Suppose that the marginal cost of producing output, q, in the short-run for a co

Question

Suppose that the marginal cost of producing output, q, in the short-run for a competitive firm is MC = 10 + 8q. The market price of the firm’s product is $25. a. (2 pts) What level of output will the firm produce to maximize its profits? b. (3 pts) Assume that the firm’s fixed costs are $5, and the firm’s average variable cost is given by AVC = 10 + 4q. What are the short-run total costs at the level of output the firm produces? c. (3 pts) What are the profits in the short-run? d. (10 pts) Show the level of profits in a graph.

Explanation / Answer

Part a)

The level of output at which firm maximize is when Market Price = MC

25$ = 10+ 8q

Hence, q = 1.875 maximizes profit.

Part b)

Fixed cost = 5$

AVC = 10 + 4q, so TVC = q( AVC) = q(10+4q) = 10q + 4q2

Hence, Total Cost (TC) = TVC + Fixed cost = 10q + 4q2 + 5

Total cost at the output the firm produces =

10 (1.875) + 4(1.875)2 + 5 = 37.8125

Part c)

Profits = Total Revenue - Total Cost

= Market price (q) - Total Cost

= 25 (1.875) - 37.8125

= 9.0625

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