homework8 2009 - born at t therefore receive (1 + r t +1 )...

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ECN/APEC 6000/7230 Fall 2009 Homework 8 Due 12/3/09 1) Show that with Cobb-Douglas production and CRRA utility that the capital map k t +1 ( k t ) that arises under general equilibrium in the two-period OLG model is always strictly increasing in k . 2) Consider the two-period OLG model with g = 0, f ( k ) = k α , and u ( c ) = ln c . We consider two different Social Security programs. i) Pay-as-you-go (PAYGO): The government taxes each young individual an amount T and uses the proceeds to pay benefits to old individuals, who receive (1 + n ) T . ii) Fully funded: The government taxes each young person an amount T and uses the proceeds to purchase capital, which finances benefits when the person is old. Individuals
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Unformatted text preview: born at t therefore receive (1 + r t +1 ) T when they are old. a) How does k t +1 ( k t ) change under the PAYGO and fully funded programs? b) How does the balanced-growth k * change under the PAYGO and fully funded programs? c) If the economy is initially on a balanced growth path that is dynamically efficient, how does a marginal increase in T under the PAYGO plan affect the welfare of current and future generations? What happens if the initial balanced growth path is dynamically inefficient? You may assume for small changes in T that the change on factor prices is small enough that it can be neglected in this welfare analysis....
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This note was uploaded on 01/09/2011 for the course ECON 7230 taught by Professor Feigenbaum during the Spring '10 term at Utah Valley University.

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