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##### 1.Suppose that a monopolist?s product could be eit...

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1.Suppose that a monopolist?s product could be either high quality (H) or low quality (L).There are 10 identical consumers, each of whom values a low-quality product at vL and a high-quality product at vH=8/5vL.(So if consumers believe that a good is of quality i, then the monopolist can sell 10 units at any price p?vi.) The cost of producing q units of a good of quality i is 1/10ciq?. If vH/cH=vL/cL=25/16, how much would a high-quality producer have to restrict his supply to convince consumers that his product was actually of quality H?[Hint:Quantity for a high-quality firm must be sufficiently small that a low-quality producer would prefer to sell all 10 units and openly reveal them as low quality,rather than disquising these goods as high-quality items.] 2.(Requires Calculus).A monopolist produces a product whose demand price and production costs vary with quality s and quantity q according to P(s,q)=s(1-q) C(s,q)=s?q a)Calculate the price and quality levels that a monopolist would choose, and the corresponding quantity sold. b)Consumer surplus at any (s,q) combinations can be derived as ?sq?. The corresponding value for profit is (p(s,q)-s?)q=(s-sq-s?)q. Substitute the monopolist's profit-maximizing quantity from (a) and then derive optimal quality for that quantity choice (the level of quality that maximizes consumer plus producer surplus). Show that the monopolist's actual quality choice is lower than optimal quality, given the quantity chosen. 3.Consider the game in Figure 7.13: ___L_______R____ T __a,-a__ _0,0___ B __c,c___ _1,-1__ a)Solve for a and c such that there is a mixed-strategy equilibrium in which Player 1 plays T with probability ?, B with probability ?, and Player 2 plays L with probability ?, R with probability with ?. b) Are there any pure-strategy equilibria? You can also find these questions at http://works.bepress.com/cgi/viewcontent.cgi?article=1022&context=jeffrey_church Chapter 6: question 2(pg.203) and 6(pg.204), chapter 7 question 6(pg.229).

Paper#13621 | Written in 18-Jul-2015

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