5.A firm sells in a competitive market in which price is $10. Its marginal cost

Question

5.A firm sells in a competitive market in which price is $10. Its marginal cost is 2 + .5Q. Determine the profit-maximizing level of output. 6. . Assume that a firm has measured demand carefully and thinks that the following table accurately displays this. The total cost has been measured and can be given as TC-20+ Q + Q2 where Q is the level of output. Complete the table and determine the profit-maximizing level of output. Total Cost Total Revenue $ 90 160 210 240 250 240 210 Output Profit 4 160 90 10

Explanation / Answer

(5)

A perfectly competitive firm maximizes profit by equating price with Marginal cost (MC).

10 = 2 + 0.5Q

0.5Q = 10 - 2 = 8

Q = 8/0.5 = 16 (Profit maximizing output)

(6)

Profit = Total Revenue (TR) - TC

Marginal revenue (MR) = Change in TR / Change in Quantity (Q)

Marginal cost (MC) = Change in TC / Change in Q

Profit is maximized (= 200) when MR = MC. This holds true (MR = MC = 10) when Q = 5 and Price = TR / Q = 250 / 5 = 50.

Q TR TC PROFIT MR MC 1 90 22 68 2 160 26 134 70 4 3 210 32 178 50 6 4 240 40 200 30 8 5 250 50 200 10 10 6 240 62 178 -10 12 7 210 76 134 -30 14 8 160 92 68 -50 16 9 90 110 -20 -70 18 10 0 130 -130 -90 20

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