Table 1 Average (Per Cow) Number of Cows Total Digestible Average (per cow) 4% Fat in Each Group Nutrients Consumed Corrected Milk Produced (pounds per year) (pounds per year) 65 5,654 7,626 60 6,117 8,184 66 6,575 8,824 55 7,132 9,400 52 7,531 9,780 94 7,899 9,965 "These production figures can be used to estimate the costs of a hypothetical dairy farm. Imagine a 25-cow farm near one of the large cities on the eastern seaboard. Let it produce enough hay, silage, and pasture to provide 3,000 pounds of feed per cow per year [at zero cost]. For simplicity, assume that purchased feed [that is, above the 3,000 pounds the cows get from foraging] is the only variable cost. The farm might have the following fixed costs per year: Table 2 Depreciation and Maintenance of $4,800 Buildings and Equipment Property Taxes $2,400 Miscellaneous (For Example, Seed, Fertilizer, Gasoline, $7,800 Veterinarian, Marketing) Labor (3,300 Hours at $6.00) $19,800 Interest (5% on $144,000) $7,200 Total $42,000"Labor is treated as a fixed cost because the operator and his family do all the work. In many nonfarm businesses, labor is the leading variable cost, but in American agriculture, three quarters of the labor is supplied by the farmers and their families. This sort of labor will be employed no matter what the farm produces. A farmer can hardly fire his wife if he has a bad year.\" [Note: The divorce rate was much lower in the 19605. Is this still true?] "The only way to put a value on this family labor is by looking at its opportunity cost, that is, what it can earn in its best alternative employment. In 1964, hired farm labor was paid about [$6.00] an hour on average. The farmer undoubtedly could earn more than this in the city, but for most American farmers, a dollar on the farm is worth more than one in the city.\" We can calculate cost figures for this farm based on the production data in Table 1 and the assumption that "total digestible nutrients\" cost $0.24 per pound. Applying this feed cost to each of the 25 cows on our hypothetical farm for the six feed levels shown in Table 1 and adding in fixed costs from Table 2, we get the approximate relationship shown in Table 3 between milk output and fixed and variable costs. Table 3 Total Output (10005 of Total Fixed Costs Total Variable Costs Total Costs pounds of milk per year) (dollars per year) (dollars per year) (dollars per year) 0 42,000 0 42,000 200 42,000 18,000 60,000 210 42,000 19,500 61,500 220 42,000 21,300 63,300 230 42,000 23,400 65,400 240 42,000 26,100 68,100 250 42,000 30,000 72,000 260 42,000 36,000 78,000 This analysis has assumed a farm size of 25 cows; however, there may be important differences in costs associated with having farms that are smaller or larger than this. The 19605 were a period of transition for the agriculture sector of the U.S. economy. Average farm size was getting larger, with automation of farm processes causing small family operations to be merged into larger enterprises. Because the transition to large farms was just beginning, there was a wide distribution of farm sizes, and it was easy to observe the costs of small and large farms side by side. This section of the case focuses on data about dairy farms from the 1964 Census of Agriculture. Using the data collected by the Census about the operations of dairy farms, it is possible to construct estimated cost curves for farms of various sizes. Table 4 (ta ken from Weiss) describes the operations of farms broken down into six size categories: Class | is "largescale farms" (more than $40,000 annual sales, or $210,800 in 1998 dollars), Class II is "large family farms" ($20,000 $39,999 annual sales, or above $105,400 in 1998 dollars), Class III is "upper medium family farms\" (S10,000$19,999, or above $57,700 in 1998 dollars), Class IV is "lower medium family farms" (535,000139,999, or above $28,800 in 1998 dollars), Class V is \"small family farms" ($2,500S4,999, or above $14,400 in 1998 dollars), and Class VI is \"small scale,\" which is anything smaller than Class V. Farms that were operated by individuals over 55 years old or where the operator worked more than 100 days during the year away from the farm were excluded as not being representative of \"full-time farms.\" Table 4 Milk Total . Average Gross Sales Purchased Estimated Cost Number of Produced Investment Census Number of per Man- Inputs per of $100 of Farms per Cow per $100 of Class Cows per Year 5100 of Gross Gross Sales (10005) (pounds Gross Sales Farm (dollars) Sales (dollars) (dollars) per year) (dollars) I 130 15.4 10,250 20,000 345 54.5 78 || 49 53.2 9,590 14,500 407 42.9 84 Ill 31 117.3 8,463 10,450 450 38.9 97 IV 20 104 7,050 6,100 531 38 126 V 13 59.3 5,350 3,345 670 43.4 183 VI 7 17.7 3,778 1,402 1,078 55.2 346 We can think of these cost figures for farms of various scales as representing observations on the long-run cost curve for dairy farming. The final column is interpreted as an estimate of average cost for farms in each scale category. For each category, there is presumably a short-run average cost curve that is "enveloped\" inside the long-run average cost curve as in Baye and Prince Figure 513. Questions 1. Compute and graph the total product curve (per cow) and the marginal product curve for nutrients based on the numbers in Table 1. Use two separate graphs, one for the total product curve and one of the marginal products. Do these curves follow the patterns of that are typical as described in the textbook (Figure 51}? At what quantity of nutrients does diminishing returns begin to occur? Calculate the actual cost values (fixed, variable, and total) for each of the six feed levels in Table 1. 00 the approximations in Table 3 seem to represent them faithfully? Consider units carefully, remembering that the farm in question has 25 cows and that each cow consumes 3,000 pounds of feed for free by grazing. To demonstrate your answer, create a graph with the total cost as you derived from Tables 1 and 2 as well as the total cost as provided by Table 3. From this, you should be able to evaluate how closely the results match. Using the data from Table 3, create a table with the marginal cost, average total cost, and average variable cost. Using this table, create two graphs: one with the total cost curve and one with the marginal and average total and average variable costs. Are these curves similar to the typical curves in the textbook (Figure 512}? Remember that cost curves relate costs to output, not input, so you need output or the change in output in the denominator of your calculations and the level of output on the horizontal axis. For a dairy farm in this analysis, what are fixed inputs and what are variable inputs in the short run? Does 'It seem likely (from what you anecdotally know about farming, not from the table) that the short-run average cost curves have the U shape that we usually draw? Based on the data in Table 4, what shape does the long-run average cost curve have for the dairy industry? Explain how you reached that conclusion. What do the data indicate about whether there are economies of diseconomies of scale in dairy farming? Would you expect that trend to continue if farms were to become large enough (that is, much bigger than the ones in the table)? Based on this analysis of costs, would you expect that dairy farms should have increased or decreased in size since 1964? Is this conclusion supported by what you know about trends in farm size? (If you have time, you may want to explore internet sources for current distribution of farms by size.)