homework2 - (5) Problem 2.4, SLP p. 15 2 Quadratic Utility...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ECO 475 Homework 2 Jay H. Hong Due: Monday, Sep 20, 2010 1 Consider the following problem. max { c t ,k t +1 } t =0 X t =0 β t u ( c t ) subject to an initial k 0 and a law of motion for capital k t +1 = F ( k t ) + (1 - δ ) k t - c t . (1) Write down the Bellman equation. Now assume that u ( c ) = log( c ) ,F ( k ) = Ak α where A > 0 (0 , 1) (0 , 1) and δ = 1. (2) Let V 0 ( k ) = 0 and derive V 1 ( k ) ,V 2 ( k ) ,V n ( k ). (3) Derive V ( k ). (by n → ∞ ) (4) Let’s make a guess on the value function V ( k ) = P log( k ) + Q and solve for P,Q by “guess and verify”. Compare the result with (3).
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (5) Problem 2.4, SLP p. 15 2 Quadratic Utility and Linear Technology Assume that F ( k ) = Ak and u ( c ) = a + bc + dc 2 where b > 0 and d < 0. Solve for the closed form solutions for V ( k ) and decision rule. Explain why c is constant. 3 Metric Space Problem 3.3 and 3.4 from SLP p. 45 4 Completeness of ( C ,d ) Show that C the set of bounded continuous real-valued functions with the sup norm d is a complete metric space. 1...
View Full Document

This note was uploaded on 09/06/2011 for the course ECO 475 taught by Professor Hong during the Fall '07 term at Rochester.

Ask a homework question - tutors are online