PRICING FAT and SKIM COMPONE HfORNIA AGRICULTURAL [PERIMENT STATION D airy scientists have known for some time that a general relationship exists between the amount of fat and nonfat solids in milk. Until re- cently, in evaluating whole milk, emphasis has been placed largely on the fat content. Since the early years of World War II, however, the nonfat constituent has become increasingly important. This shift in emphasis has complicated the problem of establishing equitable pro- ducer prices for whole milk of varying fat and nonfat solids content. A pricing system that would treat all producers equitably, regard- less of fat content of the raw milk sold to processors, is suggested in this bulletin. Such a system must "price" both fat and skim compo- nents as nearly as possible on their real values. A series of equations is presented herein which may be used as a guide to establishing these values. Under a pricing plan of this type, a producer would not be penalized for milk of specified fat content, nor would he feel forced to augment purebred stock with other breeds in order to raise the average fat content output of his herd. In addition, inequities exist under classified pricing of market milk where accounting for utilization is based solely on the fat constituent. This bulletin further suggests methods of establishing separate prices for fat and skim which, if adopted, would serve to correct these inequities. THE AUTHORS: D. A. Clarke, Jr., is Assistant Professor of Agricultural Economics, Assistant Agricul- tural Economist in the Experiment Station and on the Giannini Foundation, Berkeley. J. B. Hassler is Lecturer in Agricultural Economics, Assistant Agricultural Economist in the Experiment Station and on the Giannini Foundation, Berkeley. AUGUST, 1953 PRICING FAT and SKIM COMPONENTS of MILK D. A. CLARKE, Jr. J. B. HASSLER VARIATIONS IN MILK COMPOSITION The problems of establishing producer prices for milk are made more complex by variations in its physical and chemi- cal composition. Milk sold by producers commonly varies in content from about 3 per cent milk fat to nearly 6 per cent. Furthermore, the nonfat solids content of "normal" milk may range from a little under 8V2 to almost 10 per cent. Since the values of all components enter into the value — or price — of whole milk, va- riations in constituents must be con- sidered in determining a pricing sched- ule if it is to be fair and equitable to all concerned. 1 This bulletin presents the results of work which was undertaken by the University of Cali- fornia in response to Senate Resolution No. 74 of the 1947 California Legislative Session. The determination of the physical relationship be- tween fat and nonfat solids was carried on by the Department of Dairy Industry under the supervision of Professor E. L. Jack. The pricing problems were undertaken by the Department of Agricultural Economics. Statements concern- ing the bearing of this problem on pricing poli- cies have previously been made by members of the latter department at public milk hearings. The present authors wish to acknowledge the contributions of Professors R. G. Bressler and J. M. Tinley. It has long been recognized that a given amount of milk has a greater value when it contains a large rather than small amount of milk fat. Because of this, the pricing systems in effect in most markets in the United States include a "butterfat differential." 2 As most milk is sold by weight, this differential provides for a higher price per hundredweight for milk of high fat content than for the same amount of milk with a lower fat content. More recently — particularly since the early years of World War II — increased emphasis has been placed on the relative importance of the nonfat constituent of milk. This is true in both the manufac- turing and the market milk industries. In the former, it is reflected in the in- creased importance of whole milk and 2 The butterfat differential is usually defined as the amount to be added or subtracted from the base price per hundredweight for each 1/10 of 1 per cent above or below the basic fat con- tent — which in California is 3.8 per cent. In markets where a "direct ratio" price system — payment is made solely on the amount of fat content — is used (such as in California for Grade A milk, prior to 1948) , the butterfat dif- ferential would be 1/10 the price of a pound of milk fat. [3] skim milk products relative to that of butter. On the market — or fluid milk — side, the same type of change can be noted. The average fat content of fluid milk has been decreased, sales of "heavy" cream have given way to lower fat items — especially "half-and-half"' — and ice cream sales have not kept up with increases in the sales of ice milk. Pricing milk on the basis of fat test has been made possible largely through the use of the Babcock Test. Developed in 1890, this test provides a reasonably accurate, simple, and inexpensive means by which the percentage of milk fat in a given sample of milk can be determined. On the other hand, there is at present no practically adaptable test by which the nonfat solids content of each individual shipment can be measured. 4 Accurate and reliable methods of determination of nonfat solids do exist, but they are ex- pensive and time consuming. Dairy chemists have long been aware of a general relationship between the amount of fat and nonfat solids in milk. Milk with a relatively high fat content also contains relatively large amounts of nonfat solids. Furthermore, on the basis of the results of a large number of sam- ple cases, a reasonably reliable average 3 The term used by the industry for a product which is half table cream and half milk, with a resulting milk fat content of approximately 12 per cent. 4 The lactometer — which has often been used to measure the nonfat solids content of milk — ■ has not been considered sufficiently accurate for this purpose. This technique is based on dif- ferences in the specific gravity of milk with high and low solids content. These nonfat solids, however, are not homogeneous, but include all of the elements of milk other than fat and water — such as casein, albumen, sugar, and ash. Changes in the proportions of these nonfat solids elements influence the specific gravity, and so influence the accuracy of the tests. This method has not been officially accepted by the Association of Official Agricultural Chemists. At the time of writing, it has been announced that the University of Maryland and the United States Department of Agriculture are cooperat- ing on a project to develop more accurate lac- tometer tests. relation can be determined. This average relationship can then be used to estimate the nonfat solids in milk of any specified fat content. Perhaps the best known study of this fat-nonfat solids relationship has been Jacobson's analysis of 150,000 samples of milk produced in New England. 5 This indicated that a 1 per cent difference in fat content was, on the average, associ- ated with a difference in the same direc- tion of 4 / 10 of 1 per cent in the amount of nonfat solids. Milk with a fat test of 4 per cent contained, on the average, 8.67 per cent nonfat solids, while milk with 5 per cent fat would have 9.07 per cent of these associated serum solids. Due to the importance of the problem of pricing the nonfat milk components, the Dairy Industry Department of the College of Agriculture, University of California, has recently completed a study of the composition of milk pro- duced under California conditions. 6 In all, nearly 21,000 samples of milk were analyzed during a two-year period. These samples were taken every two weeks from shipments received at processing plants from representative shippers of both manufacturing and market grade milk. For the purpose of obtaining the samples and analyzing the results, the state was divided into 10 separate areas. These areas, in turn, were selected to provide reasonable uniformity in types of feed- ing and management practices and in predominant breeds of cattle. On the basis of the samples so collected, the authors determined — by mathemati- 5 This is the so-called "Jacobson relation" which, in mathematical terms, can be expressed as: SNF = 7.07 + 0.40F, where SNF is the percent- age of nonfat solids and F, the percentage of fat content. ( Reported in Journal of Dairy Sci- ence, XIX, 1936, 171-76.) 