Introduction to Economic Analysis
Fall 2004
Midterm Exam: November 15
Time: 1 hour and 15 minutes.
Try to answer all questions.
Good luck!
Question 1 (30 points)
Consider a two period economy. Agents are all identical, that is, there is one
representative agent. The representative agent is alive at time
t
and
t
+ 1,
and has preferences:
lnx
t
+
βlnx
t
+1
, β <
1
.
This agent is endowed with 10 units of the consumption good at time
t
and
at time
t
+ 1.
There is no inﬂation in this economy,
and hence you can
assume throughout that the price for the good at time
t
is 1.
1. Write down the consumer maximization problem of the representative
agent (call the real interest rate
r
in the budget constraint), ﬁrst order
conditions, and demand functions.
2. Write down the market clearing conditions (that is, feasibility condi
tions) for the whole economy.
3. Solve for the equilibrium interest rate and for the representative agent
equilibrium allocation.
4. Suppose the agent cannot borrow and lend, that is, savings are zero
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 Spring '11
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