## Stabilizing Aggregate Demand -- The Role of the Fed (Chapter 14)

Problem 1. Christmas shopping and the demand for money

1. The money demand curve will shift out -- cash for quickly buying last minute gifts is in demand. Do you really want to add to your wait in line while your credit card is verified?
2. With a shift out in the demand for money and no change in money supply, nominal interest rates rise.
3. Nominal rates do not change significantly because the Fed increases the money supply temporarily at Christmas time.

Note that one of the main problems which led to the establishment of the Fed was the sharp and predictable increase in interest rates at harvest time, when farmers would want to borrow money to get their crops to market. Not only farmers, but the rest of the economy, paid the price of not having what was called an "elastic" currency -- one whose supply would be responsive to seasonal changes in demand.

Problem 2. Uma's costs and benefits of holding money
Note that the total cost at 5 percent is always less than the total benefit.
However, the optimal economic decision is based here (as always) on marginal costs and benefits.
Uma will therefore hold \$ 900 in cash when the interest rate is 5 percent; it is at that level that we come closest to satisfying the marginal condition MC = MB .

Money holding Cost at 5 percent MC at 5 percent Total benefit Marginal Benefit
\$ 500 \$ 25 xxxxx \$ 35 xxxxx
\$ 600 \$ 30 \$ 5 \$ 47 \$ 12
\$ 700 \$ 35 \$ 5 \$ 57 \$ 10
\$ 800 \$ 40 \$ 5 \$ 65 \$ 8
\$ 900 \$ 45 \$ 5 \$ 71 \$ 6
\$ 1000 \$ 50 \$ 5 \$ 75 \$ 4
\$ 1100 \$ 55 \$ 5 \$ 77 \$ 2
\$ 1200 \$ 60 \$ 5 \$ 77 \$ 2

Similiar tables should be created for interest rates of 9 percent and 3 percent.

Note that the marginal cost of an extra \$ 100 is always \$ 9 at 9 percent, so the closest one can come to equating marginal cost and marginal benefit (without MC being greater than marginal benefit) is at \$ 700 on the table.
If you are willing to interpolate between the rows of the table, you might suspect that a money holding of about \$ 750 would just about equate marginal cost and marginal benefits.

Likewise, for an interest rate of 3 percent, the MC of an extra \$ 100 is always \$ 3.
Here, MC = MB at a bit above \$ 1000.

Taking the three points together, we could draw up a downward sloping demand schedule for money, with the interest rate on the vertical axis.

Problem 3 -- Shifts in the Demand for Money

1. If the commission charge for selling bonds and stocks drop, they become more liquid -- that is, more easily convertible into money. Hence bonds and stocks are better substitutes for money, and the demand for money will decrease -- less money will be held at any given interest rate.
2. If grocery stores accept credit cards in payment, credit cards become better substitutes for cash in your wallet. Again, the demand curve for money shifts back; the demand for money decreases.
3. If financial investors are more concerned about the risk of stocks, they will find stocks a worse substitute for money than before. Some will prefer to hold money as an asset, and the demand for money will increase .
4. If online banking means you can easily transfer funds between checking and mutual fund investments, mutual fund investments (which are not money) become a better substitute for checking account deposits (which are money). Many will prefer to keep more funds in higher-yielding mutual funds than in their checking account, and the demand for money will decrease .
5. If the economy enters a boom period, money demand will increase along with income. Note that if the money supply does not also increase, nominal interest rates will rise -- which is exactly what usually happens during a boom period.
6. Political instability in developing economies has often gone along with increased demand for U.S. currency -- if you suspect your own currency might become worthless, you would obviously prefer assets denominated in U.S. dollars. If you suspect you may be taking a sudden trip out of your country, a suitcase full of dollars might be especially convenient. A good part of the U.S. money supply -- estimates ran above one-fourth in the late 1980s -- is in fact abroad; and foreign demand for U.S. currency is part of the overall demand for money.