6 For a more complete report of the results of this study, see "Relationship of Solids-not-fat to Fat in California Milk," by E. L. Jack, E. B. Roessler, F. H. Abbott, and A. W. Irwin. Calif. Agr. Exp. Sta. Bui. 726, 1951. [4] cal means — a linear, weighted, composite relationship that differs slightly from Jacobson's results. In equation form, this is: MFS=7.07 + 0.444F where NFS represents the amount of non- fat solids, and F the amount of milk fat present in a hundredweight of milk. This same relationship is shown graphically in Figure 1. From this relationship it can be seen that milk of 3.8 per cent fat content contains, on the average, 8.75 pounds of nonfat solids per hundredweight. For each change of % per cent in fat con- tent, the nonfat solids change (in the same direction) by 0.0444 per cent. Therefore, on the average, milk with 3.9 per cent fat will contain 8.80 per cent nonfat solids, while that with 3.7 per cent fat will con- tain only 8.71 per cent nonfat solids. This relationship is considered applicable through all ranges of fat test analyzed, that is, from 3 per cent to 6 per cent. Figure 2 presents this same relation- ship, and provides a comparison with other procedures commonly used in milk payment plans. These include the previ- ously mentioned "Jacobson relation" and a representation of a "direct ratio" be- tween fat and nonfat solids. The latter case depicts a situation in which the non- fat solids increase in a direct and constant proportion with increases in fat, and where the ratio of fat to nonfat solids is arbitrarily determined at the level indi- cated by the California relation for milk 7 As an indication of the reliability of this relationship, the authors have further deter- mined that, on the basis of chance alone, they would expect an error between estimated (based on this mathematical equation) and actual (based on individual laboratory determination) nonfat solids content that would be greater than 0.71 per cent only once in 20 tests. If, for ex- ample, a series of tests were to be made of groups of 20 samples, it would be expected that, on the average, only one sample in each 20 would result in a difference between esti- mated and actual nonfat solids of as much as 0.71 per cent in either direction. Furthermore, if weekly composite samples were used, only one in 20 tests would have an error of greater than 0.29 per cent. of 3.8 per cent fat content. For milk of this test, there are 2.3 pounds of nonfat solids per pound of milk fat. Also shown in Figure 2 are points which represent averages of fat and non- fat solids content for groups of samples of milk produced by herds classified accord- ing to predominant breeds. 8 As can be seen from the "scatter" of these points, the use of the linear function represented by the line labeled "California relation" is at best an approximation for determining nonfat solids on the basis of fat content. 9 It can be noted that Holstein milk of 4.2 per cent fat content (a high test for the breed) averaged slightly less than 8.8 per cent nonfat solids, while Jersey milk of the same fat test (a relatively low test for this breed) averaged more than 9.2 per cent nonfat solids. Furthermore, minor inconsistencies exist between these ob- served averages within breeds due to sampling variability. For example, Jersey milk samples of 4.8, 4.9, and 5.0 per cent average fat content all contained the same amount of nonfat solids, while milk from the same breed of cows, that averaged 4.7 per cent fat, contained approximately one-half per cent less nonfat solids. In spite of the variation apparent in Figure 2, two points can be made to just- ify the adoption of the California rela- tionship for pricing purposes under cur- rent conditions. These are: 1. The greatest departure of the actual averages from the estimating relation occurs at the high and low limits of fat content for the particular breed under consideration. For example, the error 8 These group averages were determined by Professor Jack and his associates, and made available to the present writers for this purpose. These data do not appear in Bulletin 726, from which all other information relative to the com- position of milk produced under California conditions has been drawn. 9 The statistical measure of the reliability of this relation and estimates of the magnitude of error resulting from the use of this relation as an estimating equation have been presented in footnote 7. [5] FIGURE 1. RELATIONSHIP OF SOLIDS-NOT-FAT TO FAT IN CALIFORNIA MILK* 9.8 9.6 9.2 £ 8.8 8.4 8.0 - 1 I » 1 - - S NF = 7.07 + 0.444 F _ ; _ — - - k I 1 | 3.0 4.0 Per cent fat content 5.0 6.0 Source: California Agricultural Experiment Station Bulletin 726. [6] FIGURE 2. RELATIONSHIP BETWEEN THE FAT AND NONFAT SOLIDS CONTENT OF CALIFORNIA MILK 4.0 5.0 Per cent milkfat content [7] of the greatest magnitude occurs for Jersey milk of approximately 4.0 per cent fat content. By far the bulk of Jersey milk produced has a much higher fat content — near the average test for the breed — which is more than 5 per cent. For any particular breed, the linear relation provides a very close approximation to the normal average fat test for that breed. Futhermore, over a period of time, the average fat test for a herd of a given breed will shift around the normal average fat test for that breed, so that compensat- ing errors will tend to balance. 2. The California relation was mathe- matically determined to be the "best fitting" straight line describing the average relationship between fat and nonfat solids in milk produced under California conditions. 10 As can be seen from Figure 2, it provides a better representation than does the Jacobson relation which consistently results in a lower estimate of nonfat solids for any level of fat content. In addition, the California relation is a substantially better basis for pricing than is the direct ratio procedure which overpays for milk of higher than the average fat content while underpaying for the By the method of "least squared residuals. below-average tests of milk in relation to the available evidence concerning nonfat solids content. In view of the above and of the afore- mentioned difficulties of direct determi- nation, it appears that the California rela- tion provides the best available informa- tion for use in estimating nonfat solids content of milk, and it will therefore be used in the development of pricing plans discussed herein. It should be empha- sized, however, that when new methods of determination become available, either in the form of new and improved esti- mating procedures or in the form of tech- niques for direct measurement, these more accurate devices can, and should, be substituted in the pricing process. Figure 3 shows the different volumes of milk and the amounts of fat and non- fat solids which are associated with vari- ous types of milk per pound of milk fat. For every pound of fat in 3 per cent milk, there are 32.3 pounds of skim milk which contain an average of 2.8 pounds of non- fat solids. Correspondingly, a pound of fat in 4 per cent milk is associated with 24 pounds of skim milk and some 2.2 pounds of nonfat solids; 5 per cent milk has 19 pounds of skim milk and an average of 1.9 pounds of nonfat solids; while a pound of fat in 6 per cent milk has only 15.7 pounds of skim milk and about 1.6 pounds of nonfat solids per pound of fat. [8] FIGURE 3. CONSTITUENTS PER POUND OF MILKFAT OF MILK OF VARIOUS LEVELS OF FAT CONTENT 4.0 o -g 3.0 o QL Q- c 3 o 2.0 1.0 3.0 4.0 5.0 Per cent fat content 6.0 o 4.0 4.0 5.0 Per cent fat content Estimate of nonfat solids based on California relationship: NFS = 7.07 + 0.444 F PRICING BASED ON DIFFERENTIAL VALUES The major premise upon which this report is based is that a pricing system or schedule should be designed to reflect as nearly as possible the real values of milk of varying fat and nonfat solids content. To accomplish this, the pricing plan should "price" both the fat and skim milk components realistically — according to values of the constituents as set by the market. Under such an ideal system, where standardization is legal, it would make no difference, in raw product cost to a processor, whether milk of high or low fat content were received. If the incoming milk from producers contained too much fat relative to the skim compo- nents, the surplus fat could be sold — or conversely, additional skim milk could be purchased — at prices consistent with those paid for the different types of whole milk. 11 Furthermore, there would be no basis for discriminating against pro- ducers of milk with high or low fat con- tent. Nor would there be any economic pressures for breeders of purebred stock to add cows of different breeds and so influence the average fat content of the herd. Manufacturing Grade Milk Prices. — The solids content of milk has a direct influence on the yields of manu- factured dairy products and so on the problem of pricing milk used for this purpose. Where differences in product yields occur, the net return from the sale of products by the manufacturer is affected. For this reason, the processing plant can afford to pay producers a higher price for milk which yields relatively large amounts of products per hundred- weight than for that which has low pro- duct yields. 