m omm.© 4.0H mcnwm com eee.e mee.ea cmH.OH e.- wem.a mm:.oa «mm.» e.mm 0mm emm.e Hmm.m e.mm mem.a «me.oa o~a.oa e.wa eem.a mme.oa mmm.e m.w~ omo.a mem.m Hmm.m e.ma mma.a ees.e o~a.oa m.w eem.a ewe.aa Nmm.e m.w emm.a mme.ma Hmm.m m.e mcawm coacomwpm emanmnovco women 433 *moasoa 3.. 38 mod the: 3». 980 no 093 many new: me one e93 mag coapoeooaa ommaoeed . 9.35:2: mo noneSz 932.60 b no nongz mo mono: pcooaem «mea .om mmmzmeemm u amee .H mmmoeoo .ammm eeHz eHomema a: E E 5% no message no muesli madame ea meme eo BE HH> awed. 75 for four percent milk. To make use of the curve for predicting pur- .poses, the snaps of the curve must be altered.by presenting it in terms of 3.68 percent milk and shifting it laterally to adjust for the bias toward.large producers that resulted from sampling a special group of producers with a mail questionnaire. Further, in using the curve for any year other than the base year, adjustments for year to year changes in number of producers, herd size, quality of cow, and input prices must be made. adjusting the curve to present butterfat content. The input- output relationships used in deriving the individual marginal cost curves were in tenms of four percent fat corrected.milk. Data of the Michigan.Milk Producers'.Association indicated that for the fiscal year under consideration, the weighted.average butterfat content of the milk produced was 3.68 percent butterfat. The production figures as ascertained from the mail questionnaire were therefore converted from 3.68 percent to four percent fat corrected milk for purposes of analysis. The composite curve as presented in the last section was in terms of milk with this fat content. Tb be useful for predicting purposes the curve must be converted back to 3.68 percent milk. This was done by taking the quantity pro- duced.at each of the specified.prices used in.locating the curve, and multiplying that quantity by four percent. This gives the butterfat produced.at each price, and the quantity of 3.68 percent milk can be determined.by dividing the pounds of butterfat'by .0368. The resulting curve is given in Figure 20. .wmea .8 neeaeeeem .. HRH .H 3938 .85. can $293 Jane emeeehee an.“ N £893.“ when 3 oopoohoo «adagewaeoev Hume do mouse was”? you oshso human .8 98mg #52 Ho mus—om Ho sowing BJBIIOQ 8le Son 8%; 84; owe; 8w; 8m; . p 1 8A .. 8.; 4 cos l 8.0 00;. 77 The shape of this curve is valid for the year under consideration. If in the future the average butterfat content of the milk changes signi- ficantly, the curve can be converted to the new content. Changes in the average butterfat content of the milk are slow in being made, however, unless there is a change from one breed to another. Shifting the curve to correct for bias. It was expected that the unadjusted curve would indicate an excess of production at each price due to the twofold bias resulting from taking a mail sample of a special group of. producers. The reapondents to any mail questionnaire are pro- bably the larger, more efficient, more conscientious producers. Tneir herd size is p‘obably larger than average and their average production per cow is probably greater than the average for the area. The population used in drawing the sample was biased, too, as indicated in Chapter II. The questionnaire was sent only to members of the Michigan Milk Producers' Association. Members of this organization are probably larger and more efficient than the average producer in the area as indicated by their average daily delivery of 3214.8 pounds as com- pared to 292.2 pounds for the non-members and 319.7 pounds average for the total shippers. These two factors would cause production to be overestimated at each price level. No measure of the exact magnitude of these biases is available, but an alternate method of adjusting for them is presented below. The shape of the curve as it is given in Figure 20 is probably quite valid, as pointed out earlier, because it is based on the 78 production functions and proportion each function contributes to the composite response. Therefore, the curve can be corrected for bias by locating a point based on the actual production for the period October 1, 1951 to September 30, 1952, and the average price for the year preceeding the period1 and shifting the curve laterally2 to pass through this point. The result of doing this is given in Figure 21. This is the aggregate supply curve for fluid milk in the Detroit milk shed for the period from October 1, 1951 to September 30, 1952. It is based on the given cost structure and the given number of Iroducers. Adjustigg the composite supply curve for year t3 near chagges i_p number (i cows, quality pf cows, and input prices. Three adjustments should be made in using the curve for year to year prediction purposes. In the first place, the curve will shift vertically in response to a change in the cost structure on which the curve is based. If the variable costs of producing milk rise, the curve will move upward, 1 Comparisons were made between prices and Iroduction over a six year period. Comparing the reported production for a given year and the corresponding average price indicates that there is a much closer correlation between the price in the preceeding year and the pro- duction in the current year than between the current price and the current production. This indicates that farmers base their expected price of milk on past experience. 2 A lateral shift is used because the cost structure remains the same. The bias is the result of a greater production at each cost level. Holding the cost constant, and reducing the production at each level would involve only a lateral shift in the curve. 9 7 8e; .eeee ease .Nmee .8 eastern .. d3 4 e838 30.58 id? @3353 as.“ perched $.m assume you ego human—m .Hm enema Md“: mo raccoon Mo goflag oom.a ooe.a oom.H oo~.a ooH.H oooea r _ _ _ _ new Till nonposeonm nonsense 1 8cm :1 80: u 8.m 00.0 84. 