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Unformatted text preview: Department of Economics W3211 Columbia University Fall 2011 Probl e m S e t 9 Int e rm e diat e Mi c ro ec onomi c s Prof . S e yhan E rd e n A rkona c 1 . Suppose the demand for pizza in a small isolated town is p = 10 - Q. The only two firms, A and B, behave as Cournot duopolists. Each has a cost function TC = 2 + Q. (a) Determine the Cournot equilibrium. (b) Determine the equilibrium quantities of each if firm A is the Stackelberg leader. ( c ) If the government wants to subsidize firm A to raise its output to that of a Stackelberg leader, how large should the subsidy be? 2 . Explain why the intersection of the best-response functions is the Cournot equilibrium. 3 . Draw a graph that shows the effect on the equilibrium quantities if the government subsidizes one firm in a Cournot duopoly with a per-unit subsidy. Assume that the best-response functions are linear. Explain the new equilibrium quantities. 4 . Consider a market with just one firm. The demand in the market is p = 18 Q and the firm has a linear cost function C ( Q ) = 2 Q . (a) How much output will this firm produce. What will be the profit and consumers surplus? (b) Suppose a second firm with the same cost function enters the market and the two firms compete in a Cournot style (simultaneous output choice). What will be the equilibrium price and quantity in the market? What is the total market profit and CS? What is the total market profit and CS?...
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