ECN 712Fall 2009Professor SchleeProblem Set X, Due 17 November1.Price discrimination (of the third degree). A monopolist produces a single good under constant returnsto scale.It sells the good in two markets, 1 and 2, and the demands are independent (fori6=j,the price it charges in marketidoes not affect the demand in marketj, implying that it can chargedifferent prices in the markets).(a) Letεi(pi) denote the price elasticity of demand in marketias a function of the price in marketi. Show that, at any interior solutionp1> p2if and only ifε1(p1)> ε2(p2): at any solution themarket with the higher price has a more inelastic demand.(b) Suppose now that the inverse demand in each market is a straight-line (as long as price is positive).The demand in market 1 is more price elastic than the demand for market 2when the demandcurves are evaluated at the same quantity.Evaluate:“The firm will charge a higher price inmarket 2.” How do you reconcile your answer with part (a)?
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