Econ 150 Problem Set 4

# Econ 150 Problem Set 4 - 1 Question 1 a Part a i Short-Run...

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1. Question 1 a. Part a i. Short-Run Total Cost = wL + p k K ii. TC = 1,000L + 57.60 * 8,000 iii. TC = 1,000L + 460,800 iv. Q = 1.25 * K 1/3 * L 2/3 v. Q = 1.25 * (8,000) 1/3 * L 2/3 vi. Q = 25L 2/3 vii. L = (Q/25) 3/2 = Q 3/2 /125 viii. TC = 1,000Q 3/2 /125 + 460,800 ix. TC = 8Q 3/2 + 460,800 b. Part b i. Average Total Cost = (Total Cost)/(Quantity) ii. AC = (8Q 3/2 + 460,800)/(Q) = 8Q 1/2 + 460,800/Q iii. Marginal Cost = dTC/dQ iv. MC = d/dQ (8Q 3/2 + 460,800) = 12Q 1/2 c. Part c i. Profit is maximized with Q | MC = MR ii. MR = P (price is exogenous) iii. 12Q 1/2 = 288 iv. Q = (288/12) 2 = 576 units d. Part d i. Profit = Total Revenue – Total Costs ii. Profit = PQ – (8Q 3/2 + 460,800) iii. Profit = 288 * 576 – (8*576 3/2 + 460,800) = -405,504 iv. The firm suffers a loss of \$405,504 e. Part e i. Average Variable Cost = (Variable Costs)/(Quantity) ii. AVC = (8Q 3/2 )/(Q) = 8Q 1/2 = 8*576 1/2 = \$192 iii. Since MR = P and MR = 288 > 192 = AVC, the firm loses less by continuing to operate in the short-run (\$405,504 versus \$460,800) and should therefore should not shut-down production in the short-run. f. Part f i. Since the rental rate = the user cost of capital, the capital market is perfectly competitive and p k = (r+d)X.

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