Baumol & Blinder MACROECONOMICS (11th ed)

lower the equilibrium level of GDP, depending on how much spending and taxing it does.

MULTIPLIERS FOR TAX POLICY

Now let us turn our attention, as in the chapter, to multipliers for tax changes. They are more complicated than multipliers for spending because they work indirectly via consumption. For this reason, we restrict ourselves to the multiplier for fixed taxes, leaving the more complicated case of variable taxes to more advanced courses. Tax multipliers must be worked out in two steps:

1.Figure out how much any proposed or actual changes in the tax law will affect consumer spending.

2.Enter this vertical shift of the consumption schedule in the 45° line diagram and see how it affects output.

To create a simple and familiar numerical example, suppose income taxes fall by a fixed amount at each level of GDP—say, by $400 billion. Step 1 instructs us to multiply the $400 billion tax cut by the marginal propensity to consume (MPC), which is 0.75, to get $300 billion as the increase in consumer spending—that is, as the vertical shift of the consumption schedule.

Next, Step 2 instructs us to multiply this $300 billion increase in consumption by the multiplier— which is 2.5 in our example—giving $750 billion as the rise in GDP. Figure 11 verifies that this result is correct by depicting a $300 billion upward shift of the consumption function in the 45° line diagram and

noting that GDP does indeed rise by $750 billion as a consequence—from $6,000 billion to $6,750 billion.

Notice that the $400 billion tax cut raises GDP by $750 billion, whereas the multiplier effect of the $400 billion increase in government purchases depicted in the chapter in Figure 2 (page 224) raised GDP by $1,000 billion. This is a specific numerical example of something we learned in the chapter. Because some of the change in disposable income affects saving rather than spending, a dollar of tax cut does not pack as much punch as a dollar of G. That is why we multiplied the $400 billion change in taxes by 0.75 to get the $300 billion shift of the C schedule shown in Figure 11.

FIGURE 11

The Multiplier for a Reduction in Fixed Taxes

45°

C1 + I + G + (X – IM )

C0 + I + G + (X – IM )

1.Precisely how a tax change affects the consumption schedule depends on whether fixed taxes or variable taxes are changed.

2.Shifts of the consumption function caused by tax policy are subject to the same multiplier as autonomous shifts in G, I, or X 2 IM.

3.Because tax changes affect C only indirectly, the multiplier for a change in T is smaller than the multiplier for a change in G.

4.The government’s net effect on aggregate demand—and hence on equilibrium output and prices—depends on whether the expansionary effects of its spending are greater or smaller than the contractionary effects of its taxes.

1.Which of the following is considered a fixed tax and which a variable tax?

a.The gasoline tax

b.The corporate income tax

c.The estate tax

d.The payroll tax

2.In a certain economy, the multiplier for government purchases is 2 and the multiplier for changes in fixed taxes is 1.5. The government then proposes to raise both

spending and taxes by $100 billion. What should happen to equilibrium GDP on the demand side?

3.(More difficult) Suppose real GDP is $10,000 billion and the basic expenditure multiplier is 2. If two tax changes are made at the same time:

a.fixed taxes are raised by $100 billion,

b.the income-tax rate is reduced from 20 percent to 18 percent,

will equilibrium GDP on the demand side rise or fall?

1.When the income-tax rate declines, as it did in the United States early in this decade, does the multiplier go up or down? Explain why.

2.Discuss the pros and cons of having a higher or lower multiplier.

In this appendix, we explain the simple algebra behind the fiscal policy multipliers discussed in the chapter. In so doing, we deal only with a simplified case in which prices do not change. Although it is possible to work out the corresponding algebra for the more realistic aggregate demand-and-supply analysis with variable prices, the analysis is rather complicated and is best left to more advanced courses.