3.191103 60 indicating that less milk will be proauced at each price. If the variable costs decrease, the curve will shift downward, indicating that more milk will be produced at each price. The curve can be adjusted to some measure of the change in costs and reasonably accurate predictions made. Over the range of the indivi- dual cost curves included in the composite curve, concentrates make up the major portion of marginal costs. In addition to being the most important single cost, it is the cost item that is most likely to vary in price from year to year. ‘As a result, the change in the cost of a hundred pounds of concentrates is a useful guide in deciding how much and in which directions (up or down, vertically) to shift the curve. The percentage that concentrate cost is of the total variable costs at three points on the cost curve is indicated in.Table VIII. TABLE VIII PERCENTAGE mNOETTRATE COST IS OF TOTAL VARIABLE COSTS AT THREE POINTS ON THE MARCIth COST CURVES, DETROIT MILK SHED, OCTOBER 1, 1951 - SEPTEMBER 30, 1952 Percent concentrate cost is of total Marginal cost* variable cost 2.50 58.22 14.00 71.38 5.50 75.73 *Dollars per hundredweight. 61 These percentages were found by straight line interpolation be- tween points on the marginal cost curves for each of the representative enterprises. The percentages were then.averaged by weighting the re- sults for each kind of herd.according to the relative importance of that kind of herd in the market. The results indicate that the curve does not shift parallel, but has a larger response to changing costs towards the high cost end than towards the low cost end. The United States Department of Agriculture published estinates for the United States of the cost of a hundred pounds of concentrate.3 For the period for which the supply curve is estimated, the cost of a hundred pounds of grain was three dollars and seventy four cents.h This is a more expensive ration than was used in making the computations but is readily available and, hence, serves as a practical basis for quickly computing the results of a change in input price. To determine how much to shift the curve, the percentage change in cost per hundred pounds of the ration is multiplied by the percentage importance of the grain in the total costs at the several levels to establish the percentage change in cost. This percentage at each of the several levels is multiplied by the cost at that level and the result is the amount, in cents, that the curve has to be shifted.at each of the three levels. 3 Rations ng‘png igy Cows, United States Department of.Agri- culture, Bureau of.Agricultural Economics, Washington, D. C. h Ibid, January, 1953, p.2. 82 As an illustration, a prediction of the amount of milk produced in 1953 was made. The cost of‘a hundred pounds of grain ration dropped to three dollars and forth-three cents - an 8.28 percent decrease since 1952. Multiplying this by the relative importance of grain in the variable costs at two dollars and fifty cents, four dollars, and five dollars and fifty cent levels, it was found that the curve should be lowered h.82 percent at the two dollar and fifty cent level, 5.91 per- cent at the fOur dollar level and 6.27 percent at the five dollar and fifty cent level. These involve shifts of 12 cents, 23 cents, and 3h cents reSpectively. These points are plotted and the curve shifted so as to be drawn through them. See Figure 22. Using the average blend price of the previous year, 1952, it is estimated that the milk production will be 1,1;38 million pounds. This assumes that.the producing ability of the cows has remained constant and that the number of producers and the size of the herds have re- mained constant. Thus, the estimate still must be adjusted to allow for changes in these three things to be accurate. Milk production per cow has increased rather steadily over a long period of years.5 Over the 8 year period from l9hh to 1952 the average production per cow in Michigan increased 2. 50 percent per year. This change in production ability has varied from year to year, but for purposes of prediction, a trend may be used unless a more accurate figure is known. Judgment can be used in estimating what 5 Milk Production 33 Farms, Bureau of Agricultural Economics, United States Department of Agriculture, 1953. 3 8 .33 .. Rafi use» fins fiesta Joana use: Mo mHobmH 388.36 «M53. covcouhoo emu essence moon 3.3:. no.“ cogs DEE—m cum 933m 3.3: He mus—Sm me 303 Se; 08; 8:: 8m; 08; 8a; o8; . a _ _ in _ . PM" 1 Dean .. .. 8.: 83.3 pass mmma ill.» new? Ergo banana TI! to.» Home.“ SS 23 .. 8.m he“ opens hHamsm |.oo.w 00¢. szextoq 81: this change will be from year to year if it varies considerably from this trend. Multiplying 1,1438 million by 2.50 percent indicates a thirty-six million increase in the estimate due to an increase in the production ability per cow. This is added to the l,h38 million pounds to secure an estimate of l,h7h million pounds. A change in the number of producers or a Change in the average size of the herd would be indicated by a change in the number of cows and heifers two years old and over kept for milk, and the number of heifers one to two years old being kept for milk cows. The change in number of cows kept for milk innMichigan from January 1, 1952 to Jan- uary l, 1953 was an increase of 6.15 percent.6 8 The number of heifers one to two years old being kept for milk cows increased 5.81 percent over the same period. It was decided to consider only half of this increase in the number of heifers as con- tributing to an increase in milk production because probably only about half of them will come into production in that period. Therefore, averaging these increases, it was estimated that the number of milk cows in the area increased by 6.03 percent during the period under consideration. The estimate of l,h7h.million pounds of milk based on an in- creased production capacity for the cows mustfibe increased by this 6 January 1, 1952 was used as a base, because figures are not given for October 1, 1951. Since eight of the 12 months are in 1952, it is felt that the difference would not be significant. 