Problem 4 -- The demand for money: algebraic analysis
We are given the following information (I use a star rather than the text bar over a variable to denote the exogenously given variables):

• Demand for money: Md = P ( 0.2 Y - 250 i)
-- note that the interest rate is expressed as a whole number.
• P = 3.0
• Y = 10,000
• Md = 3 ( 0.2 (10,000) - 250 i)
• Md = 6,000 - 250 i
• If i = 4 percent, Md = 6,000 - 1,000 = 5,000 .
Hence if the Fed set the money supply at 5,000, the nominal interest rate would be 4 percent.
• If i = 6 percent, Md = 6,000 - 1,500 = 4,500
Hence if the Fed reduced the money supply to 4,500, interest rates would rise to 6 percent.

Problem 5 -- Pegging the interest rate

This is very similar to the last problem, except that the target for the interest rate is given as 5 percent, and the level of GDP or Y is what changes.
• Demand for money: Md = 0.2 Y - 100 i
• -- note that the interest rate is expressed as a whole number.
• Md = 0.2 Y - 500 if the Fed accomplishes its goal of setting the interest rate at 5 percent.
• Ms = 0.2 Y - 500 will therefore be the target money supply for the Fed.
• If Y = 2000, Ms = 1200 - 100 (5) = 700
• If Y = 3000, Ms = 1500 - 100 (5) = 1,000 .
• If the Federal Reserve set an 8 percent target for the nominal interest rate, the required money supply would be:
• At Y = 2000, Ms = 1200 - 100 (8) = 400
• At Y = 3000, Ms = 1500 - 100 (8) = 700

Problem 6 -- Keynesian equilbrium and Fed policy
Collect the information given into the Keynesian equilibrium equation:

Y = C + I + G + NX

Y = 2,600 + 0.8 Y - 0.8 T + 2,000 - 200 R + 1,800 + 0

Y = 6,400 + 0.8 Y - 0.8 (3000) - 200 R (substituting in taxes and collecting the other numbers)

Y = 4,000 + 0.8 Y - 200 R (subtracting .8 T from autonomous demand)

.2 Y = 4,000 - 200 R (subtracting .8 Y from each side of the equation)

Y = 20,000 - 1,000 R (multiplying through by 5)

Y = 10,000

(if the interest rate is initally 10 percent).
Note that Keynesian equilbrium output is below potential GDP by 2,000.

Problem 7 -- Keynesian equilbrium and Fed policy, continued

Note that the term autonomous consumption means that part of consumption which does not depend on income; in this problem, it is given by the equation:

C0 = 2,600 - 100 R

Note that the Keynesian multiplier in the last question is 5.

Hence if we increase investment and autonomous consumption by 400, we will increase GDP by 2,000.

To increase investment and autonomus consumption, we must decrease interest rates; the investment equation will tell us by how much. Since

C0 + I + G = 2,600 - 100 R + 2,000 - 100 R - 0.8 (3,000) + 1,800

C0 + I + G = 4,000 - 200 R

a reduction of 2 percent in interest rates will increase investment and autonomous consumption by 400.

At interest rates of 10 percent, we have C0 + I + G = 2,000, and GDP or Y is 10,000 (as in the last problem) At interest rates of 8 percent, we would have

C0 + I + G = 4,000 - 200 (8) = 2,400

and Y = 5 (2,400) = 12,000.

The Fed will hit its target GDP by cutting interest rates by 2 percent.

Note that if it does so, we would have:

1. Disposable income = Y - T = 12,000 - 3,000 = 9,000
2. Consumption = 2,600 + .8 DI - 100 R = 2,600 + .8 (9,000) - 100 (8) or
Consumption = 2,600 + 7,200 - 800 = 9,000
3. Household savings = 0, since consumption = disposable income (so where is the money coming from to finance investment? )
4. Investment = 2,000 - 100 R = 2,000 - 100 (8) = 1,200.
5. Taxes - Govt spending = 3,000 - 1,800 = 1,200.
6. Public saving provides the funds necessary to finance private investment in this problem.

