In: Economics
A firm produces a product in a competitive industry and has a total cost function TC = 50 + 4Q +2Q² and MC = 4 + 4Q. At the given market price of $20, the firm is producing 5 units of output. Is the firm maximizing profit ? What quantity of output should the firm produce in the long run?
A perfectly competitive firm produces at MC=P
equating both
4+4Q=20
4Q=16
Q=4
the firm is not maximizing production at Q=5; it should produce Q=4 units to maximize profit.
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A long run price is equal to the minimum ATC
ATC=TC/Q
ATC=50/Q+4+2Q
the ATC is minimum at MC=ATC
equating both
4+4Q=50/Q+4+2Q
2Q=50/Q
Q^2=25
Q=5
the long run quantity the firm produce is 5 units