2. (a) Consider a perfectly competitive firm with the following total cost funct

ID: 1187425 • Letter: 2

Question

2. (a) Consider a perfectly competitive firm with the following total cost function in the short run:

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STC = 100 + 100Q+ 5Q^2 + (1/3)Q^3

Given the market price of its product is P=$300 per unit, determine its profit-maximizing output and profit for the short run.

(b) Now suppose its long-run total cost is:

LTC= 54Q - 2.4Q^2 + 0.03Q^3

Indicate the firmâ€™s long-run price, quantity sold, and profit, assuming the industry is in long-run equilibrium.

for profit max, MC=P

MC = dTC/dQ = 100 + 10Q + Q^2

100 + 10Q + Q^2 = 300

Q = 10

Profit = Total Revenue - Total Cost

= P*Q - (100 + 100*10+ 5*10^2 + (1/3)*10^3)

= 300*10 - 5800/3

= 1066.67

In long run equilibrium, ATC=MC

ATC = TC/Q = 54 - 2.4Q + 0.03Q^2

MC = dTC/dQ = 54 - 4.8Q + .09Q^2

-2.4Q + 0.03Q^2 = -4.8Q + 0.09Q^2

0.06Q = 2.4

Q = 2.4/0.06 =40

P = MC = 54-4.8*40+0.09*40^2 = 6

Profit = PQ - TC

= 6*40 - (54*40-2.4*40^2+0.03*40^3)

= 240-240

= 0

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