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Unformatted text preview: ECN 713 Spring 2010 Natalia Kovrijnykh Problem Set 1: Due on February 2 in class (100 points total) 1. [10 pts] Prove the contraction mapping theorem that we stated in class. 2. [15 pts] Assume that X = R + ; & ( x ) = R and F is C 2 , F x & ; F y ¡ ; and strictly concave. Show that if F xy & then g is increasing in x . (Hint: Graph F y ( x; y ) and &v ( y ) as functions of y .) 3. [15 pts] Consider the problem of an agent with wages w that saves with safe gross rate of return (1 + r ) : The budget constraint is y + c = x (1 + r ) + w where x is the beginning of period wealth, and y are savings. Let (1 + r ) & = 1 ; w > ; and the utility function U ( c ) be strictly increasing, bounded, strictly concave, and C 2 . Write down the Bellman equation for this problem. Show that for all x 2 R + ; c ( x ) = w + rx; g ( x ) = x; v ( x ) = U ( w + rx ) 1 ¢ & : 4. [15 pts] Consider the neoclassical growth model in which the representative household values leisure. The per period utility function is denoted byvalues leisure....
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 Spring '10
 natalia
 Economics, Recursion, Utility, Neoclassical economics, Convex function

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