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hat the short-run cost function is C(q) = q3-342+34+7 e this price-taking firm f

ID: 1125679 • Letter: H

Question

hat the short-run cost function is C(q) = q3-342+34+7 e this price-taking firm faces a market price of $3. Answer the following (do not (point) The total revenue functionis: TR(a)- (1 point) The profit-maximizing quantity ofproduction is: q= (1 point) Therefore, the maximum profit at a price of $3 is: ound quantities): c) 's describe this firm's short-run supply curve more fully: d) (4 points total) If the market price is greater than (2 points), the firm's inverse supply function is given by P(q) = (1 point). Otherwise, the firm shuts down (produces 0 units), and accepts a profit of(1 point).

Explanation / Answer

a) Total revenue = p x q = 3q

b) Profit = TR - TC

Profit (P) = 3q - q3 + 3q2 -3q - 7

Profit would be maximized where dP/dq = 0

3 - 3q2 + 6q - 3 = 0

q = 2

c) Maximum profit = 6 - 8 +12 -6 - 7 = - $3

Supply curve is same as the marginal cost curve of the firm above the minimum average variable cost.

VC =  q3 - 3q2 +3q

AVC = VC/q = q2 - 3q + 3

AVC would be minimum where d(AVC)/dq = 0 :

2q - 3 = 0 or q = 1.5

AVC (min) = $ 0.75

MC = dC/dq = 3q2 - 6q + 3

If the market price is greater than $0.75, the firm's inverse supply function is given by P =  3q2 - 6q + 3 .

Otherwise, the firm shuts down, and accepts a profit of -$ 7 ( Loss, fixed cost is still incurred)