85 amount, then, assuming the new cows are of the higher producing ability. The result is an estimated fluid milk production for 1953 of 1,563 million pounds. The curve is adjusted laterally to pass through this point. (A lateral movement is used because there is no change in input prices.) See Figure 23. Actua1.production for that period was 1,591 million pounds, giving an.error of prediction of 1.76 percent. There was an actual change in.production from 1952 to 1953 of 206 million pounds of milk or an increase of lh.8 percent. Eighty- six and four tenths of this increase in production was predicted. As further illustration, the production for 1951 was estimated at 1,337 million pounds by using the same kind of adjustments, except that the average capacity of the cows was increased from the 1951 base. (See adjusted curve in Figure 2h.) Actual reported production for 1951 ‘was 1,3h0 million.pounds - a predicting error of .22 percent. The decrease in production from 1952 back to 1951 was 3.3 percent. The direction of this change was predicted in addition to 93.5 of its magnitude. This is more accurate than the prediction for 1953 from a 1952 base. As a word of caution, it should be pointed out that a high degree of accuracy cannot be expected year after year. Deviations of an unr explained nature do occur, and in addition, the factor used in adjusting the curve makes up around 75 percent,tas a.maximum, of the total varia- ble costs. Wide variations in the prices of other inputs could affect the curve, the productive ability of the cows may change by'a greater oMMmH «pone made awouaon «saws possesses new accused co.m .xHHE_nom obese thdsw .mw oaswnm 6 8 an: «a menace no 335”: 8a.: 08; com; 8:; 8m; cow; 8}” — 41 4 5 u A a wa .loo.m i831 mmma new cowpospon .t- . mmma you : voahomem :iv nowaoncOHQ pseudonym oo-m .186 .l:.-8..~. QJBIIOQ 87 or less amount in response to unusual circumstances, and the weather may vary widely, causing the quality of the pasture to significantly influence the prediction in any one year. However, shifting the base continually from one year to the next would reduce the cumulative importance of these phenomenon by constantly correcting for them. There is evidence to indicate that as the number of cows in.the area decreases significantly, the prediction is less valid. An attempt to estimate the production in 1950, when there were about ten percent more cows in the area, on the basis of the 1951 - 1952 base resulted in.an approximate error of ten.percent. The estimated production was greater in magnitude than the quantity that was actually produced. A possible explanation for this is that as the number of cows decreased, the low producers were culled, leaving only the higher producing cows, and significantly raising the average production per cow. is a result, the average production ability of the cow probab- 1y increased more than the 2.50 percent per year from 1950 to 1951. As a check, the curve was adjusted to a 1950 base, and an attempt was made to predict the production in 1951. In this case the esti- mated production for 1951 was below the actual production by 9.h percent. This indicates that the improvement in production was greater than.expected, and had this been adjusted for, the prediction would have been.more accurate. Economic judgment of this and other factors must be considered when doing all outlook or predicting work. It is felt that if all 8 8 A»? 623 ads 9838 was eoaooEoo use anootoa $.m one: .3.“ arse sass 3m 8&2. ads so maggot no salads as: com: 8:; 8m; 8w; 81H 08; J 7 _ a 1 e e new \ .83 .62” you new sowvogoam octagon Illw . mlllnowaosoohm Eugen...“ 00.: 1 80m 1 Bow 00¢. \ 1 8cm BJ‘B flog 89 factors are considered, and that if the curve is annually adjusted for 'what is known about changes in production ability, number of cows, and changes in costs, reasonably accurate estimates can be Obtained ever a period of years. Several suggestions for additional research to in- prove the accuracy of predictions will be presented in the next chapter. CHAPTER V Significance and Implications of the Results The results of this study are significant in three broad areas. In terms of a semi-macro type of analysis, the supply curve estimates have implications for the operation of price support programs and fed- eral milk marketing orders. In terms of micro-analysis, the marginal cost data are potentially useful guides for the individual producer seeking to lower his costs in the face of a cost-price squeeze. Third and lastly - both the supply curve and marginal cost estimates are use- fU1 in analyzing the position of the milk producer in the Detroit area with respect to interregional competition. The Semi-Macro Analyjis Controlling production for the operation 2f 3 price support program. Since world.War II a price support program has been in exist- ence. .An apparent assumption behind a price support program is that the eQuilibrium price determined in a free market for a product is too low to provide the farmer with a "fair” income. Therefore, at times, the support prices are often established above the equilibrium level. On the basis of static Marshalliam economics, this results in mal- allocation of resources and.over-production of the commodity as well as higher incomes for the producers concerned. In.the case of price supports for dairy products, large quantities of butter have been put in government storage and.means of reducing these 91 stocks have been sought. It has been suggested, as a remedy, that milk production be controlled by restricting herd sizes for the individual producer. This study indicates that production control based on this policy would be only partially effective in reducing the supply of milk. The supply curve indicates that for the snort length of run in which feed is the only variable, milk production can be varied from 1,000 million pounds to 1,500 million pounds in the Detroit milk shed in response to price changes from two dollars and forty cents to six dollars per hundred weight. In addition, there is always the possibility of moving into the longer length of run in which the producer can shift from one production function to another by changing to a higher quality of cow. On many farms production could be doubled by the simple ex- pedient of replacing the low quality cows with cows of high inherent producing ability. . Beyond the fact that production controls based on restricted herd size for the individual producer are ineffective in controlling milk production, is the danger of freezing herd sizes at inefficient levels. The cost studies by Caull and Wells? indicate that increasing herd size is very effective in reducing average total costs. Federal milk marketing ordegg. Producers in a fluid milk area have practically no bargaining power as individuals when dealing with 1 92- 212-. Gaul. 2 92. 31.3., Wells. 