Suppose that a competitive firm that produces keyboards has short-run AV C = 3 +

Question

Suppose that a competitive firm that produces keyboards has short-run AV C = 3 + q, and F C = 3. Assume that the market price for keyboard is 9 per unit.

a What is the short-run total cost function? What is the marginal cost MC? b What is the firm’s short-run profit-maximization problem?
c What level of output will the firm produce?
d What is the firm’s profit?

e Will the firm be earning a positive, negative or zero profit in the short run?

f How low does the market price of keyboard need to be so that the firm will not produce in the short run?

g Plot the firm’s short-run supply curve.

h Assume that in the long run the firm can either quit the market or remain in the market with the same relevant costs, in particular F C = 3 (imagine this is the rental cost of a factory building.) How low does the market price of keyboard need to be so that the firm will quit in the long run?

Explanation / Answer

AVC = 3+Q, we have AVC=VC/Q or VC = AVC*Q

VC= AVC*Q = 3Q+Q^2

FC = 3

we know that TC = FC+VC = 3+3Q+Q^2 (short run total cost function)

ATC=TC/Q = 3/Q+3+Q

MC = dTC/dQ = 3+2Q

Equilibrium at P = MC (Profit maximization in short run)

9 = 3+2Q

2Q = 6

Q = 3 Output, the firm will produce is 3 units

ATC at Q = 3, = 3/Q+3+Q = 3/3+3+3 = 7

Profits = (P-ATC)*Q = (9-7)*3 = 6

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