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Professor Salyer, Economics 200E, Spring 2000
Economics 200E: Midterm Examination
Directions: Answer all questions. While the details are important, I am most interested in the intuition.
1. Consider a stochastic growth model in which output is a linear function of the beginning of period
capital stock and a random technology shock. That is
ttt
kzy = . The shock follows a two state Markov
process; the transition probability matrix is symmetric with diagonal elements 21>pi . The social
planner chooses sequences for consumption and capital in order to maximize:
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1
1
1
0
1
1
t
tt
c
E
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Given this environment, answer the following questions:
a. Express the maximization problem as a dynamic programming problem. Be explicit in identifying the
state and policy variables.
b. Derive and interpret the associated necessary conditions.
c. Make an educated guess for the form of the policy function describing optimal...

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