92 milk handlers. Their problem is further complicated by the fact that all milk produced in a fluid milk shed is not used for fluid purposes. Some part, and the proportion varies with the season, is used for cream and manufactured products which bring a lower return than that used as fluid.mi1k. Federal milk marketing orders have been instituted, in part, to balance the bargaining power of the producer and the handler and.to price raw milk so as to equate supply with demand. This study indicates that milk production is quite responsive to price changes. Using the composite curve as a guide, the price necessary to call forth a given production from a given dairy cow population can be estimated. Pro- cedures for adjusting for year to year changes in cow population, in- herent production ability, and input prices are also available. Sucn estimates can reduce the economic waste resulting when re- sources are guided into the wrong channels of production. When this happens the consumer suffers from not having his wants properly satis- fied , the producer from low incomes, and the taxpayer from high taxes. Proper allocation of resources increases the aggregative well-being in the economy by maximizing consumer satisfactions and producer in- comes within a given distribution of wants, preferences, and desires. Interregional competition. Most factors influencing the location of production can be lumped under the two headings of supply and demand. This study has dealt with some of the factors under the former heading. 93 When considering supply, all of the things that affect the pro- duction costs and the quantities of milk that farmers will. produce at each price should be included. The composite supply curve for the area gives an indication of the (pantity response, while the marginal cost curves for the firms give an indication of some of the factors af- fecting cost of production. They do not give the entire cost situation, though, for only variable costs are included in marginal costs. That production costs are important in determining the location of production can be illustrated by the procuction of process‘milk in Michigan and Kentucky for distribution in New York and New Orleans. Milk is produced this distance from market only because it can be pro- duced and put on the New York and New Orleans markets at a lower aver- age cost per unit than production areas closer to the markets can. This may be because of the low opportunity costs for the production re- sources rather than a specific efficiency of production. Nevertheless, the milk has to be put on the market at a lower cost than competing areas can in order for these distant areas to stay in production. The milk producers in the Detroit milk shed probably will not have to deal with other areas putting fluid milk on the Detroit market cheaper than they can. Their problem will be to deal with processed milk producers in neighboring states who can put processed milk on the distant markets, such as New York and New Orleans, at a lower cost than the Michigan producer can. Once these distant markets are gone for the local producers their only alternative is to sell their milk on the Detroit market - unless they go into alternative production opportunities. 9h To the extent that this excess milk is put on the Detroit market with an unchanged demand pattern, the blend price will be lowered, reducing the income of the producers already in the market. This pressure to lower prices in the Detroit market is partly counter-balanced by an increasing demand in the Detroit area for fluid milk. Tnis market is growing, and as a result, attracting processed milk producers in the shed.to change over'to fluid milk production. Processed milk and fluid.milk are produced under different cost structures. Fluid milk costs more per hundred.weight to produce than processed milk. It is produced in the near proximity of large markets because of its bulky nature and the high cost of transporting it from the farm to the city. Neighboring areas, even though they may be able to produce the milk cheaper, cannot compete on the Detroit market for fluid milk because of the high transportation costs. In the production of process milk, tranSportation costs are considerably reduced because the milk is p‘ocessed close to the farm and.a less bulky product is shipped to the market. It is in this area that local producers are likely to meet the most competition, directly and indirectly, particularly with respect to distant markets such as New York and New Orleans. In order accurately to estimate the competitive position of the farmers in this area, supply curves for other areas must be compared with the one from this area. However, partial information about the relative position of producers in an.area can be estimated from its supply curve alone. 95 With the cost structure and input prices as they existed during the 1952 fiscal year, producers in the Detroit milk shed could compete profitably with other areas down to a cost of production of two dollars and forty cents per hundred weight. For instance, if producers in Kentucky could put fluid milk on the Detroit market at a cost of three dollars when Detroit producers were getting three dollars and fifty cents, the producers in the local area could continue operation by cutting back production so as to reduce their marginal costs. They would then be able to meet the Kentucky competition. If other areas could put the milk on the Detroit market at a lower cost than two dollars and forty cents per hundred weight, some of the producers in the Detroit milk shed would no longer be able to compete, even in the short run, with the quality of cows, input prices, and cost structure existing in 1952. They would have to either cease production or reorganize their operation with respect to quality of cows. A discussion of the needed adjustments will be presented in the next section. It should be pointed out that the ability of farmers in the Michi- gan area to compete with neighboring areas, particularly to the south, hinges on the low opportunity costs for the fixed assets in the area. Dairy farming requires an abundance of forage production. Climatic and soil conditions in Michigan are such that over much of the state forage prodmtion is the only alternative. This becomes a fixed asset for the farm due to the low opportunity cost, and the only way the far- mer can profitably utilize it is to produce milk or beef. At the present 96 time dairy seems to have a comparative advantage over beef herds due to the extensive type of operation required with beef. Most farms are small and beef herds would not supply a large enough source of income. The farmer's flexibility is decreased even more after he has com- :mitted himself in longer lengths of run to such things as specialized dairy barns and.equipment. These