Title

Northeastern University

University College

Economic Principles II November 18, 1994

ECN 4116 Fall 1994

Indicative Solution to Problem Set #2

1. Cotractionary monetary policy, also known as tight money policy, refers to reducing the stock of money supply in the economy in order to reduce the aggregate demand. Such a policy is preferred when an economy is overheating at or above the full-employment level with high inflation. The Fed can sell securities to public, business firms or the banking system, or increase the required reserve ratio to demand deposits, or increase discount rates and federal fund rates.

Now I leave it on you, to show Fed carries out an expansionary policy.

Answering (a), (b) and (c) requires a bit more information.

Notes of Federal Reserve Banks, also considered as high power money, can be kept in two different forms; as cash balance held by public or as a reserve money held by the banking system. If the excess reserve is zero, then the stock of money is divided between currency and reserves. Therefore total stock of money supply in the economy at any point of time is a multiple of high power money, which can be expressed in the following formula (If you are interested in derivation of the formula please see me or look at page 412 of Macroeconomics 4th ed. by R. Dornbush and S.Fisher).

Where

M = Stock of money in the economy

H = Stock of high power money at a point of time

cu = Ratio of currency held by people to demand deposit

re = required reserve ratio of the banking system

The term (1+cu)/(cu+re) on the right hand side of equation (1) is the money multiplier, when people held a part of high power money in cash balances and when commercial banks keep another part as reserves that are enough to satisfy contingent cash demand from their customers.

A simple way to derive above formula is following.

Money stock (M) consists of two components, currency held by people (CU) and demand deposit in the banking system (DD):

M = CU + DD ..............(2)

Similarly the high power money can be decomposed into two parts, currency held by people (CU) and required reserve of the banking system (RR).

H = CU + RR (3)

Dividing equation (2) by (3) we get

Dividing both numerator and denominator on the right hand side by DD we get

Now multiplying both sides by H we get

Answer to 1(a).

Given this formula, the Fed can change money supply (M) by changing either re or H, or people's can also affect money supply by changing cu.

Given that cu = 25 percent, and re = 20 percent; the multiplier (1+cu)/(cu+re) = (1.25)/(.45) = 2.78.

If H = 10 millions, the condition of zero excess reserve implies that M= (2.78)*10 = 27.8 millions.

Now the Board of Governers of the Fed wants to reduce money supply by 2 millions by changing reserve requirement.

This implies desired money stock will be 25.8 millions. Given H = 10. cu = .25, we can solve for re that is consistent with the changed money supply. Notice that changing re means also changing the money multiplier.

This means to reduce the stock of money by 2 millions the Fed should increase the reserve requirement ratio to 23.45 percent. This is valid for any size of H, as far as H and M are related by the multiplier we derived above.

b) Reducing $2 million by an open market operation is very simple. The Fed will sell securities worth 2 millions to the public or the banking system. If the Fed buys from the public, currency in circulation will be diminished by 2 millions. If Fed buys from the banking system it will reduce the reserves of the banking system in exchange of the securities to the banks. The composition of assets of commercial banks changes; they will have more securities and less reserves. In both of these transaction high power money changes by 2 millions. Recall that increased supply of bonds will reduce its price which in turn causes a rise in the rate of interest on those bonds.

c) To expand money supply by 2 million dollars the Fed should reduce the required reserve ratio. How much change in re is required. Again use the above formula.

Therefore, the Fed should reduce the required reserve ratio to 16.95 percent to increase the money supply by 2 millions.

If the Fed operates the open market operation to increase money supply by $2 millions, it should buy $2 million worth of securities from the public in exchange of currency or reserves. An increased demand for bonds will increase bond prices, then the interest rate is likely to decline.

2. Construct a table of consolidated balanced sheet of commercial banks and the Federal Reserve System.

Refer to the following table to answer (a), (b) and (c).

Consolidated balance Sheet of Commercial Banks

Assets

(1)

(2)

(3)

Liabilities

(1)

(2)

(3)

Reserves

$33

$34

$30

$35

Demand Deposits

$150

$147

$150

Securities

Loans from Fed

Loans

Consolidated Balance Sheet of the Federal Reserve Banks

Assets

(1)

(2)

(3)

Liabilities

(1)

(2)

(3)

Securities

$60

$57

$62

Reserve of Comm Banks

$33

$34

$30

$35

Loans to Com. Banks

Treasury Deposits

Federal Reserve Notes

d) Money creating potential of the banking system increases by $5 ($1*5) billion in (a); decreases by $12 billions in (b) Note that the sale of $3 billion worth of bonds to public reduced the demand deposits by $3 billion, thus freeing $0.6 billion of reserves. Three billion dollars - $0.6 billion = $2.4 billion and this times money multiplier of 5 = $12 billion); and increases by $10 billion ($2*5) in (c).

In a closed economy, which is above the full employment level (classical range in AS) a reduction in AD might lower the price level but not the output and employment in the economy. However, if the ratchet effect works, then aggregate supply curve will move upward, lowering the level of output and employment at the higher price level.

In an open economy tight money policy at home might cause an increased inflow of foreign funds because of higher domestic rate of interest. This will lead to appreciation of dollar, reducing the foreign demand for US goods (exports). Similarly imports at home may increase as the foreign goods become relatively cheaper due to an appreciation of the dollar. Final result would be an increase in the trade deficit.

5. The best way to answer this question is to present graphical exposition of Keynesian, Monetarist and Rational Expectation approaches, as we discussed in the class.

In Keynesian model an increase in AD lead to higher level of output and employment and no increase in prices. In monetarist model an expansion in AD will have a small effect in income and output and a greater impact on prices as the aggregate supply curve is relatively steeper. In rational expectation approach any increase in AD will directly result in higher prices as the prices and wages adjust immediately after an increase in AD. Output and employment remain at the full employment level.