I = 1,000 - 4,000R Where R = the Interest Rate

1. Recall:

C = 250 + .8Yd where Yd = disposable income

I = 1,000 - 4,000r where r = the interest rate

G = T = 100

Ms = 500 is money supply

MD = 900 - 2,000r is money demand where r is the interest rate

The required reserve ratio = 10%

The economy is experiencing no inflation and banks hold no excess reserves, and no currency is held by households or businesses.

a. The equilibrium interest rate is determined by setting MD = MS.
Therefore: [900 - 2,000(r*)] = 500, so that r* = .20 = 20%

b. Calculate the equilibrium level of investment.
At r* = 20%, I = 1,000 - 4,000(.2) = 200

c. Calculate the equilibrium level of national income.
Equilibrium national income is given by:

AE = C + I + G + X - M

AE = 250 + .8(Y-100) + 200 + 100 + 0 - 0

AE = 550 + .8Y - 80

In equilibrium Y = AE

Y* = 470 + .8Y*

.2Y* = 470

Y* = 2,350

d.In this model the government multiplier is simply 1/(1-mpc) = 5. Aggregate Y* is currently 2,350. To increase it to $4000 we need to increase equilibrium income by $1650 (which is 4000-2350). We know: Y* = G * KG. So, we have 1650 = G*5 which means G must be increased by 330.

e.Want to get Y* = $4000 via monetary policy? Start with the investment multiplier. In this model it is simply 1/(1-mpc) = 5. So, we quickly see that the increase in investment must be $330 to a level of $530. For investment to be at $530 we need to look at the investment function and see what interest rate is consistent with investment being $530. So: $530 = 1,000 - 4000(r) which implies that r = .1175 = 11.75%. Now use the money demand equation to see what level of money is demanded at r = .1175. So: MD = 900 - 2000(.1175) = 665. Money supply is currently at $500. We need it to be $665. It must be increased by $165. The money multiplier in this economy is 1/.10 = 10. So to generate an additional $165 in money we need to increase excess reserves by $16.5. The FED can do this by buying $16.5 worth of securities.

f.(i) In the simple fiscal policy here, we see that the role of G increases and we will have a larger budget deficit if we do not raise taxes. The size of the government is larger as a result of this policy.

(ii) With the simple monetary policy note that it is private investment that is stimulated by the government changing the money supply, changing the interest rate and the interest rate changing the level of I. The role of the government is not as direct and the role of G in GDP is not increased.

1. For the most effective monetary policy, hope that money demand and money supply are both rather insensitive to interest rates and that investment is very interest sensitive. Just the opposite set of sensitivities is best for fiscal policy to work best. In this case you want very sensitive money demand and supply w.r.t. the interest rate and a very interest insensitive planned investment function.

1. If everyone saves and not much else changes in the economy, then aggregate desired expenditure decreases and causes a decrease in the equilibrium level of national income. If you increase savings and thereby increase demand deposits thereby increasing the money supply and lowering the interest rates in the economy, you may stimulate investment and the increase in investment might overpower the reduction in consumption leading to an increase in equilibrium level of national income. Also, if the investment decisions lead to more productive plants and factories, you may even see a larger increase in equilibrium level of national income.

1. Consider the following open economy. The tables give you economic relationships in billions of dollars. Note: There is no inflation; the current interest rate is 15% and full employment national income, YFE = $700 billion.

a.The equilibrium level of national income, Y* = $600.

b.What is the:

(i) marginal propensity to consume out of Y? mpc=.90

(ii) marginal propensity to invest out of Y? mpi = 0

(iii) marginal propensity to export out of Y? mpx = 0

(iv) marginal propensity to import out of Y? mpm = .10

(v) marginal propensity to government spend out of Y? mpg = 0

c.What is the:

(i)equation representing the government multiplier? KG = 1/(1-mpc+mpm)

(ii)equation representing the investment multiplier? KI = 1/(1-mpc+mpm)

(iii)numerical value of these multipliers? They both are equal to 5

d.To reach full employment income = 700, the administration should increase G by $20.

e.The FED must buy bonds to lower the interest rate and stimulate investment. It must generate a $20 increase in investment. Investment must go from 40 to 60. To do that the interest rate must be lowered from 15% to 5%. Note that this is as far as you can get with numbers since you were not given the money demand equation, so you can not determine how much in bonds the Fed has to buy in order for the interest rate to fall the required amount.

1. a. If the required reserve ratio = 20%, then the money multiplier = 1/.20 = 5 and we know that: expansion of the money supply = (excess reserves * the money multiplier). Therefore $2 million = ER * 5 which implies that $400,000 in excess reserves must be created to expand the money supply by $2 million given a required reserve ratio of 20%. Thus, $.4 million in government bonds must be bought to generate a $2 million dollar increase in the money supply.

b. The Feds new balance sheet would be as follows:

FED’s Assets FED’s Liabilities

Gold and Foreign Exchange 10,000 Federal Reserve Notes in Circulation 15,000.4

U.S. Govt. Securities 10,000.4 Banks Deposits 5,000

c. and d.

1. Multiple Choice and simple (no explanation) True/False:

1. A monetary system in which the price of gold in terms of paper money is fixed by the government is said to on the:

A. money multiplier system.

B. Federal Reserve System.

C. European Monetary System.

D. gold standard.

2. If the required reserve ratio falls, the money multiplier rises.

A. True

B. False

3. Which of the following is not considered part of the assets of a bank?

A. Reserves held at the Fed.

B. Loans made to individuals and firms.

C. Bonds held by the bank.

D. Deposits made by individuals and firms.

4. The money multiplier is typically

A. less than 0.

B. between 0 and 1.

C. equal to 1.

D. greater than 1.

5. The set of actions taken by the government that affect the money supply and the interest rate is called.

A. fiscal policy.

B. monetary policy.

C. open market operations.

D. monetarist policy.

6. The ______is the rate that commercial banks are charged when they borrow short term from the Federal Reserve Bank.

A. federal funds rate

B. discount rate

C. interest rate

D. market rate

7. How many Federal Reserve Banks are there in the United States?

A. 1

B. 6

C. 10

D. 12