ps7 - ECO 310, Fall 2007 Problem Set 7: Oligopoly Due in...

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ECO 310, Fall 2007 Problem Set 7: Oligopoly Due in class on December 11 Question 1 Consider a Cournot duopoly with homogeneous products and an industry de- mand function P =( q 1 + q 2 ) - 3 / 2 . Each Frm’s marginal cost is constant and equal to c> 0. (a) ±ind expressions for the Cournot equilibrium price, total quantity, and proFt (as functions of c ). (b) Verify that as c increases, each Frm’s proFt increases. What is the eco- nomic intuition for this? Question 2 There are two goods, whose quantities are denoted by q 1 , q 2 and prices by p 1 , p 2 . The demand functions are q 1 =2 - p 1 + kp 2 ,q 2 =2+ 1 - p 2 . Here k is an algebraic constant (parameter) whose value is somewhere in the range - 1 <k< 1. Each good is produced by one Frm. The marginal cost of production of each good is constant and equal to 1. (a) ±or what range of possible values of k are the two goods substitutes? When are they complements? (b) Obtain expressions for the proFts Π 1 and Π 2 of the two Frms in terms of their prices (and the constant k ).
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This note was uploaded on 04/07/2008 for the course ECO 310 taught by Professor Stephene.morris during the Fall '08 term at Princeton.

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ps7 - ECO 310, Fall 2007 Problem Set 7: Oligopoly Due in...

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