Problem 8 -- Fed policy and Government spending
The problem has relevance in a period in which government spending increases substantially, or large tax cuts create a stimulus which place the economy above potential output. While this does not sound bad, it runs the risk of generating inflation -- and in the late 1970s, threatened to generate accelerating inflation. The Fed will respond with monetary tightening and an increase in interest rates to choke off inflation. In the early 1980s, this meant extremely high interest rates and the high interest rates meant:

1. Crowding out of investment

In the problem, we are given (again I treat R as a whole number rather than a decimal):

• C = 14,400 + 0.5 (Y - T) - 400 R
• I = 8,000 - 200 R
• G = 7,000
• NX = -1,800
---------------------------------------------
• AD = 27,600 + 0.5 Y - 4000 - 600 R (note that 0.5 T = 0.5 (8000) = 4000)
• AD = 23,600 + 0.5 Y - 600 R
Hence the economy has the Keynesian equilibrium Y = AD or

Y - 0.5 Y = 23,600 - 600 R

0.5 Y = 23,600 - 600 R

Y = 47,200 - 1200 R (** referred to below)

And the Fed's job is simple: if you want Y at 40,000, you will have to set R at 6 percent .

Suppose government spending increases to 7,600. What will the Fed do if it wants to maintain Y at its equilibrium level of 40,000?

You could rework the problem, but it is simpler to note that with a multiplier of 2, an increase of 600 in government spending will increase Y by 1,200. The Fed, if it wishes to offset the increase, will have to raise interest rates by 1 percent to counter the increase (note that the final version of the Keynesian equilbrium equation above (**) says this algebraically -- when R goes up by 1, Y goes down by 1200).

Hence, in order to counter the impact of expansionary fiscal policy, the Fed will raise interest rates by launching a contractionary monetary policy.

See the beginning of the next chapter for the story of how Paul Volcker applied this policy.

Problem 9 -- The Taylor Rule John Taylor (currently Undersecretary of the Treasury and in one poll a leading candidate to succeed Alan Greenspan) proposed the following simple rule as descriptive of the Fed's reaction function :

R = 1.0 - 0.5 YGAP + 0.5 INFL
where:
• R = REAL rate of interest
Note that the NOMINAL rate will be (by the Fisher relation ) this real rate PLUS INFLATION
• YGAP = (Y* - Y) / Y* as in Okun's law, so that a positive YGAP means the economy is below potential output Y*, and the Fed will cut interest rates to try to stimulate the economy.
• INFL = inflation rate so that with a positive inflation rate the Fed will respond by raising real interest rates.
• the constant term 1.0 is the real interest rate expected if the economy is at potential output and the inflation rate is zero.
Applying the rule is simple, and a few examples will prepare you for the problems:
1. if YGAP = 0 and INFL is 10 percent, the Fed's target real rate will be 6 percent. Note that this means that the NOMINAL rate of interest will be 16 percent (the real rate plus inflation).
2. if YGAP = 0 and INFL is 3 percent, the Fed's target real rate will be 2.5 percent and the target nominal rate 5.5 percent.
3. if INFL = 0 and YGAP = 4, the Fed's target real rate will be -1 percent. It is not possible to do this at zero inflation, but it would be possible to do so by generating inflation in the future. Suppose the current nominal rate is one percent (and at zero inflation is equal to the current real rate). The Fed could generate 2 percent inflation and thereby reduce real rates to minus one percent.
Note that this is not a purely theoretical consideration: Japan has had below normal output for some time, and very low nominal interest rates. Several economists have proposed that the only way out of Japan's recession is precisely to generate enough inflation to ensure negative real interest rates. (See Paul Krugman's book, The Return of Depression Economics ).
4. If INFL = 0 and YGAP = - 4 (so that the economy is overheating), the Fed's target real rate will be 3 percent. Since there is no inflation, this will also be the target nominal rate.
The problems in the text should be worked through; the answers are:

Problem YGAP INFL Target
REAL rate
Target
NOMINAL rate
a -1 4 3.5 7.5
b 2 2 1.0 3.0
c 0 6 4.0 10.0
d 5 2 -0.5 1.5

Note that the text language "expansionary gap" translates into a negative number for YGAP.
Note again that the nominal target rate is the real target plus the rate of inflation.
In the final row, note that to get a negative real interest rate, the Fed would have to set a target for the nominal rate below the rate of inflation.