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# 100B HW3 Answers - Econ 100B Tang Homework 3 Ch 8 and Ch 9...

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Econ 100B: Tang Spring Quarter 2008 Homework 3: Ch 8 and Ch 9 Due Thursday May 8, at the beginning of class. Please write your name and PID on your homework. 1) Suppose the competitive market price for lunchboxes is \$11/unit. Short run total costs for lunchboxes have been found to be: C = 9 + 3 Q + Q 2 a) How many lunchboxes will this firm make? b) Does the second-order condition for this problem hold? c) At what price does profit maximizing supply fall to 0 (what’s the shutdown point)? d) What’s the profit at the optimal point? e) Graph profit-maximizing supply as a function of the market price P . a) max profit, profit=TR-TC π Q ( 29 = 11 Q - 9 + 3 Q + Q 2 ( 29 π Q ( 29 Q = 11 - 3 - 2 Q = 0 2 Q = 8 Q * = 4 could also jump directly to FOC set Q* where P=MC, solve for Q in 11=3+2Q b) 2 π Q ( 29 Q 2 = - 2 < 0. yep c) shut-down when P<min AVC min AVC where MC(Q)=AVC(Q) 3+2Q=3+Q, so at Q=0 MC(0)=3 -> shutdown when P<3 d) π Q * ( 29 = 11 4 ( 29 - 9 + 3 4 ( 29 + 4 ( 29 2 = 7 e) Supply equals MC while MC>AVC and equals 0 when MC is below AVC (recall min AVC, where MC=AVC, is the shutdown point). MC=3+2Q

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Econ 100B: Tang Spring Quarter 2008 2) A firm’s short-run production function is given by: Q = KL where the level of capital is fixed at K Define the wage as the constant w , and the rental price of capital to be r . The competitive price of output is P . a) What is the firm’s short run marginal cost? b) At what levels of P (with respect to the other variables) will the firm want to shut down?
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