11 As will be discussed later, with any given price schedule for whole milk there is only one set of prices that will accomplish this consist- ency. They establish specific relationships among the price of whole milk, the separate prices of fat and skim milk, and the butterfat differential. Table 1 shows how the yields of pro- ducts from a butter-powder operation and from a condensery operation vary with different levels of solids content. For this purpose, the amounts of nonfat solids have been calculated according to the California relationship described in pre- vious sections. The physical yields of the different manufactured dairy products have been calculated on the basis of legal standards set for the fat and nonfat solids content of these final products. Adjust- ments have been made for such plant losses of solids as typically occur in rea- sonably efficient processing plants. The different types of by-products derived from the condensery operation — butter and powder — result from the standard- ization of milk going into evaporated milk. Whole milk of 3.9 per cent fat nor- mally contains fat and nonfat solids in about the ratio legally required for this product. Milk of lower test is standard- ized to the desired ratio by reducing the proportion of nonfat solids, that is, by separating out skim milk which, in this example, is then made into dried, nonfat solids milk powder. Milk of higher test contains an excess of fat relative to non- fat solids, and so in this case cream is removed and made into butter. 12 Because the solids content of milk en- ters so directly into the determination of product yields, the value of these dif- ferences in yields can be used to deter- mine pricing schedules. Given the yields and f.o.b. plant product prices, adjust- ment allowances for processing costs could be made, and the result would pro- vide the net value, or "paying ability" of milk of different fat tests, to the processing plant. These net values rise 12 It is also true that this standardization could take place through purchases of skim milk or cream from outside plants. With a competitive market for these components — that is, consistent market prices — the result would be equivalent to standardizing within the plant as indicated above. [10] Table 1. Calculated Yields of Manufactured Dairy Products per Hundred- weight of Milk of Varying Solids Content — Butter Powder and Condensery Operations* Fat content Nonfat solids content Butter powder Butter Powder Condensery Evaporated milk Powder Butter pounds per hundredweight of whole milk 3.0 8.40 3.57 8.49 36.98 1.59 3.5 8.62 4.18 8.71 43.30 0.66 4.0 8.85 4.80 8.93 47.94 0.18 4.5 9.07 5.41 9.15 48.22 0.80 5.0 9.29 6.03 9.38 48.50 1.42 5.5 9.51 6.64 9.60 48.79 2.04 6.0 9.73 7.26 9.82 49.07 2.66 * Hypothetical 3xamples of plant operations in which it is assumed that the use of milk in the former operation is solely for butter and nonfat dry milk solids and that in the latter operation, the principal product is evaporated milk with a by-product operation of butter or powder utilizing the residual resulting from stand- ardization. according to increased product yields associated with the higher levels of fat — and so nonfat solids — content. The amount of the value increase depends, of course, on the relative net prices of the specific products. Since there is no direct ratio between increases in product yield and increases in fat test (except in the butter part of the butter-powder opera- tion), these net values will reflect dif- ferences which are not in direct propor- tion to differences in fat content. This means, essentially, that a hundredweight of 6 per cent milk is not so valuable as 200 pounds of 3 per cent milk. Yet, with a direct ratio-to-fat pricing system — such as used by many manufacturing milk plants — the same amount of money is paid for these different quantities of low- and high-test milk. Plants which pay pro- ducers a fixed amount per pound of but- terfat, in other words, are penalizing low fat producers and overpaying high fat producers relative to the "net value" of the different types of milk received. Milk used for manufacturing purposes can be priced according to the net value of the products obtained, as indicated in the above section. Under such a pric- ing system, differences in prices received by producers will directly reflect the dif- ferences in the values of the products manufactured from these milks. 13 In this sense, producers of milk of differing com- position will be treated equitably with respect to the prices they receive. Unless these net values of milk of different fat and nonfat solids content are respectively equal in all economically alternative uses, however, there is no assurance that a single uniform payment schedule for a given area will be appropriate. 14 13 A similar argument relating to the deter- mination of butterfat differentials is presented in the University of Wisconsin Research Bul- letin 143, "Paying Producers for Fat and Solids- Not-Fat in Milk," by Rudolph K. Froker and Clifford M. Hardin, 1942. 14 With reference to the "consistency" of prices of the various manufactured dairy prod- ucts, it is of interest to note that a study of interproduct price relationships has recently been completed by the junior author. This study is currently in the process of publication under the title, "Pricing Efficiency in the Manufac- tured Dairy Products Industry." The conclu- sions indicate that, historically, the prices of [ii There are, of course, differential prices for milk at different levels of the mar- keting system. For example, the combined value of the fat and skim elements in cream and skim milk per hundredweight of whole milk is greater — by the cost of receiving and separating the milk — than the value, at the delivery platform, of the whole milk to be separated. Also, the value of milk at the receiving plant is higher — by the necessary transport cost — than the value of the same milk at the farm level. Because it is sometimes necessary or desirable, for payment pur- poses, to announce prices at different levels, that is, f.o.b. farm and f.o.b. plant, some adjustment must be made to con- vert these prices from one level to the other. This creates a problem in manu- factured milk pricing — where milk values are considered related to the fat and non- fat solids content — of a different nature from that encountered in the fluid milk pricing field where the value of the non- fat elements may be considered as a func- tion of the volume of skim milk. The material presented here on manu- facturing grade milk values develops "net values" for the separate components by assigning all costs that are specifically identifiable with the fat or with the non- fat solids directly to the cost influencing element. For example, costs of churning butter are assigned to the fat component, while powder drying costs are directly charged to the nonfat solids constituent. Some of the relevant costs involved are joint costs and are not uniquely identi- fied with either one or the other com- ponent. Such costs are those associated with handling the whole milk — for ex- butter, cheese, and whole milk powder have been reasonably consistent. Evaporated milk price quotations — particularly for the so-called "advertised brands" — appear to be high rela- tive to those of the other major manufactured dairy products. Under such circumstances, the "net value" of milk used for evaporated milk operations would be higher than that for butter and cheese. ample, receiving and separating costs, and costs of transport from farm to plant. Any attempt to deduct costs of this type from separate fat and nonfat solids prices determined at plant level will in- volve an arbitrary and essentially un- equitable allocation of these joint costs. The major difficulty in attempting to make an arbitrary allocation of these costs, wherein they may then be directly charged to either the fat or the nonfat solids, is that costs of this type — such as transportation, receiving, and separat- ing — are independent of the amount of fat or nonfat solids involved. The costs are a function of the volume or weight of milk handled and, since the fat and nonfat elements vary for any given volume of milk, the cost per unit of fat and nonfat solids varies among milk types having different tests. This means that the cost of transporting, receiving, and separating, per unit of fat and nonfat solids, is lower for high-test than for low-test milk. Any attempt to assign a constant unit cost to the specific item, therefore, will of necessity underprice the fat and nonfat solids in high-test milk and overvalue these solids in low-test milk at the farm level relative to the actual costs involved for a particular type. A system of direct allocation of farm-to-plant costs to the individual com- ponents would necessarily involve a di- rect butterfat differential that is lower at the farm level than at the plant. A logical alternative to a procedure of quoting separate prices for fat and skim solids f.o.b. farm level, therefore, might involve the use of separate prices f.o.b. plant level wherein these separate prices are ultimately combined into a hundred- weight basis, with deductions of these joint costs made according to the weight or to some other cost-affecting variable. The major impact of this procedure would be that the resulting on-farm prices would involve the same calculated butterfat differential as milk at the plant level. This does not mean, of course, [12] either that producers receive the same prices for the fat and nonfat components at the farm as would