# hw5 - c What is the short run supply equation of the firm...

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Eco 300 Homework 5 Due Thursday, 04/14 Total points are 50. 1. (10pts) Explain why the profit-maximizing rule for a perfectly competitive firm requires P = MC, assuming MC is increasing with output Q. 2. (20pts) John's Lawn Mowing Service is a small business that acts as a price taker. John's short-run total cost is given by STC = 0.1q 2 + 10q + 50 , where q is the number of acres John chooses to cut a day. The short-run marginal cost is SMC = 0.2q + 10 . Fixed cost is equal to 50. Assume that all fixed costs are sunk. a. Suppose the prevailing market price of lawn mowing is P = \$20 per acre. How many acres ( q ) should John choose to cut in order to maximize profit? How much is John's maximum daily profit? b. What is the average variable cost (AVC) as a function of q ? What is the minimum AVC (at which AVC = SMC)? At what prices will this firm shut down in the short run?
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Unformatted text preview: c. What is the short run supply equation of the firm? Graph the supply curve of the firm. d. Suppose the market demand is Q d = 1000 – 100P. If there are 100 firms, then what are the short-run equilibrium price and quantity? 3. (20pts) A perfectly competitive industry consists of a number of identical firms. Each firm has the following long-run marginal and average cost functions: LRMC(q) = 40 – 12q + q 2 LRAC(q) = 40 – 6q + (q 2 )/3 The market demand curve is given by Q d = 2200 – 100P. (a) In the long run equilibrium, how much would each firm produce? (b) What is the long-run equilibrium price? (c) How many firms will be operating in this equilibrium? (d) Plot two side-by-side graphs to illustrate the long run equilibrium; one should show a typical firm, the other should show the market....
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