factors, combined with the distance of industry, combine to lower the opportunity cost of labor, too. It 'becomes a fixed asset, then, and.milk production is the only way of utilizing it. Opportunities for alternative uses of the resources may arise in the future, and if milk can be put on the Detroit market at a lower cost from neighboring areas, research.may be required.to develop these alternatives or to raise the earning power of the resources in their present use. For the present, though, milk is produced in the Michigan area not so much because it has a comparative advantage, but because by producing milk the resources are utilized so as to minimize their comp parative disadvantage. The Micro Analysis The contribution that this study makes to farm management inn volves the marginal cost of producing milk by the firm and how it is affected by the Quality of the cow. Tnis section presents a discussion of the alternatives open to the individual producer if it is desired to lower the marginal costs of production. 97 The nature of the individual marginal cost curves indicate that one way of lowering costs is to snift to higher quality cows. With fine given cost structure, the marginal cost of producing milk can be re- duced.to one dollar and ninety-two cents per hundred weight by producing milk with cows that average 10,120 pounds of four percent fat corrected milk when fed one pound of grain to four pounds of milk. The data also indicates that so long as the producer has to cover only variable costs, size of herd does not greatly affect the ability of farmers to withstand competition from other areas. Wells3 found similar results in his cost study at Kentucky, but by computing costs for longer lengths of run, he found that when the planning qaan was long enough to require the covering of average total costs, the small herds became vulnerable first. The explanation seems to be that for the length of run in which only feed is variable, the associated variable cost of labor makes up such a small part of the total variable costs that it has no effect on the marginal cost of production. In longer lengths of run in which the entire saving in labor per cow can be considered as herd size is vari- able, it does give the larger producer a competitive advantage. Logically, it would seem that as neighboring areas were able to put milk on the Detroit market at a lower cost, the producers with the low Qiality of cow would be squeezed out of production first. How- ever, due to the nature of the cost curves for the lowest giality 3 92. £23., wells, p. 52. 98 of cow considered, producers with this kind of cows have two alter- natives. So long as their marginal value productivity does not become less than salvage value, they can cut back production and produce at a lower marginal cost. When doing this, the aforementioned work of Gaul indicates they no longer cover fixed costs, but in the short run they need only cover variable costs so long as the capitalized.value of the marginal value productivity of the cow'plus her discounted salvage value is greater than her present salvage value. As a second alternative, it may be that the marginal value productivity of the cow would become less than her salvage value when production is cut back. If this happens, the longer length of run in which herd size is variable is entered into and the producer sells the cow to stop his losses on her. However, he may be able to resume pro- fitable production of milk by replacing the low quality cows with high quality cowBo In considering cost-price squeezes, it is not known exactly at what price the producers with the lowest Qiality of cow would be unable to compete, for this price depends to a considerable extent on the disposal,value of the cow. However, logically it would seem that these pmodueers will be the first to either drop out of milk production en- tirely or replace their low quality cows with higher quality cows. For the individual producer, converting to higher quality cows is often impossible due to lack of resources. In this case they will 99 shift to alternate income opportunities or else begin to mark down the income of some of their other assets. Caul's work indicates pro- ducers with 7,332 pound cows could produce profitably in the short run at 1952 costs, as long as the price for milk is above two dollars and thirty cents per hundred weight. If the price drops below this, they logically dispose of their cows and go into alternative income opportun- ities or else replace their cows with higher quality cows. If these producers are unable to replace their cows with higher quality cows and have no alternative production opportunities, they, too, may write down the income to their fixed factors and continue to produce. In this case, they would.follow the scale line to get lower marginal costs than com- puted for this study by reducing the feeding level to less than stomach capacity. No indication of their production response or costs at these levels of the stomach limit line is given in this study because ade- Quate experimental data are unavailable. Within the limits of this study, the next lowest marginal cost of production can be secured by going to the cow with an inherent pro- duction ability of 8,350 pounds of four percent fat-corrected milk. \\\ ' The costs for this quality of cow were computed on the basis of a pen type barn, but since labor appears to be insignificantib‘at the minimum points on the marginal cost curves, the quality of the cow is the de- ciding factor in lowering the marginal costs of producing the milk. \ The data indicate that under the given conditions, producers with ”this Quality of cow could.reduce marginal costs to a minimum of one dollar and ninety-eight cents per hundred weight by reducing the level of 100 grain feeding and could continue to produce in the short run as long as price was above this level. If competition drives price down lower yet, the producer has the same alternatives he had with the lower quality cows. By shifting to cows of a still higher production ability of 10,120 pounds of four per- cent fat-corredted.milk, the marginal costs can be reduced to a minimum of one dollar and ninetybtwo cents per hundred weight. If he is unable to shift to cows of this higher quality, he too can lower the return to his fixed factors and feed at less than the stomach limit with the lower quality cows. If the milk can be put on the