exist at the plant, or that these joint costs do not ultimately become assigned to the value components of the milk. It merely means that the pro- ducer bears these charges in the manner in which they accrue — according to the volume or weight of whole milk trans- ported and handled. Under this system, the producer will tend to receive, at the plant, the net value of the milk he pro- duces less the necessary charges involved in moving his milk from farm to plant. SUGGESTED FORMULAS FOR USE IN COMPUTING PRICES AND BUTTERFAT DIFFERENTIALS FOR MANUFACTURING GRADE MILK 13 The above sections have put forth the logical argument that an equitable pric- ing system is one which reflects the net values of milk of different constituency and quality standards. To accomplish this, it is necessary that the following in- formation be available: (1) the physical quantities of the relevant milk product or products obtainable from milks of varying constituency, and (2) the net value (price less processing and other appropriate costs, such as transportation and marketing) of the milk products so obtained. Relationships have been developed from which it is possible to determine the product yields for several alternative types of dairy operations. Where manu- factured dairy products — butter, nonfat dried milk solids, and evaporated milk — are concerned, federal standards for fat and nonfat solids content have been used, and allowances have been made for such losses as normally- occur in reasonably efficient operating plants. 16 In a similar 15 The theoretical basis for the procedure in this section is essentially the same as that pre- sented for establishing butterfat differentials for butterpowder and cheese factories by Froker and Hardin (see footnote 13). The major dif- ferences involved are in terms of the develop- ment of yield formulations and the extensions of the net value concept to include evaporated milk operations. 16 For a complete discussion of the develop- ment of these yield relationships, including the federal standards and the operating loss allow- ances, see Hassler, James B., "Pricing Efficiency in the Manufactured Dairy Products Industry," Appendix A (in press). manner, the yields of cream and skim milk have been computed, based on the fat test of the cream, with allowances made for separating and other plant losses. Butter-Powder Operations. — Milk entering a processing plant to be con- verted into butter and dried nonfat solids is first separated into cream and skim milk. Normally, there is about a Y 10 of 1 per cent loss of fat in this separating operation, that is, this amount of fat re- mains with the skim milk and does not enter into the butter operation. The cream entering into the churn is, typically, about 40 per cent milk fat, and therefore contains some nonfat solids. These solids can be reclaimed from the residual but- termilk and aggregated with the solids obtained directly from the skim milk, and in these calculations it has been as- sumed that this procedure is followed. Considering standard allowances for moisture, and with typical product losses during the processing operation, the quantities of butter that can be obtained from a hundredweight of milk may be represented : Q b = 1.23F-.U3 which means that each pound of fat in a hundredweight of milk will produce 1.23 pounds of butter, but that the over-all loss of fat in the separating operation (0.1 per cent) amounts to the equivalent of .123 pound of butter. The dried non- fat solids which can be obtained from [13 this joint butter-powder operation may be determined by : Qnfa = 7.l7 + MIF where .441 represents the added pounds of dried nonfat solids that can be pro- duced from the additional nonfat solids in whole milk which are associated with a variation of 1 per cent in fat content, as determined from the use of the California relation between fat and solids-not-fat. The difference between this and the basic California relation reflects the influence of the fat carried over into the skim milk and the allowance made for the physical losses in separation. It is further assumed that processing losses in the drying oper- ation are exactly compensated for by moisture retention. The net values of milk used for butter and powder, therefore, can be expressed : V m = (1.23F-.123) (P b -C b ) + (7.17 + .441F) (Pnfs-C nfs )~Crs where V m is the net value of whole milk per hundred pounds; F is again the milk fat test; P b the price of butter; C b the di- rect costs per pound of processing butter, including such marketing costs as are necessary to bring the butter to the point of sale; P n fs the price of nonfat dried solids; Cnfs the direct costs per pound of processing and marketing nonfat solids; and Crs the costs per hundredweight of receiving and separating the whole milk, which are not included in the direct pro- duction costs. The butterfat differential — or the dif- ference in net value of whole milk for each change of % of 1 per cent in fat test — can also be computed directly. The formula for such computation will be: BFD bp = .l23'(P b -C b )+.0U(P n f S -Cnfs) where BFD bp refers to the butterfat dif- ferential appropriate for a butter-powder operation, in dollars per hundredweight per Yio of 1 per cent change in fat test; the expression (P b - C b ) reflecting the net value per pound — price less process- ing and marketing costs — of butter; and (Pnfs -Cnfs) the net value per pound of dried nonfat solids. A "computing table" has been set up in table 2 which indicates how the above equations might be used to determine values for any specific time period. To do this, of course, it is necessary to apply appropriate cost and price figures, which change from one period to another. It is essential, therefore, that the cost and price data used be those which relate to the time period for which the values are to be calculated. In this example, the fol- lowing have been used: price of butter, per pound (Pb) , $0,685; price of nonfat solids (Pnfs), $0.18 per pound; direct processing and marketing costs for but- ter (Cb), $0.05 per pound; direct proc- essing and marketing costs for dried non- fat solids (Cnfs), $0.07 per pound; and the receiving and separating cost, $0.20 per hundredweight of whole milk. It will be further assumed that milk of 4.0 per cent fat content is to be used. Evaporated Milk Operations. — Milk to be processed into unsweetened, unskimmed, evaporated milk is typically standardized to a desired ratio of fat and nonfat solids before being concen- trated since these ratios of fat and nonfat solids vary, as do the absolute quantities present. Milk with low fat test contains a high proportion of nonfat solids rela- tive to fat, and, conversely, high fat milk contains a high percentage of fat in rela- tion to the nonfat solids. Milk of 3.9 per cent fat content contains these solids in approximately the proportion that re- quires no standardization, according to the California relationship of fat to solids-not-fat. 17 For this reason, an evap- orated milk operation will be accom- panied by a by-product operation when- ever the average test of incoming whole 17 According to the standards used, and the level of nonfat solids indicated by the California relation, the test of milk is normally in the cor- rect ratio at 3.855 per cent fat. For simplicity of statement, this is rounded to 3.9 per cent. [14] milk differs from 3.9 per cent. It is, for the purpose of this example, assumed that milk of lower test will be standardized by the removal of skim milk which, in turn, will be processed into nonfat dried milk solids. Milk of a higher average test than 3.9 will be standardized by the removal of 40 per cent cream which will be con- verted into butter with the buttermilk yield omitted because of its negligible size. Under such conditions, the follow- ing product yields will result: (a) for milk with less than 3.9 per cent fat (? e = .291F-.023and Q nf8 = 7.14 -I.85F (b) for milk with more than 3.9 per cent fat Q e = M3F + lM o o ■* to O OS CO 3 k CO 00 O) b- CO M ^t OWN .s N «£ t- H rj OJ O tN O r- 4- T-i ■^ t> 00 CO tJ« 3 CO a 8 G £ JO 6 ■3 o: L^ ^ a> a iH ■** -U -!_ ■•^ a. a •^H -PH •!- • -H + o i e3 o CO c< T- 2 o 3 «4 o O > fl *■ g © Z I * T3 o "3 c O i "e3 k •^ o 4- g o g Q £ £ +■ "S U 2 a o M T3 V 1 43 0) o Pi o "S 4? "5 "5 u § O 1 ! 5 42 2 *o "S ^ -§ si 1 co « o> 5 "S § ' C p o E ^ * c S? as * 3 o •5 cS M J. O 4) .a J) o C a a> 3 ■■a S T3 o © ^a Stj-O fl-C 73 fe 0) t ° « a ^ §•3 *3 © **-' ^ < «h > -a ° > ° o n -° £ 4* T3 2 -*» « fep 0) +a V <♦-. 3 73 2 > *3 > +a "S -P 4a +a 3 > « O +^ +J O .2 © O « o o ^ H £ iz; Eh >h ^J Eh J? P4 » PQ * iH CO CO "^ io «o t^ 00 OS c tH [15] o m co i-i Oth 1 ©0*HOOtOi-J cn Ul W C £ (N lO SO 00 S •a "> g oo _ g g g^ c *o s h u s tj o s ,-s ^ +; 'i + 1X1 1 X + J 1 + 0) >> (^^rH^X^cO^t-^ CO H ^ B N ^ S B Be! -*» lH +j +j +j> 4) £ •"^ i CO i-H 8 5 «A 3 > ^ O Z c i l. © o *- J) c V © to 1 o, E X CO *£ CO 3J t3 § o ft ». ft* *■ £ d a a o u 3 w "5 u CO J) 11 * lis- M e« > ■3 fe CD ts if ° fc > ® J. 2 ® =» £ • '3 u • B tac » © X! •= ! Sft* > S 1 8 "c > > .s-s J CO "O & X I . a 1- £a©£!:s©s3.Sat3 OesCO e jfl , 3P { j , g *S +» 5 'S ■« S *» o -p S .