14.02 Principles of Macroeconomics

Fall 2000

Prof. Ricardo Caballero

Problem Set 2

posted: 9/20

due: 9/27

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

(a) (3 points) An expansionary open market operation increases the money supply and decreases the interest rate.

(b) (4 points) With higher interest rates people will save more, therefore money demand goes up.

(c) (4 points) Investment always equals private saving.

(d) (4 points) The use of credit cards increases the velocity of money.

**Question 2. The Saving Paradox.**

Consider our standard model of the Goods Market:

C = c_{0} + c_{1} *(Y-T)

G, I and T are fixed

In addition, we assume that the government budget is balanced, so G=T.

(a) (10 points) Argue that an decrease in c_{1 }can
be thought of as an increase in the saving rate. What happens to the
equilibrium level of output if c_{1} decreases?

(b) (10 points) Why is this phenomena called the "Paradox of Saving"? How would you reconcile the output drop you found in part (b) with the common wisdom of higher saving increasing output?

(c) (5 points) What happens to private saving? Explain.

**Question 3. Simple Dynamics in the Goods Market Model**

Consider the following modification of the consumption function:

C_{t}=c_{0 }+ c_{1}*(1/2*Y_{t}+1/2*Y_{t-1})

(a) (5 points) What might be the economic intuition behind this type of consumption function?

(b) (5 points) What does it imply for the effects of a fiscal expansion? (Fiscal expansion is an increase in government spending.) Explain only the main idea, no details or algebra are necessary.

**Question 4. Money Demand and Supply**

(a) (4 points) Explain why money demand is a decreasing function of the interest rate, and an increasing function of nominal income.

(b) (8 points) Suppose that money demand is given by M^{D}
= PY/i, and money supply is M^{S}. Graph money demand and money supply.
Derive the interest rate as a function of the money stock and nominal income.

(c) (8 points) Show the effect of a contractionary open market operation on the interest rate, both with algebra and with a graph. Explain.