Midterm 2014 Solutions

S c the slutsky equation in question is x1 xh 1 p2 p2

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Unformatted text preview: ky equation in question is @x1 @xh 1 = @p2 @p2 1 x2 @ x1 : @y Given the results from (a) and (b) and that p1 = 1=2, we have @x1 = @p2 164 y ; (164 =2 + p2 )2 @xh 1 = 0; @p2 x2 = y ; 4 =2 + p 16 2 @x1 164 =4 : @y 16 =2 + p2 Obviously, the Slutsky equation does hold here. Solution 2 [All students get full credit for this question as it is outside the coverage.] See notes 11, pp. 6-11. Solution 3 (a) Given Roy’ identity, the group-1’ Marshallian demand for good 1 is s s x1 = 1 x2 = 1 @ v1 (p; y) =@p1 = @v1 (p; y) =@y @ v2 (p; y) =@p1 = @v2 (p; y) =@y 1=p1 y = 2=y 2p1 2 2 y =p1 y = 2y=p1 2p1 Then the aggregate demand is Qd = 40 200 8000 100 + 60 = : 2p1 2p1 p1 (b) The …rm’ pro…t-maximization problem is given by s max p1 q q c(q ) = p1 q q2: The …rst-order condition is p1 2q = 0: Solving the above gives the output supply function q (p2 ) = p1 =2 and the pro…t function is p2 =4. 1 To solve for the price, use the market-clearing condition: 8000 p1 = Qd = Qs = 160 : p1 2 Thus, the price is p1 = 10. (c,i) The equilibrium price should be p1 = 2q . This is a direct result of the theorem that says an equilibrium in the Bertrand competition is when at least two …rms charge the same price equal to the marginal cost. (c,ii) Given p1 = 4000, we have q = p1 =2 = 2000. The market-clearing condition is 8000 8000 = = Qd = Qs = 2000n: p1 4000 2 Thus n = 1=1000. 3...
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This document was uploaded on 03/26/2014 for the course ECON 310 at Queens University.

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