^©o.S^o©©©^ i-ic4co"^u3«dt^o6a>c> •»- ( marketing costs — of the respective prod- ucts where the subscript e refers to cases of evaporated milk, nfs to pounds of dried nonfat solids, and b to butter in pounds; and where C rs refers to the joint costs of receiving and separating whole milk. In this instance, the butterfat differ- entials which would directly express the difference in net values per 34 o of 1 per cent change in fat content per hundred- weight of milk are : (a) for milk of less than 3.9 per cent fat BFD e = .029 (P e - C e ) - .185 {Pnfs —C n fs) (b) for milk of more than 3.9 per cent fat BFDe = .0013 (Pe-Ce) +.124 (P b -C h ) where BFD e refers to the butterfat dif- ferential in dollars per 100 pounds of milk appropriate for a plant primarily manufacturing evaporated milk; and the parenthetical expressions again reflect the net values per unit of the respective products. An example showing a set of calcula- tions using these relations, similar to those shown in table 2, is presented for a condensery operation. These appear in table 3, and involve the following as- sumed prices and costs : evaporated milk prices per case (P e ), $6.24; dried nonfat solids price per pound (P n f S ), $0.18; butter price per pound (Pb), $0,685; processing and marketing costs of evap- orated milk per case (C e ), $2.05; proc- essing and marketing costs of butter per pound (C&), $0.05; processing and mar- keting costs of dried nonfat solids [C n fs), $0.07 ; and the cost of receiving and sep- arating whole milk per hundredweight (Crs), $0.20. As with the example in table 2, it will be assumed that milk of 4.0 per cent fat content is used. Fluid Cream and Skim Milk Oper- ations. — Another alternative outlet for manufacturing grade milk, by California [16 plants, involves the sale or use of fluid cream and skim milk for other manufac- tured dairy products, especially for ice cream and cottage cheese. Following simi- lar procedures to those outlined above, the net value of milk going into such operations can be calculated. The quan- tities of fluid cream and fluid skim milk that can be obtained from a hundred- weight of milk are: () 40 = 2.48F-.248and Q s = 99.248 -2.48F where Q 40 refers to the number of pounds of cream of 40 per cent fat content, Q s , the number of pounds of fluid skim milk, and F, the fat test of milk being processed. The net value of milk for these pur- poses can again be stated as the quantity of product valued at the current net prices (or values) per pound. This equation is: V m = (2.48F-.248) (P 40 - C 40 ) + (99.248 - 2.48F) (P s - C s ) - C rs where V m is the net value of milk used for separation into fluid cream and skim milk for sale or use in these other manu- factured dairy products, P 40 and P s refer to the prices of 40 per cent cream and skim milk, respectively, C 40 and C s are the direct costs (if any) of processing and marketing cream and skim milk, re- spectively, and C r8 , the costs of receiving and separating the whole milk. The butterfat differential appropriate for an operation of this type may be ex- pressed : BFD C8 =.2A8[(Pt -Ct )-(P 8 -C a )] where BFD CS refers to the butterfat dif- ferential in dollars per hundredweight of milk used in a cream-skim milk opera- tion, per % o °f 1 P er cent change in fat test, and where the parenthetical expres- sions relate to net prices or values for 40 per cent cream and skim milk, respec- tively. A "calculating table" illustrating the application of the above equations relat- ing to a manufacturing grade fluid cream and skim milk operation appears in table 4. For the purpose of this example, the following prices and costs are used: the price of manufacturing grade cream of 40 per cent fat content per pound of cream (F 40 ), $0,364; the price of manu- facturing grade skim milk per pound of skim milk (P 8 ), $0,012; the direct costs of processing and marketing the cream and skim milk (C 40 ) and (C s ) are both considered to be zero; and the cost of receiving and separating whole milk (C rs ), $0.20 per hundredweight. Again it will be assumed that milk of 4.0 per cent fat content is entering the plant. Market Milk Prices. — Although the variation in fat and nonfat solids con- tent is as great in market milk as in manu- facturing grade milk, the problem of evaluating the separate components in fluid use becomes more complex. For one thing, it is difficult to determine the in- fluence of different amounts of nonfat solids on the value of milk used for fluid purposes. While nutritional differences do exist, most consumers would find it difficult to recognize such variations as are normally found in the nonfat solids content of the milk they buy. Unless thoroughly convinced of the differences in nutritional benefits involved, and at the same time advised of the variation in the content of solids of this type, it is unlikely that consumers would be willing to pay a premium for relatively high nonfat solids in fluid milk. This being the case, the variation in nonfat solids con- tent is not a satisfactory basis for mak- ing direct determination of the difference in value of different types of milk when used for fluid purposes. 18 The following discussion, therefore, is not concerned 18 It should be noted that increased emphasis on nonfat solids, in the future, may make it desirable to include price variations as a result of the difference in the nonfat solids content of the skim milk when used for fluid purposes. Some tendency in this direction is indicated by the fact that some fluid skim milk sold to con- sumers is enriched with added nonfat solids. In addition, others — particularly Professor Misner [17] with the differences in the solids content of the skim milk. For practical purposes, the compo- nents of market milk are cream and fluid skim milk. Under California pricing and sanitary regulations, cream and fluid skim milk made from Grade A milk may have a higher value than physically iden- tical cream and skim milk derived from milk of manufacturing grade quality. This is due to the fact that such Grade A cream and skim milk can be combined into products such as market milk, cream, and half-and-half, which yield a greater net return per hundredweight of raw product than do butter, evaporated milk, and the other manufactured dairy prod- ucts. 19 The difference in value between market milk and manufacturing milk of similar physical characteristics may be called the "Grade A premium" or, in cases where the two terms are not synon- ymous (as they are in California), the "Class I premium." The amounts of cream and skim milk per hundredweight of whole milk are, of course, directly related to the amount of fat present in the original milk. For ex- ample, approximately 7.2 pounds of 40 per cent cream and 91.8 pounds of skim can be obtained from 100 pounds of 3 per cent whole milk, while roughly 12.2 pounds of 40 per cent cream and 86.8 pounds of skim will be produced from of Cornell University — have emphasized that milk could be priced according to energy values as expressed in terms of calories. The point to be made here is that modifications can be adapted to the material presented here to in- corporate these or other procedures when it ap- pears desirable. As an illustration, specific formulas which will account for differences in the nonfat solids content of milk when used for fluid purposes appear in Appendix B. 19 Where a "classified price plan" is used — as in California and commonly in many other milk markets throughout the country — a price premium is paid to producers for milk which goes into fluid uses. Under California sanitary regulations, these higher priced fluid uses re- quire the use of Grade A milk, although this latter provision is not universally held in other markets. V TJ 8 k o o c I J 11 1° "8 J "5 w -1 O 8 ? £ N 8 O O 1 6 s = O 8 O C +■ •— O "8 2 $ I* 3 oooooooooco N^HOONNMOCOI> N»(NNrlf05Na>« «) co o m o q 10 "wo as co as T-i ^' ^ 00 II II II II II II X I o o o X o ■>* o O CD 00 q m ^ X I ^ N 00 N 00 H O (Ot-^H NN O CO CO (N O CO lO N " as as as' co as 00 1-1 t- O O I X + CO 00 OS "tf £ m co B B 00 '"s S °° °i o .13 o fn fc H {sh »z; H h n co^mto 3 a _ co bo ft 2 OS CO ^ O <* OS bp ■3-1 t> 06 [18] the same amount of 5 per cent milk. 20 The higher the fat content of the original milk, the greater is the amount of cream that can be derived per 100 pounds of milk and, conversely, the smaller the amount of residual skim milk. In California, any Class I milk prod- uct — such as market milk, market cream, and fluid skim milk — can be considered as a combination of Grade A fat and Grade A skim milk, provided that the solids content of the skim milk meets the minimum requirement of 8.15 per cent. 21 The value of milk of this quality to a distributor is the combined value of the quantities of fat and of skim milk which it will produce. The major difficulty in formulating specific pricing schedules arises from attempting to determine the appropriate values of these separate com- ponents in market grade milk. To