We start with the example used both in the chapter and in Appendix A. The government spends $1,300 billion on goods and services (G 5 1,300) and levies an income tax equal to 20 percent of GDP. So, if the symbol T denotes tax receipts,

T 5 0.20Y

Because the consumption function we have been working with is

C 5 300 1 0.75DI

where DI is disposable income, and because disposable income and GDP are related by the accounting identity

DI 5 Y 2 T

it follows that the C schedule used in the 45° line diagram is described by the following algebraic equation:

C 5 300 1 0.75(Y 2 T)

5 300 1 0.75(Y 2 0.20Y)

5 300 1 0.75(0.80Y)

5 300 1 0.60Y

We can now apply the equilibrium condition:

Y 5 C 1 I 1 G 1 (X 2 IM)

Because investment in this example is I 5 900 and net exports are 2100, substituting for C, I, G, and (X 2 IM) into this equation gives:

Y 5 300 1 0.60Y 1 900 1 1,300 2 100 0.40Y 5 2,400

Y 5 6,000

This is all there is to finding equilibrium GDP in an economy with a government.

To find the multiplier for government spending, increase G by 1 and solve the problem again:

Y 5 C 1 I 1 G 1 (X 2 IM)

Y 5 300 1 0.60Y 1 900 1 1,301 2 100 0.40Y 5 2,401

Y 5 6,002.5

Thus, the multiplier is 6,002.5 2 6,000 5 2.5, as stated in the text.

To find the multiplier for an increase in fixed taxes, change the tax schedule as follows:

T 5 0.20Y 1 1

Disposable income is then

DI 5 Y 2 T 5 Y 2 (0.20Y 1 1) 5 0.80Y 2 1

(2)

is the same consumption function we used in Appendix A of Chapter 9.

is the accounting identity relating disposable income to GDP.

is the tax function, where T0 represents fixed taxes (which are zero in our numerical example) and t represents the tax rate (which is 0.20 in the example). Finally, I, G, and (X 2 IM) are just fixed numbers.

We begin the solution by substituting Equations (3) and (4) into Equation (2) to derive the consumption schedule relating C to Y:

C 5 a 1 bDI

C 5 a 1 b(Y 2 T)

C 5 a 1 b(Y 2 T0 2 tY)

Notice that a change in fixed taxes (T0) shifts the intercept of the C schedule, whereas a change in the tax rate (t) changes its slope, as explained in Appendix A (pages 235–237).

Next, substitute Equation (5) into Equation (1) to find equilibrium GDP:

Y 5 C 1 I 1 G 1 (X 2 IM)

Y 5 a 2 bT0 1 b(1 2 t)Y 1 I 1 G 1 (X 2 IM)

[1 2 b(1 2 t)] Y 5 a 2 bT0 1 I 1 G 1 (X 2 IM)

1 Change in Y 5 1 2 b 11 2 t2

In Chapter 9 (page 188, we noted that if there were no income tax (t 5 0), a realistic value for b (the marginal propensity to consume) would yield a multiplier of 20, which is much bigger than the true multiplier. Now that we have added taxes to the model, our multiplier formula produces much more realistic numbers. Approximate values for these parameters for the U.S. economy are b 5 0.95 and t 5 1⁄3. The multiplier formula then gives

which is much closer to its actual estimated value— between 1.5 and 2.

Finally, we can see from Equation (6) that the multiplier for a change in fixed taxes (T0) is

2b

Tax Multiplier 5 1 2 b(1 2 t)

For the example considered in the text and earlier in this appendix, b 5 0.75 and t 5 0.20, so the formula gives

1 2 0.7511 2 0.202 5 1 2 0.7510.802

According to these figures, each $1 increase in T0 reduces Y by $1.875.

C 5 120 1 0.80DI I 5 320

G 5 480 (X 2 IM) 5 280

T 5 200 1 0.25Y

Find the equilibrium level of GDP. Next, find the multipliers for government purchases and for fixed taxes. If full employment comes at Y 5 1,800, what are some policies that would move GDP to that level?

2.This question is a variant of the previous problem that approaches things in the way that a fiscal policy planner might. In an economy whose consumption function and tax function are as given in Test Yourself Question 1, with investment fixed at 320 and net exports fixed at 280, find the value of G that would make GDP equal to 1,800.

