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# ECON 204 summer 2006

By Hector Wright,2014-06-18 00:38
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ECON 204 summer 2006 ...

ECON 204 Fall 2006

INTERMEDIATE MACROECONOMIC THEORY

ASSIGNMENT 2

Answer all questions. Total mark: 40 marks

Question 1: Textbook page 300 Q4. (10 marks)

Question2: Textbook page 300 Q5. (10 marks)

a. The downward sloping line represents the money demand function

D(M/P)?1000?100r. Wit M=1000 and P=2, the real money supply

S(M/P)?500. The real money supply is independent of the interest rate and is,

therefore, represented by the vertical line.

r

S 10 (M/P)

5

D (M/P)

500 1000 M/P

b. We can solve for the equilibrium interest rate by setting the supply and demand

for real balances equal to each other: 500=1000-100r, so r=5. Therefore, the

equilibrium real interest rate equals 5 percent.

c. If the price level remains fixed at 2 and the supply of money is raised from 1000

to 1200, then the new supply of real balances S(M/P) equals 600. We can solve

Sfor the new equilibrium interest rate by setting the new (M/P) equal to

D(M/P): 600=1000-100r, so r=4. Thus, increasing the money supply from 1000

to 1200 causes the equilibrium interest rate to fall from 5 percent to 4 percent.

d. To determine at what level the central bank should set the money supply to raise

DSthe interest rate to 7 percent, set (M/P)(M/P) equal to : M/P=1000-100r.

Setting the price level at 2 and substituting r=7, we find: M=600. For the central

bank to raise the interest rate from 5 percent to 7 percent, it must reduce the

nominal money supply from 1000 to 600.

Question 3: Textbook page 325 Q8. (10 marks)

a. The analysis of changes in government purchases is unaffected by making money

demand dependent on disposable income instead of total expenditure. An increase

in government purchases shifts the IS curve to the right, as in the standard case.

The LM curve is unaffected by this increase. Thus, the analysis is the same as it

was before.

R LM IS 2

IS 1

Y1 Y2 Y

b. A tax cut causes disposable income Y-T to increase at every level of income Y.

This increases consumption for any given level of income as well, so the IS curve

shifts to the right, as in the standard case. If money demand depends on

disposable income, however, then the tax cut increases money demand, so the LM

curve shifts upward. Thus, the analysis of a change in taxes is altered drastically

by making money demand dependent on disposable income. As shown in the

figure, it is possible for a tax cut to be contractionary.

r

LM 2

LM 1

IS 2

IS 1

Y2 Y1 Y

Question 4: Textbook page 324 Q4. (10 marks)

a. The IS curve represents the relationship between the interest rate and the level of

income that arises from equilibrium in the market for goods and services. That is, it

describes the combinations of income and the interest rate that satisfy the equation

Y=C(Y-T)+I(r)+G. If investment does not depend on the interest rate, then nothing in the

IS equation depends on the interest rate; income must adjust to ensure that the quantity of

goods produced, Y, equals the quantity of goods demanded, C+I+G. Thus, the IS curve is

vertical at this level, as shown below:

IS LM

r

Y

Monetary policy has no effect on output, because the IS curve determines Y. Monetary

policy can affect only the interest rate. In contrast, fiscal policy is effective: output

increases by the full amount that the IS curve shifts.

b. The LM curve represents the combinations of income and the interest rate at

which the money market is in equilibrium. If money demand does not depend on

the interest rate, then we can write the LM equation as M/P=L(Y). For any given

level of real balances M/P, there is only one level of income at which the money

market is in equilibrium. Thus, the LM curve is vertical, as shown below:

IS LM

r

Y

Fiscal policy now has no effect on output; it can affect only the interest rate. Monetary

policy is effective: a shift in the LM curve increases output by the full amount of the shift.

c. If money demand does not depend on income, then we can write the LM equation

as M/P=L(r). For any given level of real balances M/P, there is only one level of

the interest rate at which the money market is in equilibrium. Hence, the LM

curve is horizontal, as shown below:

IS LM1 r

LM 2

Y

Fiscal policy is very effective: output increases by the full amount that the IS curve

shifts. Monetary policy is also effective: an increase in the money supply causes the

interest rate to fall, so the LM curve shifts down.

d. The LM curve gives the combinations of income and the interest rate at which the

supply and demand for real balances are equal, so that the money market is in

equilibrium. The general form of the LM equation is M/P=L(r,Y). Suppose

income Y increases by \$1. How much must the interest rate change to keep the

money market in equilibrium? The increase in Y increases money demand. If

money demand is extremely sensitive to the interest rate, then it takes a very small

increase in the interest rate to reduce money demand and restore equilibrium in

the money market. Hence, the LM curve is nearly horizontal, as shown below: 1 r IS LM

Y

An example may make this clearer. Consider a linear version of the LM equation:

M/P=eY-f* r. Note that as f gets larger, money demand becomes increasingly sensitive to the interest rate. Rearranging this equation to solve for r, we find r=(e/f)Y-(1/f)(M/P). We

want to focus on how changes in each of the variables are related to changes in the other

variables. Hence, it is convenient to write this equation in terms of changes: ?r=(e/f) ?Y-

(1/f) ?(M/P). The slope of the LM equation tells us how much r changes when Y changes,

holding M fixed. If ?(M/P)=0, then the slope is ?r/?Y=(e/f). As f gets very large, this

slope gets closer and closer to zero.

If money demand is very sensitive to the interest rate, then fiscal policy is very effective:

with a horizontal LM curve, output increases by the full amount that the IS curve shifts.

Monetary policy is now completely ineffective: an increase in the money supply does not

shift the LM curve at all. We see this in our example by considering what happens if M

increase. For any given Y (so that we set ?Y=0), ?r/?(M/P)=(-1/f); this tells us how

much the LM curve shifts down. As f gets larger, this shift gets smaller and approaches

zero. (This is in contrast to the horizontal LM curve in part (c), which does shift down.)

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