If a firm has TC = 2q^3/2+ 18q^1/2+ 66, what is the shutdown price for this firm? A)2 B)81 C)12 D)9

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Quizplus · Accepted Answer

The shutdown price is the price at which the firm's total revenue is equal to its variable costs, implying that it cannot afford to continue operating at a price below this level. Mathematically, the shutdown price can be calculated as the minimum point of the average variable cost (AVC) curve, which is given by AVC = VC/q = (2^{^3/2} + 18^{^1/2})/q + 66/q. Taking the derivative of AVC with respect to q and setting it equal to zero yields: dAVC/dq = [-2^{^3/2} - 9^{^1/2}]/q^2 = 0 Solving for q gives: q = [2^{^3/2}]/[9^{^1/2}] = 2P1/9 Substituting this result back into the TC equation gives: TC = 2(2P1/9)^{^3/2}+ 18(2P1/9)^{^1/2}+ 66 = (4/27)P1S1U1S1P0 + 132 At the shutdown price, TR = Pq = P(2P1/9), so the shutdown price satisfies: P(2P1/9) = (4/27)P1S1U1S1P0 P = (4/27)P1S1U1S1P0/(2P1/9) = 9 Therefore, the shutdown price for this firm is $9.

If a Firm Has TC = 2q3/2 + 18q1/2

If a Firm Has TC = 2q^3/2+ 18q^1/2