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TEORIA Y POLITICA MONETARIA, SPRING 2000; INSTRUCTOR: MARCO DEL NEGRO
Midterm Exam
Rules:
- you are not allowed to consult any notes or books
- you are not allowed to talk to each other
- any infraction of these rules will negatively
affect your grade in the exam by at least one point
- the exam will last 1 hour and 20 minutes
- please write your name in every sheet you use
- please hand in only the final version of your answers
- you may use a hand calculator (although there is no need for it)
- you are allowed to answer in Spanish, if you prefer
- the number in square brackets ([.]) are the points assigned to each question,
as well as the estimated amount of time needed to complete the answer (they sum up to 80)
1) [15] Explain why, in general, real money balances enter the indirect utility function in
the Sidrauski-Brock model. Assume that the government, all of a sudden, prevents by law the
use of credit cards. Other things being equal (money supply and output) what happens
to real money balances, and the price level?
2) [15] Express Friedman's rule (the optimal rate of money growth)
and explain it. What would be wrong with a rate of money growth below Friedman's rule ?
3) [25] The household's problem is:
subject to the constraints:
where Mt+1 is the amount of money held by the households at the end of period t, c1t and
c2t represent the consumption of cash and credit goods respectively in period t, pt is
the price of both goods in terms of money, yt represents the endowment of the household at the beginning
of period t, which can be used to produce both cash goods (y1t) and credit goods (y2t),
and Tt represents nominal transfers from the government.
Solve the intratemporal problem and find the indirect utility function. Write the objective function and the
constraints for the intertemporal problem.
4) [35] Consider an economy where the government budget constraint is:
The household solves the problem:
subject to
and
,
where B is some positive number.
Assume that the utility function is of the form:
where
and
are positive numbers, and that:
a) Find equilibrium taxes (
). Discuss whether Friedman's rule is optimal in this economy.
b) Find equilibrium consumption.
Find the equilibrium real money balances as a function of
,
,
and
.
Show that the equilibrium real money balances are a decreasing function of
.
c) The following is a standard specification of the money demand equation:
Show that you can derive this money demand equation from the model you just solved, and find the
values of
and
in terms of the parameters
and
.
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Marco Del Negro
2000-03-16