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 The homework is individual.
 Students are encouraged to discuss the homework with other classmates as long as they acknowl-edge collaboration and there is no copying.
 Hand in your work at the start of next Tuesday’s class .
 If you want a question to be regraded, please resubmit it to me with a succinct written explanation
of the concerns within 7 days.
 You need to cite your sources. Otherwise, it will be considered plagiarism.

1 The Role of Ination in an OLG Model (55 Points)
Imagine you are trying to model an economy using the OLG framework. You have the following assump-tions
 There is a unique consumption good.
 The agents have the following endowment stream:
Endowment =
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y Young
0 Old
 Population grows at n > 1.
 The utility of the future generations is represented by
ln(c1;t) + ln(c2;t+1) (1.1)
 The initial old have the following utility function
ln(c2;1) (1.2)
 The initial old are given M0 units of at money.
 The central bank has set the rate of growth of the money base at z > 1.
 The scal policy uses the income generated from the creation of money as a lump-sum transfer (at)to the young generation each period. This transfer is valued by the young.
a) Discuss the importance of the assumptions made. (5 points)
b) What is the Social Planner’s Problem? Solve it. (5 points)
c) De ne and solve the competitive equilibrium with changing supply of money. (15 points)
d) Why is the allocation in c) not Pareto optimal? What is the source of the ineciency?. How should
the monetary policy change to achieve Pareto optimality? (15 points)
e) Find the ination rate for this economy in the stationary equilibrium. What explains it? (15 points)
2 Monetary Policy and the Zero Lower Bound (45 points)
The following article discusses a potential solution to the Zero Lower Bound problem of monetary policy.

a) Explain the Zero Lower Bound (ZLB) problem of monetary policy and its importance. (5 points)
b) Plot the federal funds rate upper and lower limits for all available periods. Was the economy in the US limited by this issue during the nancial crisis? (5 points)
c) How did the FED overcome this problem? (10 points)
d) What other solutions besides the one presented in the article exist to deal with the ZLB problem?
(12.5 points)
e) De ne the lower long-run equilibrium real interest rate and explain its determinants. Should economist
expect a shift to a permanently lower long-run equilibrium interest rate? (12.5 points)
Note: Remember to cite your sources.
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