Detroit market for a lower mar- ginal cost than this, it will no longer be profitable for milk to be produced in the Detroit milk shed under the given cost conditions. New technology will have to lower the cost of production if continued production is desirable or the producers will have to write down the income to their fixed factors. In the meantime, other saurces of in- come may have become more profitable. Suggestions for.Additiona1 Research Problems encountered in the course of this study have pointed up the need for additional research in several areas. A discussion of these proposals follows. Igpgtfggtpgt studies. The inability to compute the costs with inputs combined as dictated by the scale line below certain minimum levels pointed up the need for this kind of research. Studies are needed.to lOl delineate isoproduct lines with grain and roughage as variable inputs for several qualities of cows. Then when the scale line no longer fol- lows the stomach limit line, the optimum combinations can be estimated by price relationships. The need for research of this nature has also been pointed out in a report prepared by the North Central Farm Manage- ment Research Committee.b Cost computations for other lengths 2?. 5112. Studies are needed to determine the various costs when herd size is variable and when barn size is variable. Combining these studies with the present one would permit the compilation of a general treatise on the economics of milk production in Michigan. Studies of this nature may indicate ways of increasing the earning power of assets that are fixed on many farms in the area. (At the present time Ed Jones, here at Michigan State College, is studying the entry and exit of firms from the market.) Adjustments _tg risk and uncertaint . A knowledge of the way farmers react to changing conditions will enable more accurate pre- dictions to be made for outlook purposes. This study shows that even in short lengths of run the farmer has considerable flexibility in adjusting his output to changing conditions. The extent to which far- mers base their present operations on future expectations will de- termine whether production will be above or below the predicted amount. 1* Feed—Milk Relationships 3.3 Dairyin , a report prepared by the bbrth Central- Farm Management Research Committee, January, 19514. 102 (Albert Halter and Glenn Johnson, here at Michigan State College, are currently working in cooperation with the North Central Farm Management Research Committee on a study to cbtermine how farmers react in the face of risks and uncertainty.) How 93 producers enter and leave the market. Difficulty was en- countered in predicting future production when there was a sudden change in the number of cows in the area. A study is needed to determine the extent to which the average production per cow is raised by the cul- ling effect of reducing the cow population. The answer lies partly in the data presented herein, and partly in determining at what level it is no longer profitable to keep a cow. The material in this thesis is inadequate to accurately estimate the change, but it does indicate that the low producers are the first to be culled. (It was pointed out pre- viously that a study is currently under way to find a partial solution to this problem.) Converting the curve ta if}. aggregate index. If the individual cost items could be converted to indexes, and an aggregate index based on these individual indices could be developed, the outlook work could be greatly expedited, and possibly made more accurate by including the changes in all cost items. areas 3 The 1. 2. 3. h. 5. 103 Uses of the Data Synthesized in this Thesis data synthesized in this study have use in five broad The input-output relationships are useful in cost studies of practically any nature. Improving the effectiveness of production.controls. Improving the effectiveness of milk marketing orders. Estimating the position of local producers with respect to interregional competition. Studies such as Caul's in which he is estimating the value of various quality cows under changing conditions. ELAPTER V I SUI-MARY AND CO NCLUS IO [\5 The purpose of this study was to estimate a supply curve for fluid milk in the Detroit milk shed for the length of run in which only feed and its associated inputs are variable. This was accomplished by synthesizing the short run' marginal cost curves for typical firms in the industry and aggregating these curves into an aggregate short run supply curve. A mail survey was taken of the producers in the milk shed to determine the conditions under which fluid milk was produced with res- PGCt to herd size, average production per cow, and type of barn. The results of this survey were classified so as to have ten typical herds representing production conditions in the area. A marginal cost curve was computed for each of these ten herds by using a budget process and utilizing various sources of secondary data, In the short run, milk production for the farm is varied by Changing the level of feeding, which involves the substitution of grain for roughage. The basic input-output relationship for constructing the marginal cost curves considers grain and roughage as inputs and milk as a Product. Certain other inputs such as salt, minor equipment, various Portions of labor, and electricity, are varied with the level of feeding and must be considered also. The relevant relationship involved not °nly feed, then, but feed and its associated variable inputs. 