Solution Midterm Thursday

Solution Midterm Thursday - ECO 310 - Fall 2008...

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Unformatted text preview: ECO 310 - Fall 2008 Microeconomic Theory - A Mathematical Approach midterm 10/23 - Answer Key Question 1: (a)(10 points) L ( x,y, ) = ( x- x )( y- y ) + ( I- P x x- P y y ) FONCS: y- y = P x x- x = P y This implies that y- y x- x = P x P y . Substitute y = y + P x P y ( x- x ) into the budget constraint, we have x = I- P y y + P x x 2 P x ,y = I + P y y- P x x 2 P y Since I P x x + P y y , x x and y y . (b)(5 points)By the duality between the utility maximization and cost minimization problems, we get the same relationship between y and x from the first order conditions. Substitute y into ( x- x )( y- y ) = u , we have x c = r uP y P x + x ,y c = y + s uP x P y (c)(10 points)We need to verify the equation dx c dP y = dx dP y + y dx dI dx c dP y = 1 2 q u P x P y , dx dP y =- y 2 P x , dx dI = 1 2 P x , so RHS= y- y 2 P x = I- P x y- P x x 4 P x P y . By I = e ( P,u ) = P x x c + P y y c , we have I = P x x + P y y + 2 p uP x P y . Substitute I into RHS, we get RHS=LHS....
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This note was uploaded on 01/15/2011 for the course ECO 310 at Princeton.

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Solution Midterm Thursday - ECO 310 - Fall 2008...

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