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Professor Salyer, Economics 200E, Spring 01
Midterm Examination
Directions: Answer all questions. The questions are equally weighted.
1. Consider a representative agent, 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 depreciation
rate of capital is 100%. The shock follows an n-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 consumption.
Sho...

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