Intermediate Microeconomics: A Modern Approach, Seventh Edition

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14.04 Midterm Exam 1 Prof. Sergei Izmalkov Wed, Oct 1 , y t ) for t = 1 , . . . , N be a set of observed choices that satisfy WAPM, let Y I and Y O be the inner and outer bounds to the true production set Y . Let π + ( p ) , π ( p ) , and π ( p ) be pro fi t functions associated with Y O , Y , and Y I correspondingly. (a) Show that for all p , π + ( p ) π ( p ) π ( p ) . (b) If for all p , π + ( p ) = π ( p ) = π ( p ) , what you can say about Y O , Y , and Y I ? Provide formal arguments. (c) For ( p 1 , y 1 ) = ([1 , 1] , [ 3 , 4]) , and ( p 2 , y 2 ) = ([2 , 1] , [ 1 , 2]) construct Y I and Y O (graphically). What can you say about returns to scale in the technology these observations are coming from? Hint: think y = ( x, y ) . t 1. Let ( p 2. Given the production function f ( x 1 , x 2 , x 3 ) = x 1 min { x 2 , x 3 } a striction you have to impose on a ? a (a) Calculate pro fi t maximizing supply and demand functions, and the pro fi t function. What re- (b) Fix Calculate conditional demands and the cost function ( ) y c w , w , y . . 1 2 , y (c) Solve the problem py c ( w 1 , w 2 , y ) max , do you obtain the same solution as in 2 a ? Explain
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