be sure, these are at least as valuable to any given plant as the same components derived from manufacturing grade milk for, lack- ing a more profitable use, market grade fat and skim milk can be diverted into butter, cheese, and other dairy products. As mentioned earlier, however, when used for specific fluid purposes, "Class I" milk receives a price premium. The problem of pricing fluid milk with dif- ferent fat and skim yields includes the allocation of the Class I premium be- tween the two components. Like many accounting problems which involve the allocation of common or "joint" costs, there is no single "correct" 20 The theoretical yield of 40 per cent cream would be two and one-half times the butterfat content. However, milk which has been skimmed by commercial methods normally con- tains at least 1/10 of 1 per cent milk fat and, for this reason, the actual yield of cream is slightly below the theoretical level — roughly one-fourth pound per hundredweight of milk. In addition, there is normally a product loss of about 1 per cent in separating so that the cream and skim milk will total only 99 pounds per hundredweight of milk. 21 According to the California fat-nonfat solids relationship, milk with an average of 2.5 per cent fat or above will have sufficient nonfat solids to meet this requirement. procedure for the allocation of the Class I premium to the skim and to the fat constituents of market milk. Possibly a "reasonable" basis for allocating the Grade A premium could be determined that would be acceptable to all. Never- theless, there is no "correct" method or single "right answer" to this problem. There is little information available through regularly reported statistics from which indications of the market valuations of this Class I premium on the separate components of milk can be drawn. Prices for market grade cream and market grade skim milk (which in California are Grade A) have been col- lected for the period of June, 1950, to May, 1951, as a part of a previously re- ported study. 22 These prices represented interarea, interdistributor sales, and were not subject to control by the price- fixing agency of the state. The ranges of these prices are shown in table 5. As can be seen, there was considerable vari- ation between the prices for any given month at which these physically and legally identical commodities were sold. Because these prices are not subject to control, they may provide an indication of the way the market tends to operate in allocating these premiums. If it can be safely assumed that the higher prices are those paid for supplies going into Class I uses, while the lower range of prices relates to "surplus" diverted into manufactured products, then the dif- ference between the two would be a re- flection of the Class I premium on the one hand for the fat-containing product and on the other, for fluid skim milk. It should be noted that the high prices of the reported range conform closely to the price quotations of the Grade A job- bing cream market, while the low prices in general reflect the manufacturing grade cream quotations. 22 "Pricing Intermarket Transfers of Bulk Grade A Cream and Skim Milk," by D. A. Clarke, Jr. Calif. Agr. Exp. Sta. Bui. 732, 1952. 19] Table 5. The Range of Selling Prices Reported for Interplant Shipments of Grade A Cream and Skim Milk, June, 1950-May, 1951 Month Cream prices per pound of fat Low High Skim milk prices per hundredweight Low High dollars 1950: June July August. . . . September October. . . November. December. 1951: January. . . February . March April May 0.75 0.76 0.77 0.83 0.84 0.84 0.82 1.04 1.04 0.96 0.96 0.96 1.00 1.24 1.40 1.00 1.23 1.44 1.00 1.25 1.40 1.04 1.25 1.72 1.06 1.25 2.33 1.04 1.25 2.33 1.06 1.25 1.80 1.16 1.36 1.80 1.16 1.38 1.80 1.17 1.45 1.80 1.09 1.47 1.80 1.10 1.47 1.80 Source: Calif. Agr. Exp. Sta. Bui. 732, p. 21. In addition to the problem of deter- mining an "equitable" basis for the allo- cation of the Class I premium between the fat and skim components of market grade milk, there is the procedure for determining class usage and, conse- quently, the prices paid to producers. As previously mentioned, fluid milk in Cali- fornia is paid for according to a classified price plan. Certain uses, such as fluid milk, concentrated milk, fluid cream, fluid skim milk, and chocolate drink, are defined by the Agricultural Code as Class I. Thus, milk used for these purposes is paid for at the Class I prices as estab- lished by the Bureau. Market grade milk in excess of these requirements, so-called "surplus," is normally used for manu- factured products where the law does not require Grade A standards. Milk used for these purposes is paid for at Class II and III prices. These are also established by the Bureau, but at lower levels than the Class I price and normally in close rela- tionship with prices for manufacturing grade milk. 23 In spite of the fact that some of the Class I products are pri- marily fat containing, such as cream, and some predominantly skim containing, like fluid skim milk and chocolate drink, and, furthermore, that fluid milk is nor- mally standardized to a different level of fat and skim proportions than exist in whole milk received from producers, the prices paid producers under present California procedures depend solely on the class use of fat. Under these circumstances, a distrib- utor with a high Class I skim utilization relative to Class I sales of fat pays Class 23 While the Agricultural Code makes provi- sion for separate prices for Class II and III uses, where Class III includes milk used for butter and cheese other than cottage cheese, and where Class II includes all uses other than those de- fined as Class I or III, the Class II and III prices established by the Bureau quite often are identical. [20] II or III prices for the skim milk in excess of that associated with the fat ac- counted for at Class I prices. These Class II and III prices are closely related to, and in many markets identical with, manufacturing grade milk prices. Con- versely, of course, a distributor with relatively high Class I fat utilization ef- fectively pays a Class I premium for more skim milk than is used in Class I prod- ucts when these supplies are obtained from whole milk received from pro- ducers. As a result of the inequities inherent in this procedure of accounting for usage, it has been suggested that separate prices be established for both the fat and skim milk components of market grade milk. 24 These separate prices would then apply to the actual utilization of whole milk in both the fat-containing and skim- containing products, and would require that distributors further account for skim usage. Schedules of prices to be paid produc- ers for milk of varying fat content have been established in milk markets through- out the United States. These schedules — whether established by public agencies, market-wide producer-distributor nego- tiations, or by a single company — are generally of two types, namely, (1) a hundredweight price schedule or (2) a constant price per pound of fat in the whole milk with no direct value being placed on the skim milk. The hundred- weight schedule is the series of prices for 100 pounds of whole milk with different fat content. This schedule is usually postulated by means of a base price for milk having the prescribed basic fat test (3.8 per cent in California markets) in conjunction with a specific butterfat dif- ferential. Consequently, such pricing schedules are linear. The second pricing schedule listed above is usually called "direct ratio" pricing. On a hundredweight basis, milk of various fat tests, when priced in this manner, has values in direct ratios to the fat test. Direct ratio pricing is equiv- alent to a hundredweight schedule with a butterfat differential equal to 34 o °f the price per pound of fat. The reason for the discussion of whole milk paying schedules is to point out now that such schedules determine important relationships which must be understood if (under classified pricing) a system of accounting to the producer on the basis of both fat and skim utilization is to be internally consistent. The development to follow implies that skim milk used in Class I purposes is homogeneous in value, that is, variations in normal solids con- tent have no evident influence on value. With this assumption, the base price per hundredweight for milk (Pp*) would be represented by: P F * =F*P f + (100 -F*) P s or the value of F* pounds of fat at price Pf plus the value of the remaining skim (100 - F*) at the price P s for skim. 25 In addition, the butterfat differential would be BFD = 0.lP f -0AP s This means that each additional 0.1 pound of fat will mean a reduction of 0.1 pound of skim milk, and that the butterfat differential is simply the "net" increase in value, or the value of 0.1 pound of fat less the value of 0.1 pound of skim milk. It should be noted from the above re- lationships among the four defined vari- ables that the specification of the values of any two of them automatically deter- mines the consistent values for the re- 24 Calif. Agr. Exp. Sta. Bui. 732, p. 26. 