A firm has the long-run cost function C(Q)  4Q2  64.In the long run, it will supply a positive amount of output, so long as the price is greater than

A) $64.
B) $72.
C) $16.
D) $32.
E) $37.

Question

A firm has the long-run cost function C(Q)    4Q2    64.In the long run, it will supply a positive amount of output, so long as the price is greater thanA) $64.B) $72.C) $16.D) $32.E) $37.

Alyssa Eaton · Accepted Answer

Final Answer : D, Explanation :  In the long run, a firm will supply output where marginal cost (MC) equals the minimum of the AVC and ATC curves.We can find the firm's long-run AVC and ATC by dividing the long-run cost function by Q:AVC(Q) = [  +  /64] / Q = (1/64) /Q +  /64ATC(Q) = [  +  ]/Q = (1/Q)  +  /QTo find the minimum of AVC and ATC, we need to take the derivative of each with respect to Q:AVC'(Q) = - (1/64) /Q^2ATC'(Q) = - (1/Q^2)  +  /Q^2Setting these derivatives equal to each other, we get:-(1/64) /Q^2 = -(1/Q^2)  +  /Q^2Simplifying and multiplying through by Q^2, we get:  = 64 /QSolving for Q, we get:Q = √(64 / )Plugging in the given values, we get Q = √(64*64/4) = 32Therefore, the firm will supply output if P > MC = C'(Q) = (1/32)  +  /64 = $32.

A firm has the long-run cost function C(Q)  4Q2  64.In the long run, it will supply a positive amount of output, so long as the price is greater than

A) $64.
B) $72.
C) $16.
D) $32.
E) $37.

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