# Economics 201

## Case of the Day:Costs and Competition in Dairy Farming

The text of this case is taken in part from Chapter 2, Section II of Leonard Weiss, Case Studies in American Industry, 2nd ed. (New York: John Wiley, 1971). All dollar figures in the original have been multiplied by 6 to bring them approximately to current real equivalents.

"In some types of agriculture, experimental studies have been made that show short-run cost patterns quite precisely. One of the most extensive of these was in dairying. Several hundred cows at 10 experimental stations in a number of states were fed at various levels for three years and their milk production compared.

"The feed ‘inputs’ that went with the various milk outputs are shown in [Table 1]. A cow requires a certain amount of feed simply to maintain herself. Beyond that, more feed leads to more milk, but at a decreasing rate. The cows fed at high levels produced more than less generously treated cows but, as we would expect, milk output did not increase as fast as feed consumption.

Table 1

 Number of Cows in Each Group Average (per cow) Total Digestible Nutrients Consumed (pounds per year) Average (per cow) 4% Fat Corrected Milk Produced (pounds per year) 65 5654 7626 60 6117 8184 66 6575 8824 55 7132 9400 52 7531 9780 94 7899 9965

"These production figures can be used to estimate the costs of a hypothetical diary 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 3000 pounds of feed per cow per year [at zero cost]. For simplicity, assume that purchased feed [i.e., above the 3000 pounds the cows get from foraging] is the only variable cost. The farm might have the following fixed costs per year:

 Depreciation and maintenance of buildings and equipment \$4,800 Property taxes \$2,400 Miscellaneous (seed, fertilizer, gasoline, veterinarian, marketing, etc.) \$7,800 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 1960s. 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 could undoubtedly 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, we get the approximate relationship shown in Table 2 between milk output and fixed and variable costs.

Table 2

 Total Output (1000s of pounds of milk per year) Total Fixed Costs (dollars per year) Total Variable Costs (dollars per year) Total Costs (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

The analysis above 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 1960s 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 3 (taken from Weiss) describes the operations of farms broken down into six size categories: Class I is "large-scale 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" (\$10,000 - \$19,999, or above \$57,700 in 1998 dollars), Class IV is "lower-medium family farms" (\$5,000 - \$9,999, or above \$28,800 in 1998 dollars), Class V is "small family farms" (\$2,500 - \$4,999, 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 65 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 3

 Census Class Average Number of Cows per Farm Milk Sold per Cow (pounds per year) Gross Sales per Man-Year (dollars) Total Investment per \$100 of Gross Sales (dollars) Purchased Inputs per \$100 of Gross Sales (dollars) Estimated Cost of \$100 of Gross Sales (dollars) I 130 10,250 20,000 345 54.5 78 II 49 9,590 14,500 407 42.9 84 III 31 8,463 10,450 450 38.9 97 IV 20 7,050 6,100 531 38.0 126 V 13 5,350 3,345 670 43.4 183 VI 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 Pindyck & Rubinfeld’s Figure 7.9 on page 239.

Questions for Friday, September 24 (Bring your answers to class; you will submit them on Wednesday, September 29 as Problem Set #4.)

1. Graph the production function and the marginal product curve for feed based on the numbers in Table 1. Do they follow the patterns that Pindyck & Rubinfeld’s Chapter 6 represents as typical?

2. Calculate the actual cost values for each of the six feed levels in Table 1. Do the approximations in Table 2 seem to represent them faithfully? Be sure to consider units carefully, remember that the farm in question has 25 cows, and that each cow consumes 3,000 pounds of feed for free by grazing.

3. Graph the corresponding total, average, and marginal cost curves based on Table 2 and on your calculations from the previous problem. Are they similar to Pindyck & Rubinfeld’s typical curves? (Since the units differ, you should put total cost on one graph and average and marginal on a second. Remember that cost curves relate costs to output, not to 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.)

Questions for Monday, September 27 (Bring your answers to class; you will submit them on Wednesday, September 29 as Problem Set #4.)

4. Based on the data in Table 3, what shape does the long-run average cost curve have for the dairy industry? Explain how you reached that conclusion.

5. For a dairy farm, what are fixed inputs and what are variable inputs in the short run? Does it seem likely (from what you know about farming, not from the table) that the short-run average cost curves have the U shape that we usually draw, as shown by the ATC curve in Pindyck & Rubinfeld’s Figure 7.1 on page 222? Show in a diagram how the six hypothetical short-run ATC curves (one for each category of farm in the table) would relate to the long-run average cost curve you discussed in the previous question.

6. Do the data indicate the presence of increasing, constant, or decreasing returns to scale in dairy farming? If you found increasing or decreasing returns, do you think that if farms were to become large enough (i.e., much bigger than the ones in the table) the increasing/decreasing returns would cease?

7. 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 library sources or the Internet for data on the current distribution of farms by size.)