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Five questions due Wednesday, Nov 19, at the beginning of class




Five questions due Wednesday, Nov 19, at the beginning of class;1. A seller produces output with a constant marginal cost M C = 2. Suppose there;is one group of consumers with the demand curve P1 (Q1) = 16Q1 and another group;1;with the demand curve P2 (Q2) = 10 2 Q2.;(a) If the seller can price discriminate between the two markets, what prices would;she charge the dierent groups?;(b) If the seller cannot discriminate, but must charge the same price P1 = P2 = P;to each group, what will be her prot-maximizing price?;(c) Which, if any, consumer group benets from price discrimination?;2. Suppose that two identical rms produce widgets and that they are the only;rms in the market. Their costs are given by T C1 (Q1) = 60Q1 and T C2 (Q2) = 60Q2;where Q1 is the output of rm 1 and Q2 is the output of rm 2. Price is determined;by the following demand curve;P (Q) = 300 Q;where Q = Q1 + Q2.;(a) Find the Cournot equilibrium. Calculate each rms prot in equilibrium.;(b) Suppose the two rms form a cartel to maximize joint prots. How many widgets will be produced? Suppose the two rms split the joint prots evenly. Calculate;each rms prot.;(c) Suppose rm 1 were the only rm in the industry. How would market output;and rm 1s prot dier from that found in part (b) above?;(d) Returning to the duopoly of part (b), suppose rm 1 abides by the agreement;but rm 2 cheats by increasing production. How many widgets will rm 2 produce?;What will be each rms prots?;1;3. Two rms compete by choosing price. Their demand functions are;Q1 (P1, P2) = 20 P1 + P2;Q2 (P1, P2) = 20 + P1 P2;where P1 and P2 are the prices charged by each rm respectively, and Q1 and Q2;are the resulting demands. Note that the demand for each good depends only on the;dierence in prices. If the two rms collude and set the same price, they could make;the price as high as they wanted, and earn innite prots. Marginal costs are zero.;(a) Suppose the two rms set their prices at the same time. Find the resulting;equilibrium. What price will each rm charge? How much will it sell? And what will;its prots be? (Hint: Maximize the prot of each rm with respect to its price while;holding the other rms price constant. Find each rms best response function. An;equilibrium should be where the best responses intersect.);(b) Suppose rm 1 sets its price rst and then rm 2 sets its price. What price;will each rm charge? How much will it sell? And what will its prots be? (Hint;Find rm 2s best response function. Firm 1 takes into account rm 2s response;when setting its price rst.);(c) Suppose you are one of the rms and that there are three ways you could play;the game: (i) Both rms set prices at the same time. (ii) You set price rst. (iii) Your;competitor sets price rst. If you could choose among these options, which would you;prefer? Why?


Paper#18215 | Written in 18-Jul-2015

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