14.02 Principles of Macroeconomics

Fall 2000

Prof. Ricardo Caballero

Problem Set 3

posted: 9/27

due: 10/11

**Question 1. True or False? Give a brief but careful
explanation.**

(a) (3 points) The IS curve is downward-sloping because a higher interest rate implies lower investment, hence lower production.

(b) (4 points) An appropriate combination of monetary and fiscal policy may lead to an increase of output without changing the interest rate.

(c) (3 points) An expansionary monetary policy shifts both the IS and the LM curve to the right.

**Question 2. IS-LM**

The economy is described as follows.

Money demand: M^{D} =
PY/(10*i)

Money supply: M^{S} =
280

Consumption: C = 50 + 0.5*(Y-T)

Investment: I = 20 - 100*i

Government: G = T = 10

Price level: P = 1

(a) (4 points) Derive and graph the LM curve: the interest rate as a function of (nominal) output.

(b) (4 points) Derive and graph the IS curve: output as a function of the interest rate.

(c) (4 points) Solve for the equilibrium level of output and the interest rate. Illustrate your calculations with a graph as well.

(d) (9 points) Suppose that the government wants to boost the economy, so it decides to increase G by 15. What will be the new level of output, the interest rate and investment? Explain in words and with a graph.

(e) (9 points) Suppose that instead of the fiscal expansion, there is a monetary expansion: money supply goes up to 355. What is the new level of output, investment and the interest rate? Interpret the differences relative to part (d) (in words and with a graph).

**Question 3. Banks and Money Demand.**

Money demand is given by M^{D}=$Y *L(i). Suppose
that consumers want to keep 10% of their total money holdings in cash
(currency), and the rest in checkable deposits. Banks are required to keep
reserves equal to 1/6 of deposits.

(a) (5 points) Write down the demand for bank reserves.

(b) (5 points) Write down the demand for Central Bank Money (H).

(c) (5 points) Write down the equilibrium condition for the money market, both in terms of M (Money) and H (Central Bank, or High-Powered Money). Illustrate both conditions with a graph.

(d) (10 points) What happens to the equilibrium interest rate if people want to hold a larger fraction of their money in cash (because they no longer trust banks)? Explain. Show the effect (graphically) both in terms of M and H. What should the Central Bank do in order to keep the interest rate fixed?

(e) (5 points) What happens to the interest rate if nominal income ($Y) increases? Graph the effect both in terms of H and M. Explain.