105 On the assumption that the cows were fed all the hay they were able to eat, six alternative levels of grain feeding were postulated. These ranged from a ration containing no grain to one in which fifty percent of the total digestible nutrients were derived from grain. For each of these levels the physical quantities of the various inputs and also the amount of milk produced were determined. These quantities were multiplied by their respective prices and the results summed in order to determine the variable cost of producing milk in this short length of run. Frcm this information the marginal cost of procucing an addi- tional hundred pounds of milk was determined by dividing the change in variable costs from one level of feeding to the next by the change in milk production. The Imrginal cost so determined was an average mar- ginal cost over the range from one feeding level to the next higher level. when these costs are plotted and a smoth curve fitted to them, the curve does give an estimate of the marginal cost of each unit of output. From the marginal cost curve for each of the typical herds, the Qua ntity of milk each producer would supply at prices ranging from two dollars and forty cents per hundred to six dollars per hundred was de- termined. The Quantity at each price was multiplied by the number of PTOCiucers represented by that typical herd. This was done for each of the typical herds and the resulting production at each price was summed to get the aggregate supply response for all of the producers in the Detro it shed. 106 The shape of this supply curve has important policy implications, but its value could be increased immeasurably if the curve could be used to predict milk production from one year to the next. A change in input prices, a change in the number of milk cows, and a change in the average production per cow are the three most important variables causing the curve to become out of date. Adjusting the curve from year to year to allow for changes in these variables makes the supply curve quite usable for predicting year to year changes in milk production. A consideration of both the individual marginal cost curves and the aggregate supply curve leads to the following general conclusions: 1. In the length of run in which only feed and associated inputs are variable, the production of fluid milk can be varied from 1,000 million pounds to 1,500 million pounds in response to price changes from two dollars and forty cents per hundred to six dollars per hundred. 2. Production controls based on restricting the herd size of the individual producer will be only partially effective in controlling the production of fluid milk. 3. The production of fluid milk can be regulated by adjusting the price of milk and the cost of the inputs used in producing it. h. From a farm management standpoint, the marginal cost of producing milk can be significantly lowered by keeping high quality cows. 5. Producers in the Detroit milk shed can cut back on the level of feeding and reduce marginal costs in.the face of a cost-price squeeze so long as the discounted capitalized value of the marginal value pro- ductivity stream of the cow in milk production plus the discounted 107 salvage value of the cow when discarded in the future does not become less than her present salvage value. 6. Producers do operate in a rational manner and adjust their {reduction in response to price relationships. This is indicated by the ability to. accurately predict the production of milk from the supply curve. 7. From a methodological aspect, the study shows that tradi- tional economic theory can be combined with results of primary experi- mental work and modifications of +he theory to s olve practical problems. l. 2. 3. h. 5. 7. 8. 9. 10. 108 B IBLIOGRAPHY Annual Report and Proceeding, Michigan Milk Producers? Association, Thirty-Sixty Annual Meeting, November 6, 1952. Boulding, K. E. , Economic Analysis, Harper and Brothers, New York, New York, 19113. Bradford, 1.. A., and Johnson, G. L., Farm Management Analysig, John Wiley and Sons, Inc., New York, 19%. Bronfenbrenner, 11., "Production Functions, Cobb Doubles, Inter- firm,‘I Econometrics, Volume 12, January, 19bit. Brown, 1.. R., "A Comparative Analysis of Stanchion and Milking Parlor Barns,“ Work Simplification News Letty-J Purdue Work Simplification Laboratory, Issue No. 19, (Lafayette, Indiana: Agricultural Hall Annex), July 191:8. Brown, L. R., Cargill, B. F., and Bookout, B. R., Pen-t Dai Barns Michigan Agricultural Experiment Station Specie Bulletin 533, 1950. \ Gaul, Denio, A tentative Master's thesis on estimating the value of various quality of cows. Ezekiel, E., Rauchenstein, E., and Wells, 0. V., Farmers' Res nee Pg Price in the Production 93 Market Milk, (Processedi, Unité States Department of Agriculture, Bureau of Agricultural Economics, (Washington, 1932). Farm Business Analysis Repgrt £35 Area 2, Agricultural Experiment Station, Michigan State College, 1935. Feed-Milk Relationships 39. 2m, 8. report prepared by the Nah-Central Farm Management Research Committee, January. 1951:. Graves, R. R., Bateman, George Q., Shepherd, J. B. , and Caine, George 3., Milk and Butterfat Production Lay Dairy Cows on Four Different Plan' 'e's 3g Feeding, United States Department o?‘Agr1"c'u1- t'ure, Technical Bulletin 72h, 19m. Headley, F. B., The Economics 53f Feeding Alfalfg Iggy and Grain _tg _Hglstein Cows, Nevada Agricultural Experiment Station Bulls-tin 110, 1935. 17. 18. 19. 20. 21. 22. 23. 2h. 25. 26. 109 Henderson, H. G. , Larson, Carl W., and Pudney, Fred 3., Daig Cattle Feeding and Management John Wiley and Sons, Inc. , New York, 19W. . Hoglund, C. R., and Wright, K. T., Reducigg Dairy Costs gnMidligan Farms Michigan Agricultural Experiment Station, East Lansing, Michigan, and United States Department of Agriculture, Washington, D. C., 1952. Jensen, E. , et. al., In ut-Output Relationships in Milk Production, Technical Bulletin 81, United States Department— of Agriculture, Washington, D. 0., 19M. Knight, F. H. , R_isk, Uncertainty, and Profit, Houghton Mifflin and Comparw, Boston and New York, 1921. Lowry, B. H. , "Labor, Equipment and Building Costs in Dairy Farming with Special Reference to Work Methods" (Unpublished Master‘s Thesis, Department of Farm Economics, University of Kentucky, 19149). Michigan Agricultural Statistics, May, 1953. Mighell, R. L., and Black, J. D. , Interregional Competition in Aggi culture, Harvard University Press, Cambridge, Massachusetts, 1951. Milk Production in Farms, Bureau of Agricultural Economics, United States Department of Agriculture, 1953. Morrison, F. B., Feeds and Feeding, The Morrison Publishing Company, Ithaca, New York, 19148. Morrison, F. 3., Feeds and Feeding, The Morrison Publishing Compamr, Ithaca, New York,19500 Mosely, T. 11., Stuart, Duncan, and Groves, R. R., De Work at the Huntly, Montana, Field Station Huntly, Montana 8'“??? United States Department of Agriculture Technical BulIE'tE'IIETi929. Rations Fed 22 Dairy Cow_s, United States Department of Agriculture, Bureau of Agricultural Economics, Washington, D. C. Badman, J. 0., "Economic Aspects of Feeding for Milk Production," Journal 9}; Farm Economics, Volume XXXIV, August, 1952. Hadrian, J. 0., "Economic Consideration of Grain Roughage Substi- tution in Feeding for Milk Production," unpublished Ph.D. thesis University of Kentucky, 1951. _ . 