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Econ 313.1 - Wissink - Fall 2005 PS#5 - XtraQ DUE: In class on Halloween (Oct 31) 1. Suppose there are 100 identical demanders in the widget market and that each demander’s demand function is: x = 10-P. The production function for any firm is x = min{S, T} and the market prices for S and T are Ps and Pt respectively. a. What is the market demand function? b. What is the representative firm’s long run total cost function? c. If the widget market is a perfectly competitive constant cost industry and if the prices of S and T are each $1, then what is the number of widgets traded in the long-run equilibrium? d. If the widget industry were to produce 700 widgets in total, then what is the industry’s total demand for the inputs S and T? e. If the prices of S and T depend on aggregate input demand in the following way: Ps=S/200 and Pt=T/200, then is the industry still a constant cost industry? f. Is it possible to determine the long run equilibrium number of firms in this problem and why or why not? 2. A competitive firm has the following short-run cost function: srtc(x) = x3 – 8x2 + 30x + 5 a. b. c. d. e. f. Find the firm’s marginal cost function. Find the firm’s average variable cost function. Graph the firm’s marginal cost function and average variable cost function. Assuming all fixed costs are sunk, at what price will the firm shut down in the short run? At what price would the firm supply 5 units of x to profit maximize? At what price would the firm make zero profit? 3. The cheese business in Lake Fon-du-lac, Wisconsin, is a competitive industry. All cheese manufacturers have the cost function lrtc = q2 +9, while demand for cheese in the town is given by QD = 120 - P. What is the long-run equilibrium number of firms in this industry?