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ARE 100 ps3-10ans - University of California Davis...

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University of California, Davis Department of Agricultural and Resource Economics ARE 100B Winter 2010 Dr. Larson Problem Set 3 Answers 1. Intel is a monopolist manufacturing computer chips with a competitive fringe of firms that act as price takers of the price Intel sets. The market willingness to pay for the P80 chip is given by 400 , p Q = with p in dollars per chip and Q in thousands of chips per month. The fringe marginal cost curve is 40 .5 F F MC Q = + (with F Q and F MC also in thousands of chips and dollars per chip, respectively), and Intel's marginal cost of producing chips is constant at $50 per chip. Intel is planning its strategy to set the P80 chip price. (a) Determine the residual demand Intel faces after accounting for the quantity supplied by the competitive fringe for any level of price. The residual demand that Intel can work with is the difference between total quantity demanded and the quantity supplied by the fringe at any given price. Total demand is 400 , Q p = and fringe supply is 2( 40), f Q p = for prices above 40. Thus the residual demand is (400 ) 2( 40) 480 3 . r f Q Q Q p p p = = = (b) How many P80 chips will Intel supply per month? The inverse demand facing Intel is 160 (1/3) , r r p Q = so Intel's marginal revenue is 160 (2/3) . r r MR Q = Setting this equal to Intel's MC, 160 (2/3) 50 , r r r MR Q MC = = = (160 50) /(2/3) 165. r Q =− = Intel will supply 165 thousand chips per month. (c) What is the resulting world P80 chip price? The resulting world price is set from the Intel residual inverse demand: 160 (1/3) 165 $105 p = = per chip. (d) How many P80 chips are supplied by the competitive fringe? The competitive fringe takes the price of oil as given, so from its supply function 2 (105 40) 130 f Q =⋅ = thousand chips per month. 2. You and another firm are a duopoly supplying the market for bread in Davis. The inverse aggregate demand you both face is 10 .001 p Q = . You are firm 1, and your marginal cost of making bread is $1 per loaf, so 1 1 MC = ; while your competitor has marginal cost of 2 2, MC = or $2 per loaf.
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