27. 28. 29. 30. 31. 32. 33- 3h. 35. 36. 37. 110 Rider, M. W., "An Alternative Interpretation of the Cobb- Douglas Function," Econometric_a, Volume 12, July-October, 191:3. Sherwood, D. H. , and Dean, H. K. , Feeding Alfalfa Hay Alone §_._n_d_ With Concentrates to Dai Cows, Oregon Agricultural Experiment Station Bulletin 386,‘ T9510. Stigler, G. J. , The Theory 9_f_ Price, The MacMillan Company, New York, New York, I930. The Journal of Political Economy," The University of Chicago Press, Chicago, Illinois. Unpublished data, Agricultural Experiment Station, Michigan State College, 1952. Vary, K. A., Rates for Custom Work £9. Michigan, 1952 and 1953, Extension Folder F-ITEI, Michigan State College COOperative Exten- sion Service. Wagley, R. V., "Marginal Productivities of Investments and Ex- penditures, Selected Ingham County Farms, 1952," unpublished Master's Thesis, Departmsnt of Agricultural Economics, Michigan State College, 1953. Weintraub, S. , Price Theory, Pitman Publishing Corporation, New York, New York, 19149. Wells, J. A., ”A Technique for Synthesizing Cost of Production Data - With Special Reference to Dairy Enterprises in Green and Taylor Counties of Kentucky," (unpublished Master's thesis, De- partment of Farm Economics, University of Kentucky, 1951.) Wilkes, P., unpublished computations, Michigan State College, 1953. Wold, H., and Jureen, L., Demand Analysis, John Wiley and Sons, Inc., New York, New York, 1953. .. . APPENDIX A 112 MICHIGAN STATE COLLEGE East Lansing Epartment of Agricultural Economics Dear Producer: In connection with a research project at the Michigan Agricultural Experiment Station, it is very important that we have some simple information about your dairy operation. This infomation will be used to help determine the potential supply of milk from the Detroit milk shed. Enclosed is a self-addressed, stamped card on which you can conveniently check the information requested. Your cooperation will be appreciated and will contribute to the productivity of your experiment station. Sincerely, George E. Schuh Graduate Assistant Michigan State College (ES/tn 113 During the period Oct. 1, 1951 to Sept. 30, 1952. Did you have a pen-type barn or a stanchion-type barn What was the average number of cows you were milking during this period? If it is convenient for you, we would like to know the total pounds of milk produced on your farm between Oct. 1, 1951 and Sept. 30, 1952 k lbs. If this information is not available, send the card back with the other information requested. It in itself is quite valuable. MICHIGAN STATE common 11h East Lansing Lrtment of Agricultural Economics July 23, 1953 Dear Producer: Several weeks ago you received a letter requesting some information that would contribute to the work of your experiment station. Some of the replies have'been slow in coming in. In case you have lost or miSplaced the reply card, we are enclosing another card. If you have not mailed in your reply, we would greatly appreciate your doing so, new. Appreciatively yours, George E. Schuh GES/ tn Enc. 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Feeding level Avergge Production Capacity of Con (percent TDN 31.33 7332 3350 10,120 from roughage) pounds2 pounds2 pounds2 pounds2 _+ -— Pounds — _ 100 26.6 30.3 31.3 33.h 90 28.1 31.6 32.6 BM} 80 30.3 33.8 3ho9 37.1 70 32.3 35.8 37.2 39.9 60 33.9 37.h 39.1 h2.7 50 3M; 38.2 140.2 16.2 1'Theso amounts are'based.on.a requirement of .75 ounce of salt daily per 1000 pound live weight, plus .3 ounce in addition for each 10 pounds of milk produced. Morrison.Publishing Company, Ithaca, New York, 19 0. Morrison, F. 8., Feeds and Feeding, The 2 ‘Ihose quantities are the production per cow when fed at the rate of one pound of grain to four pounds of milk. 125 .omdnwaoh son.“ 3529:: 39.33»? 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HH>N 0339 138 TABLE XIX FERTILIZER ELEMENTS REACHING FIELIB FROM MANURE, VARIOUS QUALITY COWS, DETROIT MILK SHED, OCTOBER 1, 1951 - SEPTEMBER 30, 1952. apacity and Feeding Level jPercent TDN from roughaLe) Nutrient 4+ 100 90 80 70 60 5c? — Pounds __ 1 5,133 N 31.76 33.71 12.21. 5h.25 66.18 70.80 P 5.111 5.117 6.87 8.81. 10.80 11.57 53.56 16.97 h9.23 53.80 5h.80 hh.9h 7,332 hh.28 50.38 61.02 73.09 86.h9 9h.23 P 7.17 8.17 9.92 11.90 111.10 15.38 K 7h.68 73.11 76.58 78.8h 79.5h 70.21 8,350 ,- u 117. 85 52.68 63.32 77. 81 96.53 ‘ 111.10 P 6.78 7.h8 9.00 11.08 13.77 15.92 x 70.61 66.hh 68.3h 72.25 77.03 73.59 10,120 R 117.77 51.27 59.99 72.37 90.112 112.65 7.73 8.31 9.75 11.78 111.71; 18.38 80.57 7h.53 75.05 78.02 ‘ 88.20 90.01 SOURCE: Synthesized frqn secondary daEaEased on the composition of feeds and the percentage reaching the fields as indicated by Morrison, F. 3., Feeds and Feeding, The Morrison Publishing Company, Ithaca, New York, 1956. *hnount of 11 percent. fat-corrected milk produced when fed one pound of grain to four pounds of milk. _: E TABLE XI PRICES USED IN THIS THESIS 139 Itan Unit Price Shelled corn3 70 pounds 31.69 Corn and cob2 70 pounds 1.62 Outs2 32 pounds .83 Soybeanoilmeal1 100 pounds 5.58 Grain.rationh 100 pounds 3.0h Milk canal 10 gallon can 10.62 Stock saltl 100 pounds 1.h2 Hays 100 pounds 1.06 Nitrogenl pound .13 Phosphorous1 pound .09 Potassium1 pound .06 Shelling cox-66 bushel .07 Crushing corn6 bag .10 Electricity1 killowatt hour .028 Labor7 hour .50 lho 1 For these inputs uith.little or no seasonal variation in price or use, the average of the average quarterly price as secured from the Michigan Agricultu'al Statistician's Office is used. 2 'me average monthly price is weighted according to estimated use in the dairy enterprise; a nine percent weighting for October through April, and a 7.11 percent weighting for May through September. 3 A seven cent charge per bushel is added to the cost of a bushel of corn and cob meal to cover shelling charges. 1‘ Based on a grain ration made up of 110 percent corn and cob meal, 20 percent shelled corn, 20 percent oats, and 20 percent soybean oil meal. 5 Hay consists of 30 percent alfalfa, 20 percent red clover, 37.5 per- cent brome, and 12.5 percent timothy. The average monthly prices for hay were weighted at 15 percent for November through March and 12.5 percent for October and April. 6 Based on usual custom charges in Michigan; Vary, K.A., "Rates for Custom Work in Hichigan, 1952 andl953," Extension Folder F—161, M.S.C. 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