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ps9_fall11 - Department of Economics Columbia University...

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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 Erd e n Arkona 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?
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