Consider a perfectly competitive market in which each firm\'s short-run total co

Question

Consider a perfectly competitive market in which each firm's short-run total cost function is C = 64 - 15q + q2 where q is the number of units of output produced. The associated marginal cost curve is MC = 15 + 2q. In the short run each firm is willing to supply a positive amount of output at any price above $ 15. (Enter your response as a real number rounded to two decimal places.) If the market price is $22, each firm will produce 3.5 units in the short-run. (Enter your response as a real number rounded to one decimal place.) Each firm earns a profit of $ -51.75 . (Enter your response as a real number rounded to two decimal places, and use a negative sign if the firm has a loss rather than a profit.) In the long run, firms will exit the industry. Suppose the short-run cost function given above [C = 64 + 15q - q2] is the one that all firms would use in the long-run, because the corresponding SAC curve is tangent to the LAC curve at the minimum point on the LAC curve. In the long run, each firm will produce units. (Enter your response as a real number rounded to one decimal place.)

Explanation / Answer

The answer of the last part is given below:

C = 64 + 15q + q^2

LAC = AC = (64 + 15q + q^2) / q

                   = (64/q) + 15 + q

LAC would be minimum if LAC = MC

(64/q) + 15 + q = 15 + 2q

64/q = q

q^2 = 64

q = 8

Answer: Each firm will produce 8 units.

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