25 Fat, in this sense, refers specifically to the "pure" fat component, and the price for this should not be confused with the price "per pound of fat" often quoted for whole milk and for cream — both of which contain quantities of skim milk. Skim milk, in this sense, is not the common product called "skim milk" which con- tains a small portion of residual milk fat, but is a "fat free" component of whole milk. [21] maining two. For example, if F* is 3.8, P f * is $5.46, and BFD is .10, then, upon substitution, we have 3.8P, + 96.2P S = 5.46 .IPf- AP S = .10 Upon solving these equations, one se- cures P f = $1.02 and P s = $.0166. It is now apparent that any butterfat differential, given a base milk price, has an intimate connection with the consist- ent fat and skim values in the whole milk, and that the various fat and skim prices associated with various butterfat dif- ferentials will have marked differences of economic significance. This immediately suggests that one should seek in the milk marketing system some economic indica- tors of market evaluations of fat and skim milk to be used for the determination of the butterfat differential, instead of em- ploying some arbitrary butterfat differ- ential and changing it later when the "consistent" fat and skim milk prices are not in accord with market evaluations. The subsequent pages of this section will be devoted to a general discussion of some approaches to the problem of esti- mating Class I fat and skim milk values, and a more detailed presentation of these approaches will be given in a later section. GUIDES FOR DETERMINING SEPARATE PRICES FOR FAT AND SKIM MILK IN CLASS I WHOLE MILK Froker and Hardin 26 have suggested that this problem might be solved on an "alternative value" basis. In this case, values would be assigned to market grade fat and market grade skim milk in pro- portion to the relative values of these components in a butter-powder opera- tion. In other words, the net value of whole milk of specified fat content is computed on the basis of current market values of butter and nonfat dried milk solids. From this, the percentage con- tributions of the fat and the skim milk are calculated, the sum of which, of course, amounts to 100 per cent. When these percentages are applied to a given Class I price for milk of the same test, the resultants are taken to be the values of the market grade fat and the skim milk, respectively. As a simple illustration, as- sume that the net value of butter at cur- rent levels of prices and costs is 75 per cent of the net value of whole milk of 3.8 per cent fat content used for butter and powder. Seventy-five per cent of the established Class I price of 3.8 milk would then represent the value of 3.8 2(i See footnote 13. pounds of fat and, similarly, the remain- ing 25 per cent of the price of whole milk would represent the value of the residual 96.2 pounds of skim milk. In this way, the relative values of fat and skim milk for fluid uses are determined by the rela- tive values of these components in the butter and nonfat dried milk solids markets. The advantages of this procedure ap- pear to be twofold. In the first place, it is relatively familiar, and may be easily understood by the dairy industry. In the second place, it involves prices — those for butter and for nonfat dried milk solids — which are widely and currently available. The primary disadvantage is that there is no logical reason why the fat and skim components of market grade milk either would or should bear the same relation as those established by the butter and the dried milk solids market, particularly when the market prices for these products are artificially maintained at arbitrary levels under the government support program. An alternative procedure involves a second major premise — that current [22 market grade jobbing cream price quo- tations provide a "reasonable" guide to market valuations of market grade fat. This argument proceeds logically on the grounds that the only physical or legal difference between this cream and the whole milk from which it was derived is that of the relative proportions of fat and skim milk contained therein. The Grade A jobbing cream prices in California are "open market" prices, that is, not fixed by administrative order. Under such cir- cumstances, and where distributors are free to obtain market grade fat and skim milk supplies either in the form of cream or as whole milk, it may be claimed that the relative prices of these alternatives reflect the way the market evaluates the difference in constituents. The major advantage to be claimed for this alternative procedure is that it relates prices for Class I fat and Class I skim milk directly to the operation of Class I markets. In view of the classified price system used in California, and in many other milk markets, together with the existence of institutional "barriers," such as geographical supply area limitations and quotas, which prevent the free flow of milk between uses (particularly into the higher value, or Class I, uses) , the rel- ative prices derived from manufacturing operations are not necessarily, and in fact would not be expected to be, good indica- tors of those resulting from fluid milk market operations. The major criticisms of the use of this procedure are based on the following arguments. First, that the California Grade A jobbing cream market prices are not independent of the Class I whole milk prices but are, in fact, closely related, so that it may be argued that the Class I prices "set" the Grade A jobbing cream prices. Second, that there are relatively small sales made on the jobbing cream market, so that quoted prices have ques- tionable significance — particularly in certain periods of the year. The first of these objections — that con- cerning the relationship between these prices — is not a major limitation, but one of the primary bases for suggesting this procedure. As stressed previously, if the Grade A jobbing cream market operates effectively, then it will tend — within the whole milk price structure — to value the fat and skim milk when in different com- binations from those existing in whole milk and, by the difference between prices, to value the difference in Grade A skim milk content between a given quan- tity of fat in whole milk and in cream. The second criticism — that insufficient quantities of cream are sold in the job- bing market to enable establishment of "true" values — is more difficult to evalu- ate. For many commodities, however, prices are established on the basis of the operation of produce exchanges and produce auctions. Not infrequently, the quantities which actually pass through these markets are but a very minor pro- portion of the total quantities sold. Yet, it is argued that these markets — in the absence of possibilities for control or "rigging" — are sufficiently active to pro- vide a focal point for the operation of supply and demand. It should be further remembered that it is not suggested that the jobbing cream prices be used to estab- lish the level of whole milk prices. Rather, these cream prices could be used to deter- mine the allocation of the whole milk price between the fat and skim milk con- stituents and thus to determine the prices to be paid to producers for milk of dif- ferent constituencies to be used for Class I purposes. Should the market for jobbing cream operate ineffectively, distributors would find that one of the constituents was consistently overpriced while, at the same time, the other component was con- sistently underpriced, relative to values. It is felt that this situation, continuing over any length of time, would auto- matically set forces in motion which would, in turn, be reflected in the jobbing cream market in a corrective manner. [23] No attempt is made in this report to develop a formula or equation which will determine the level of Grade A milk prices. Rather, as mentioned earlier, it is assumed that these prices will continue to be established, as currently, by the Bureau of Milk Control. It is useful, how- ever, to establish the following relation- ship between the price for whole milk and the prices for the basic constituents of that milk. The following basic assump- tion will be followed throughout the later discussion: which states that the price of milk is equal to the value of the fat and skim constitu- ents contained therein. When market or Class I milk is concerned, the above must be modified to include the value of the Class I premium and its allocation be- tween the fat and skim milk under existing market conditions. Alternative procedures — both of which are by neces- sity arbitrary — are presented which would accomplish the purpose of allocat- ing this premium. 