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Unformatted text preview: Stanford University Department of Management Science and Engineering MS&E 241 Economic Analysis Problem Set 5 Winter 2009 Issued: Tuesday, March 3, 2009 Due: Tuesday, March 10, 2009 Please choose three from the following four problems. You will receive 30% extra points if you do all of the problems. Problem 5.1 (Cournot Oligopoly) Consider the case when n firms simultaneously choose their pro- duction quantities q 1 , . . . , q n in a market for undifferentiated widgets. The equilibrium price p is deter- mined by a linear inverse demand curve, p ( q ) = [ a- bQ ( q )] + , where a, b > 0 are constants, Q ( q ) = q 1 + . . . + q n is the aggregate production quantity of widgets, and q = ( q 1 , . . . , q n ) is the vector of firm outputs. Assume for simplicity that the firms unit production costs are identical and equal to c > 0 and that c < a . (i) Find the firms best-response correspondences q * i ( q- i ) and the unique NE tuple q * as a function of n . What can you say for n ? (ii) Do firms have an incentive to collude and/or to merge? Explain for the Cournot duopoly (i.e., for n = 2)....
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