Econ 387 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 ) + β 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 β i = β (so that preferences are identical). Show that the equilibrium
interest rate can be expressed as R∗ = Y2 /(βY1 ), 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 < θ < 1
of the population has an endowment (y1 , 0), while the remaining fraction (1 − θ) 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 θ.
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 their debts). What are the welfare implications of such a
legislation and how do you think this legislation will affect future (i.e., beyond date 2)
financial market transactions? Explain.
6. Is it a good idea for students to go into debt? Explain why the Simon Fraser Student
Society (SFSS) recently banned credit card vendors on campus. Does such a policy
make any sense to you?
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