27 Procedure 1. This method is based on the assumption that the relative values of fat and skim milk used for Class I pur- poses will be reasonably reflected by the relative values established by the butter and dried nonfat solids markets. Initially, the net value of milk in a butter and powder operation can be calculated in the manner previously discussed. This in- volves the basic formula: F w =(1.23F-.123)(/ > 6 -C 6 ) + (7.17 + .441F) (P nfa - Cnfs) - C rs 21 It should be noted that these two methods do not exhaust all possible procedures, but are merely presented as illustrations of logical methods. For example, other procedures might be adopted, similar to those presented for manu- facturing grade milk prices, involving "net value" formulations based on retail prices for fluid products less processing costs. However, these have not been discussed for fluid opera- tions in detail, due primarily to the nonhomo- geneity of product utilization in fluid milk operations and the corresponding differences in realized net product prices for the variety of fluid milk and cream items. where V m is the net value of whole milk per hundred pounds; F, the milk fat test; Ph, the price of butter; Cb, the direct costs of processing butter, including such mar- keting costs necessary to bring the butter to the point of sale; P n fa, the price of non- fat dried solids; C n fs, the direct cost of processing and marketing nonfat solids; and C rs , the costs of receiving and sepa- rating whole milk. If the joint receiving and separating costs are allocated according to the rel- ative values of fat and skim in the whole milk prior to the subtraction of these joint costs, then the percentage contribu- tion of the fat component to the whole milk value is given by : RVF F = (1.23F-. 123) (P b -C h ) where RVF F indicates the relative value of fat in whole milk with fat content of F per cent, and the other subscripts have the meanings indicated above. It follows that the percentage contribution of the nonfat solids to the whole milk value would be: RVNFS F =l-RVF F The value of R VF f ( and also R VNFS f ) is not constant for all values of F, but varies with the fat test of the whole milk under consideration. Consequently, when applying the relative value concept to the Class I milk, RVF F must be computed for that value of F which is the basic fat test of whole milk for which the Class I price has been established. 28 28 The fact that these relative values change for different levels of fat content can be demon- strated through the following: RVF F ^~ 1 + ( Pnfs-Cnfs \ / 7.17 + \ Pb-Cb ) V1.23F- 441F Pb-Cb / Vl.23F-.123/ For any given set of prices and costs, the first set of terms in parentheses — reflecting net prod- uct prices — will be constant. However, the second set — those which reflect the product yields — is not constant, but is functionally re- lated to the fat content, expressed here as F. For example, for 3 per cent milk, this second term has a value of approximately 2.4, while for milk of 6 per cent fat content, this paren- [24] The value that results when the basic Class I price is multiplied by RVFp, can be taken as the Class I value of the amount of fat present in the milk. To obtain the value of a pound of fat, it is only neces- sary to divide through by the fat test. Similarly, the difference between the value of fat and the Class I price reflects the skim milk value, or the value of the amount of skim milk in 100 pounds of whole milk. Assuming the situation where the basic fat test is 3.8 per cent, the above results can be stated by the following equations: ( a ) VFci.i = iP *« ){ ^ Fs - 8) and (b) VS C i, i 3.8 (P,,-VF a .i) 96.2 where VF CL j is the Class I value of a pound of milk fat; P 38 , the hundred- weight price of whole milk of 3.8 per cent fat — as independently established; RVF 3 8 , the relative value of fat as deter- mined for F equal to 3.8 from the butter powder calculations; and VS clI , the value of a pound of skim milk in whole milk having a fat content of 3.8 per cent. The butterfat differential would be given by: BFD = 0.1VF CL 7 - 0.1 VS CLJ . As an example to illustrate this proce- dure, assume that the current price of butter is $0,685 per pound; the price of dried nonfat solids is $0.18 per pound; the direct costs of processing and market- ing butter and dried nonfat solids are $0.05 and $0.07 per pound of product, respectively; the joint costs of receiving and separating whole milk are $0.20 per hundredweight; and that the current price for Class I milk, as established by the administrative agency for milk of 3.8 per cent fat content, is $5.46. The first step involves substituting the appropriate thetical term has a value of about 1.4. This results from the fact that butter yields increase more rapidly than do yields of dried nonfat solids as the fat content of milk increases. As a consequence, the relative value of fat (RVF F ) increases as the level of fat content of milk increases. prices, fat tests, and costs in order to determine the total net value of milk of 3.8 per cent fat content into the "net value" equation as follows: V m = (1.230x3.8 -.123) (.685-.05) + ( 7.17 + .441 x3.8) (.18 -.07) -.20 V m = (4.551) (0.635) + (8.846) (.11) -.20 V m = 2.890 + .973 -.20 V m = 3.663 which represents the total net value, or "paying ability" of milk of 3.8 per cent fat content used in manufacturing butter and powder under the above costs and prices. To determine the relative value of the fat in this milk, it is necessary to divide the contribution of the butter (which is taken to represent only the fat element) by the total value of the milk. This is accomplished in the following manner: 2.890 KVtm - 3.663 + .20 RVF m = .74S where, in the above, it has been further assumed that the joint costs of receiving and separating the whole milk ($0.20) will be allocated between the fat and skim milk in accordance with the relative values. As shown above, approximately 75 per cent of the value of milk in a butter-powder operation is associated with the fat. Since the theory behind this procedure involves the application of the relative value of fat in the butter-powder operation to determine the value of fat in Class I milk, the next step is the follow- ing: P, 8 (RVF, 8 ) = $5.46 x. 748 P 3 .s(RVF s J =$4,084 which may be taken to represent the value of the 3.8 pounds of fat in a hundred- weight of 3.8 per cent milk. The value per pound of fat would then be : $4,084 ci. I L o o VF a. i = $1,075 [25] As the value of skim represents the dif- ference between the value of whole milk and the fat value, the skim milk contained in 100 pounds of 3.8 milk (96.2 pounds) may be determined : 96.2 VSci i -$5.46 -$4,084 VSci.i= $0.0143 The value of the butterfat differential, consistent with these separate prices for fat and skim milk, would be: BFD = 0.1 (1.075) -0.1 (.0143) BFD= .1075 -.0014 BFD= .1061 This compares with a "direct-ratio-to-fat" butterfat differential of .1437 for each y i( ) oil per cent difference in fat content per hundredweight of milk. Procedure 2. The second alternative for the determination of the separate Class I values of fat and skim milk is based on the assumption that the Grade A jobbing cream market in California pro- vides a reasonable basis for determining the way in which the market values the individual components of market grade milk. It should be recognized that the job- bing cream price is at a different level in the marketing system from that of the established base price for whole milk. The whole milk price is established for milk entering a plant, while the cream price is associated with a milk product that is leaving a plant and has undergone phys- ical loss and processing costs. In order to use these two prices to determine the values of fat and skim milk in Class I milk, it is necessary to adjust the cream price back to a "plant entry" value. This requires the subtraction of the direct processing and marketing costs for cream and an allocated share of the general re- ceiving and separating costs as well as an adjustment for the physical loss. As stated previously, the quantities of 40 per cent cream (which correspond to the Grade A jobbing cream price quota- tions) and of skim milk that are obtain- able from 100 pounds of milk are: > u o 8 £ OJNC0C0'^»00000000«O«OCD C 03 *. 3 e3 O iHrHr-iiHT-HTHiH^-iiHiHiHT-i o £ft *• a < •a o c 3 TJ o "3 CS*Ht~COOC— COGSOSOiOOt— D o HNWIOtOIOIO^^^lOW 00 V * 3 1 9 wja E o o M IS c (-1 55 "2 NNOO^NCO^WlOin^M HCtHrlrirlrlrlHHHrl 01 4a o T3 8 u. c- 5 k. as * «s h 03 13 oooooooooooo »•■ ^OOOOOOOOOOOOOOOOOOOOOO (A iS'SS.a® loioiotfjioioiriirjirjioioirj « • 3 *k 52, 3 a * 03 V o w .3 in «n 1> O 3 2.S*/ C5J2 a> OHNNCOtf(0«0(0^r)i^ u 4- Pi 0) M N N N N N N « N M N « N £ XJ ft 8 s o a a> O)O)0)O)0)O)9) T-JrHrHrHTHiHrHT-trHiHTHTH odddodddddod "5 w "o u "3 H- Mg tf0000^W*OtfWNO« 03 0(OOWNNiO(Ol-(0^0 oqoqooNt-t-t»t>t-t»t»t- ddc>dc>oddc)dc>d c o IS o §ft pa >- ft U> j- 8 a E u « JQ D 5 H- O X c a a < s > > i ■9 h 1- -a h CS en a el* > Ofl 1 > ►-a III 3 $> O O 0> »<« X u '. fl ^ o ®N 3 »d.So ft .3 3 ^*» m M Sttj 3 S 3p, 1B _2ft 03 bo O* & " O) ■* 4) *, fe . O 3 ^ rt 03 3 s;.«e K «e.2-3^ ■3 3-3 3 » °o *ft^ lls&si g-sagg 0) 03 3 jo ■ M « S _. 03 ■» o3 - — -3 o_, "3 S <» 2 o « sa^oS* S.h's2 ft© 2"Sc-c3» £§Sft § 2 3-2 XJ fl W>£ u-°5s§a O ©-O bag a> ^ ^3 3 < t) •£ O 0) r» "O TO 2 © *" In 03 -2-T3 a4§s°sl° a SH w o -r;