output and costs

OUTPUT AND COSTS

Average total cost

		(175,000 cattle = 100)
Year	50,000 cattle	175,000 cattle	425,000 cattle	850,000 cattle	1,350,000 cattle
1992	1.104	100.0	94.3	90.6	88.5
1977	1.082	100.0	95.8	93.1	91.7
1963	1.045	100.0	98.0	98.0	96.7

Question #1:

The data in the table above show the average total costs (per head of cattle) of meatpacking firms of varying plant sizes in three different years. (MacDonald, James M. and Ollinger, Michael E. “Technology, Labor Wars, and Producer Dynamics: Explaining Consolidation in Beef Packing.” American Journal of Agricultural Economics 87(4) (November 2005): 1020-1033.) The average cost numbers are expressed as an index, using the 175,000 head plant size as the base, so a decrease in the index is a decrease in average total cost.

Explain how these data indicates the existence of economies of scale in the beef packing industry. Are there economies of scale for each of the three years? Describe the general shape of the average cost curve that is implied by these data.

Question #2:

Compare the average costs across plant sizes in 1963 with those in 1977 and 1992. Were scale economies becoming more or less significant over time?

Question #3:

The authors of this study made the following assessment of production costs in the beef packing industry:

“Large plants have substantial fixed costs, due partly to capital intensity, and partly to labor practices (weekly minimum hours guarantees to production workers). As a result, short run processing costs at large plants rise sharply as volumes fall below capacity, and packers require large and consistent flows of cattle before committing to a large plant.”

To capture the idea that there are substantial fixed costs, suppose that the formula for the beef packers total cost is:

TC = $50,000,000 + $35 x Q

where Q is the number of cattle processed per year. This formula means that the fixed cost is $50 million, but that once the plant is up and running, the marginal cost per cattle processed is $35, regardless of the level of production.

a. Is this marginal cost curve from this cost formula consistent with the law of diminishing returns? Explain.

b. Using the formula for the total cost, what is the formula for the average total cost?

c. Is there a level of output for which the marginal cost equals the average total cost?