# PS7 - ECN 713 Spring 2010 Natalia Kovrijnykh Problem Set 7...

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ECN 713 Spring 2010 Natalia Kovrijnykh Problem Set 7: Due on Tuesday, April 27, in class (100 points total) Lucas and Prescott (1974). 1. [15 points] Consider the operator corresponding to the Bellman equation we studied in class: T ( v ) ( x; z ) = max f ( x; z ) + min ± Z v ( x; z 0 ) Q ( z; dz 0 ) ±± . Show that T is a contraction. 2. [60 points] Let the island economy we studied in class have a productivity shock that takes on two possible values, f z L ; z H g with 0 < z L < z H constant from one period to another with probability ² 2 ( : 5 ; 1) , and its productivity changes to the other possible value with probability 1 ² . These symmetric transition probabilities imply a stationary distribution where half of the islands experience a given z at any point in time. Let N labor force has two possible values, f x 1 ; x 2

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PS7 - ECN 713 Spring 2010 Natalia Kovrijnykh Problem Set 7...

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