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aps5x313_f05_rev - Econ 313.1 Wissink Fall 2005 PS#5 XtraQ...

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0 5 10 15 20 25 30 35 0 2 4 6 8 10 x $ mc avc atc 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. Just add horizontally to get market demand: X D = 1000-100P. b. Note that with this production function you will always want S=T and so S* = x and T* = x, so that if lrtc=PsS*(x) + PtT*(x) then lrtc(x) = (Ps+Pt)x c. Plugging in the factor prices you get: lrtc = 2x, so that lratc = 2. So long run price must be $2. Now, plugging P*=2 into market demand you X*=800. d. S*=T*=700. e. NO. It’s an increasing cost industry now. f. No. Since the lratc curve is horizontal, you can not determine a unique value for the number of units produced by the firm in long-run equilibrium. If you were TOLD the number of firms, then you could back-out the number produced by each firm. But there are many possibilities here, so the answer is indeterminate. All we can conclude uniquely is that P*=2 and X*=800. 2. A competitive firm has the following short-run cost function: srtc(x) = x
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