# PS4 - Problem Set 4 Microeconomics Spring 2008 1. An...

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Problem Set 4 Microeconomics Spring 2008 1. An economy consists of three types of consumers: 1, 2 and 3. A consumer of type i has the utility function U i ( x i ; y i ) = A i x i i y 1 i i and has income I i ; where i = 1 ; 2 ; 3 . All consumers face the same prices p x and p y for goods X and Y; respectively. (Note: x i and y i are the amounts of X and Y consumed by the type i consumer.) (a) Set up the type i (b) Construct the Lagrangian function and set up the corresponding unconstrained problem. (c) What are the necessary FOC s for maximization? (d) Interpret and express the FOC s as the relevant economic conditions. (e) Solve these conditions to obtain the formulas for the demand functions x ± i ( p x ; p y ; I i ) and y ± i ( p x ; p y ; I i ) : (f) Suppose, that there are n i number of consumers of the i th type. If 1 = 0 : 5 2 = 0 : 4 3 = 0 : 2 and I 1 = 100 , I 2 = 200 , I 3 = 300 then, express aggregate X ± i

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## This note was uploaded on 02/15/2011 for the course ECON 101 taught by Professor Womer during the Spring '08 term at NYU.

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PS4 - Problem Set 4 Microeconomics Spring 2008 1. An...

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