C 5 0.90DI I 5 100

G 5 540 (X 2 IM) 5 240

T 5 2 1⁄3 Y

a.Find equilibrium GDP and the budget deficit.

b.Suppose the government, unhappy with the budget deficit, decides to cut government spending by precisely the amount of the deficit you just found. What actually happens to GDP and the budget deficit, and why?

4.(More difficult) In the economy considered in Test Yourself Question 3, suppose the government, seeing that it has not wiped out the deficit, keeps cutting G until it succeeds in balancing the budget. What level of GDP will then prevail?

ISSUE: WHY ARE BANKS SO HEAVILY REGULATED?

THE NATURE OF MONEY

Barter versus Monetary Exchange

The Conceptual Definition of Money

What Serves as Money?

Other Definitions of the Money Supply

THE BANKING SYSTEM

How Banking Began

Principles of Bank Management: Profits

versus Safety

BANKS AND MONEY CREATION

The Limits to Money Creation by a Single Bank Multiple Money Creation by a Series of Banks

The Process in Reverse: Multiple Contractions of the Money Supply

A run on a bank occurs when many depositors withdraw cash from their accounts all at once.

Banking has long been one of the most heavily regulated industries in America. But the pendulum of bank regulation has swung back and forth.

In the late 1970s and early 1980s, the United States eased several restrictions on interest rates and permissible bank activities. Then, after a number of banks and savings institutions went bankrupt in the 1980s, Congress and the bank regulatory agencies cracked down with stiffer regulation and much closer scrutiny.

Later, the pendulum swung back in the deregulatory direction, with two landmark banking laws passed in the 1990s. Most restrictions on banking across state lines were lifted in 1994, and the once-strict separation of banking from insurance and investment banking was more or less ended in 1999. More recently, the mortgage meltdown that began in 2007 has raised new questions about what further regulations might be needed.

In brief, we have spent decades wrestling with the question: How much bank regulation is enough—or too much? But to answer this question intelligently, we must first address a more basic one: Why are banks so heavily regulated in the first place?

A first reason is something we will learn in the next chapter: that the major “output” of the banking industry—the nation’s money supply—is an important determinant of aggregate demand. Bank managers are paid to do what is best for their stockholders. But as we will see, what is best for bank stockholders may not always be best for the economy as a whole. Consequently, the government does not allow bankers to determine the money supply and interest rates strictly on profit considerations.

A second reason for the extensive web of bank regulation is concern for the safety of depositors. In a free-enterprise system, new businesses are born and die every day; and no one other than the people immediately involved takes much notice. When a firm goes bankrupt, stockholders lose money and employees may lose their jobs. But, except for the case of very large firms, that is about all that happens.

But banking is different. If banks were treated like other firms, depositors would lose money whenever one went bankrupt. That outcome is bad enough by itself, but the real danger emerges in the case of a run on a bank. When depositors get nervous about the security of their money, they may all rush to cash in their accounts. For reasons we will learn in this chapter, most banks could not survive such a “run” and would be forced to shut their doors.

Worse yet, this disease is highly contagious. If one family hears that their neighbors just lost their life savings because their bank went broke, they are likely to rush to their own bank to withdraw their funds. In fact, fear of contagion is precisely what prompted British bank regulators to act in September 2007 when Northern Rock, a bank specializing in home mortgages, experienced a highly publicized run. (See the box “It’s Not Such a Wonderful Life” on page 249.) They first guaranteed all deposits in Northern Rock and later extended the guarantee to all British banks.1

Without modern forms of bank regulation, therefore, one bank failure might lead to another. Indeed, bank failures were common throughout most of U.S. history. (See Figure 1(a).) But since the 1930s, bank failures have been less common. (See Figure 1(b), and notice the sharply different scale.) And they have rarely been precipitated by runs because the government has taken steps to ensure that such an infectious disease will not spread. It has done so in several ways that we will mention in this chapter.

SOURCE: Federal Deposit Insurance Corporation.

