Question #3: The authors of this study made the following assessment of production costs in the beef packing industry:

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?