3. (18 points) Suppose that the marginal cost of producing output, q, in the sho

Question

3. (18 points) 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

a) Let q be he quantit.

tr = P*Q = 25q

and MR = dtr /dq = 25

Equating mr and mc

25 = 10 + 8q

q = 1.875

to maximize profit firm will produce 1.875 units.

b) total cost = variable cost + fixed cost = AVC*q + fixed cost = (10+4(1.875))1.875 + 5 = 37.8125.

c) Profits = tr - tc = 25*1.875 - 37.8125 = $9.0625.

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