Number of Bank Failures

CHAPTER 12

1,200

1,000

800

600

200

0

1915 1920 1925 1930 1935 1940 1945

Year

(a)

FIGURE 1

Bank Failures in the United States, 1915–2007

The most obvious way to trade commodities is not by using money, but by barter—a system in which people exchange one good directly for another. And the best way to appreciate what monetary exchange accomplishes is to imagine a world without it.

Barter versus Monetary Exchange

Under a system of direct barter, if Farmer Jones grows corn and has a craving for peanuts, he has to find a peanut farmer, say, Farmer Smith, with a taste for corn. If he finds such a person (a situation called the double coincidence of wants), the two farmers make the trade. If that sounds easy, try to imagine how busy Farmer Jones would be if he had to repeat the sequence for everything he consumed in a week. For the most part, the desired double coincidences of wants are more likely to turn out to be double wants of coincidence. (See the accompanying cartoon.) Jones gets no peanuts and Smith gets no corn. Worse yet, with so much time spent looking for trading partners, Jones would have far less time to grow corn. In brief:

Money greases the wheels of exchange and thus makes the whole economy more productive.

Barter is a system of exchange in which people directly trade one good for another, without using money as an intermediate step.

Dealing by Wheeling on Yap

Primitive forms of money still exist in some remote places, as this extract from an old newspaper article shows.

Yap, Micronesia—On this tiny South Pacific Island . . . the currency is as solid as a rock. In fact, it is rock. Limestone to be precise.

For nearly 2,000 years the Yapese have used large stone wheels to pay for major purchases, such as land, canoes and permission to marry. Yap is a U.S. trust territory, and the dollar is used in grocery stores and gas stations. But reliance on stone money . . . continues.

Buying property with stones is “much easier than buying it with U.S. dollars,” says John Chodad, who recently purchased a building lot with a 30-inch stone wheel. “We don’t know the value of the U.S. dollar.”

Stone wheels don’t make good pocket money, so for small transactions, Yapese use other forms of currency, such as beer. . . .

stone into large circles. The rest is history. . . .

By custom, the stones are worthless when broken. You never hear people on Yap musing about wanting a piece of the rock.

SOURCE: Excerpted from Art Pine, ”Hard Assets, or Why a Loan in Yap Is Hard to Roll Over,” The Wall Street Journal, March 29, 1984, p. 1.

Money is the standard object used in exchanging goods and services. In short, money is the medium of exchange.

The medium of exchange is the object or objects used to buy and sell other items such as goods and services.

The unit of account is the standard unit for quoting prices.

A store of value is an item used to store wealth from one point in time to another.

Under a monetary system, Farmer Jones gives up his corn for money. He does so not because he wants the money per se, but because of what that money can buy. Now he need simply locate a peanut farmer who wants money. And what peanut farmer does not? For these reasons, monetary exchange replaced barter at a very early stage of human civilization, and only extreme circumstances, such as massive wars and runaway inflations, have been able to bring barter (temporarily) back.

The Conceptual Definition of Money

Under monetary exchange, people trade money for goods when they purchase something, and they trade goods for money when they sell something, but they do not trade goods directly for other goods. This practice defines money’s principal role as the medium of exchange. But once it has become accepted as the medium of exchange, whatever serves as money is bound to serve other functions as well. For one, it will inevitably become the unit of account—that is, the standard unit for quoting prices. Thus, if inhabitants of an idyllic tropical island use coconuts as money, they would be foolish to quote prices in terms of seashells.

Money also may come to be used as a store of value. If Farmer Jones’s corn sales bring him more cash than he wants to spend right away, he may find it convenient to store the difference temporarily in the form of money. He knows that money can be sold easily for goods and services at a later date, whereas land, gold, and other stores of value might not be. Of course, if inflation is substantial, he may decide to forgo the convenience of money and store his wealth in some other form rather than see its purchasing power eroded. So money’s role as a store of value is far from inevitable.

