Assignment:
Productivity and Costs of Dairy Farming Assignment
The text of this case is taken in part, 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:
|
Table 2
|
|
|
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 non-farm 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 from Table 2, we get the approximate relationship shown in Table 3 between milk output and fixed and variable costs.
|
Table 3
|
|
|
|
|
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
|
42000
|
0
|
42000
|
|
200
|
42000
|
18000
|
60000
|
|
210
|
42000
|
19500
|
61500
|
|
220
|
42000
|
21300
|
63300
|
|
230
|
42000
|
23400
|
65400
|
|
240
|
42000
|
26100
|
68100
|
|
250
|
42000
|
30000
|
72000
|
|
260
|
42000
|
36000
|
78000
|
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 4 (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 4
|
Census Class
|
Average Number of Cows per Farm
|
Number of Farms (1000s)
|
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
|
15.4
|
10,250
|
20,000
|
345
|
54.5
|
78
|
|
II
|
49
|
53.2
|
9,590
|
14,500
|
407
|
42.9
|
84
|
|
III
|
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.
Questions
1. Compute and graph the production function (per cow) and the marginal product curve for feed based on the numbers in Table 1. Be sure to 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 below)? At what quantity of nutrients does diminishing returns begin to occur?
2. Calculate the actual cost values (fixed, variable, and total) for each of the six feed levels in Table 1. Do the approximations in Table 3 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. To demonstrate your answer, create a graph with the total cost as you derived from Table 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.
3. 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 a separate one with the marginal and average total and average variable costs. Are these curves similar to the typical curves in the textbook (Figure below)? 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.
4. For a dairy farm, 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? 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. To draw this, you will want to graph the long-run average cost curve and then overlay some hypothetical short-run average total cost curves for each farm class. Note: Figures in Baye and Prince illustrate how this graph should look.
5. 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 does the data indicate about the scale economies of dairy farming? Would you expect that trend to continue if farms were to become large enough (i.e., much bigger than the ones in the table)?
6. 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.)