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Course: ECON 306, Fall 2009
School: Sveriges...
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387 Econ Spring 1998 Assignment 3 1. Consider an economy consisting of N individuals with preferences for time-dated consumption given by: u(c1i , c2i ) = ln(c1i ) + i ln(c2i ) for i = 1, 2, ..., N. Each individual has a time-dated endowment (y1i , y2i ) and can borrow/lend freely at the (gross) real interest rate R. Solve for each person's desired saving function sD . i 2. For the economy above, solve for the...

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387 Econ Spring 1998 Assignment 3 1. Consider an economy consisting of N individuals with preferences for time-dated consumption given by: u(c1i , c2i ) = ln(c1i ) + i ln(c2i ) for i = 1, 2, ..., N. Each individual has a time-dated endowment (y1i , y2i ) and can borrow/lend freely at the (gross) real interest rate R. Solve for each person's desired saving function sD . i 2. For the economy above, solve for the equilibrium rate of interest R . How would R react to a shock that increases y2i for at least some (not necessarily all) individuals? Explain. 3. Assume now that i = (so that preferences are identical). Show that the equilibrium interest rate can be expressed as R = Y2 /(Y1 ), where Yj denotes real per capita GDP. Does your answer to the previous question change? (Note that in this case, the equilibrium interest rate does not depend on the distribution of income). 4. Continue to assume identical preferences. Assume now that a fraction 0 < < 1 of the population has an endowment (y1 , 0), while the remaining fraction (1 - ) has an endowment (0, y2 ). Write down the desired saving functions for these two groups of people. Call the former `savers' and the latter `borrowers.' What do you think motivates these labels? Derive an expression for the equilibrium interest rate and explain how it depends on . 5. Consider the economy described in question 4. Imagine now that at the beginning of date 2, the government announces legislation allowing debtors to declare bankruptcy (allowing them to discharge t...

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