Because money may not always serve as a store of value, and because other commodities may act as stores of value, we will not include the store-of-value function as part of our conceptual definition of money. Instead, we simply label as “money” whatever serves as the medium of exchange.

What Serves as Money?

Anthropologists and historians can testify that a bewildering variety of objects have served as money in different times and places. Cattle, stones, candy bars, cigarettes, woodpecker

scalps, porpoise teeth, and giraffe tails provide a few of the more colorful examples. (For another example, see the box “Dealing by Wheeling on Yap” on the previous page.)

In primitive or less organized societies, the commodities that served as money generally held value in themselves. If not used as money, cattle could be slaughtered for food, cigarettes could be smoked, and so on. But such commodity money generally runs into several severe difficulties. To be useful as a medium of exchange, a commodity must be easily divisible—which makes cattle a poor choice. It must also be of uniform, or at least readily identifiable, quality so that inferior substitutes are easy to recognize. This shortcoming may be why woodpecker scalps never achieved great popularity. The medium of exchange must also be storable and durable, which presents a serious problem for candybar money. Finally, because people will carry and store commodity money, it is helpful if the item is compact—that is, if it has high value per unit of volume and weight.

All of these traits make it natural that gold and silver have circulated as money since the first coins were struck about 2,500 years ago. Because they have high value in nonmonetary uses, a lot of purchasing power can be carried without too much weight. Pieces of gold are also storable, divisible (with a little trouble), and of identifiable quality (with a little more trouble).

The same characteristics suggest that paper would make an even better money. The Chinese invented paper money in the eleventh century, and Marco Polo brought the idea to Europe. Because we can print any number on it that we please, we can make paper money as divisible as we like. People can also carry a large value of paper money in a lightweight and compact form. Paper is easy to store and, with a little cleverness, we can make counterfeiting challenging, though never impossible. (See the box “Remaking America’s Paper Money” above.)

Paper cannot, however, serve as commodity money because its value per square inch in alternative uses is so low. A paper currency that is repudiated by its issuer can, perhaps, be used as wallpaper or to wrap fish, but these uses will surely represent only a small fraction of the paper’s value as money.2 Contrary to the popular expression, such a currency

2 The first paper money issued by the U.S. federal government, the Continental dollar, was essentially repudiated. (Actually, the new government of the United States redeemed the Continentals for 1 cent on the dollar in the 1790s.) This event gave rise to the derisive expression, “It’s not worth a Continental.”

Commodity money is an object in use as a medium of exchange, but that also has a substantial value in alternative (nonmonetary) uses.

Fiat money is money that is decreed as such by the government. It is of little value as a commodity, but it maintains its value as a medium of exchange because people have faith that the issuer will stand behind the pieces of printed paper and limit their production.

literally is worth the paper it is printed on—which is to say that it is not worth much. Thus, paper money is always fiat money.

Money in the contemporary United States is almost entirely fiat money. Look at a dollar bill. Next to George Washington’s picture it states: “This note is legal tender for all debts, public and private.” Nowhere on the certificate is there a promise, stated or implied, that the U.S. government will exchange it for anything else. A dollar bill is convertible into, say, 4 quarters or 10 dimes—but not into gold, chocolate, or any other commodity.

Why do people hold these pieces of paper? Because they know that others are willing to accept them for things of intrinsic value—food, rent, shoes, and so on. If this confidence ever evaporated, dollar bills would cease serving as a medium of exchange and, given that they make ugly wallpaper, would become virtually worthless.

But don’t panic. This series of events is hardly likely to occur. Our current monetary system has evolved over hundreds of years, during which commodity money was first replaced by full-bodied paper money—paper certificates that were backed by gold or silver of equal value held in the issuer’s vaults. Then the full-bodied paper money was replaced by certificates that were only partially backed by gold and silver. Finally, we arrived at our present system, in which paper money has no “backing” whatsoever. Like hesitant swimmers who first dip their toes, then their legs, then their whole body into a cold swimming pool, we have “tested the water” at each step of the way—and found it to our liking. It is unlikely that we will ever take a step back in the other direction.