CHAPTER 25

Spending and Output in the Short Run

How are consumer spending and GDP related?©Werner Dieterich/Photographer's Choice/Getty Images

LEARNING OBJECTIVES

After reading this chapter, you should be able to:

1. LO1Identify the key assumption of the basic Keynesian model and explain how it affects the production decisions made by firms and the consumption decisions made by households.

2. LO2Discuss the determinants of planned investment and aggregate consumption spending and how these concepts are used to develop a model of planned aggregate expenditure.

3. LO3Analyze, using graphs and numbers, how an economy reaches short-run equilibrium in the basic Keynesian model.

4. LO4Show how a change in planned aggregate expenditure can cause a change in short-run equilibrium output and how this is related to the income- expenditure multiplier.

5. LO5Explain why the basic Keynesian model suggests that fiscal policy is useful as a stabilization policy.

6. LO6Discuss the qualifications that arise in applying fiscal policy in real-world situations.

When one of the authors of this book was a small boy, he used to spend some time every summer with his grandparents, who lived a few hours from his home. A favorite activity of his during these visits was to spend a summer evening on the front porch with his grandmother, listening to her stories.

Grandma had spent the early years of her marriage in New England, during the worst part of the Great Depression. In one of her reminiscences, she remarked that, at that time, in the mid-1930s, it had been a satisfaction to her to be able to buy her children a new pair of shoes every year. In the small town where she and her family lived, many children had to wear their shoes until they fell apart, and a few unlucky boys and girls went to school barefoot. Her grandson thought this was scandalous: “Why didn’t their parents just buy them new shoes?” he demanded.

“They couldn’t,” said Grandma. “They didn’t have the money. Most of the fathers had lost their jobs because of the Depression.”

“What kind of jobs did they have?”

“They worked in the shoe factories, which had to close down.”

“Why did the factories close down?”

“Because,” Grandma explained, “nobody had any money to buy shoes.”

The grandson was only six or seven years old at the time, but even he could see that there was something badly wrong with Grandma’s logic. On the one side were boarded-up shoe factories and shoe workers with no jobs; on the other, children without shoes. Why couldn’t the shoe factories just open and produce the shoes the children so badly needed? He made his point quite firmly, but Grandma just shrugged and said it didn’t work that way.

The story of the closed-down shoe factories illustrates in a microcosm the cost to society of a recessionary gap. In an economy with a recessionary gap, available resources, which in principle could be used to produce valuable goods and services, are instead allowed to lie fallow. This waste of resources lowers the economy’s output and economic welfare, compared to its potential.

Grandma’s account also suggests how such an unfortunate situation might come about. Suppose factory owners and other producers, being reluctant to accumulate unsold goods on their shelves, produce just enough output to satisfy the demand for their products. And suppose that, for some reason, the public’s willingness or ability to spend declines. If spending declines, factories will respond by cutting their production (because they don’t want to produce goods they can’t sell) and by laying off workers who are no longer needed. And because the workers who are laid off will lose most of their income—a particularly serious loss in the 1930s, in the days before government-sponsored unemployment insurance was common—they must reduce their own spending. As their spending declines, factories will reduce their production again, laying off more workers, who in turn reduce their spending—and so on, in a vicious circle. In this scenario, the problem is not a lack of productive capacity—the factories have not lost their ability to produce—but rather insufficient spending to support the normal level of production.

The idea that a decline in aggregate spending may cause output to fall below potential output was one of the key insights of John Maynard Keynes (pronounced “canes”), perhaps the most influential economist of the twentieth century.¹ He lived from 1883 to 1946 and was a remarkable individual who combined a brilliant career as an economic theorist with an active life in diplomacy, finance, journalism, and the arts. In the period between World War I and II, among his many other activities, Keynes was a Cambridge professor, developing an imposing intellectual reputation, editing Great Britain’s leading scholarly journal in economics, writing articles for newspapers and magazines, advising the government, and playing a major role in the political and economic debates of the day.

Like other economists of the time, Keynes struggled to understand the Great Depression that gripped the world in the 1930s. His work on the problem led to the publication in 1936 of The General Theory of Employment, Interest, and Money. In The General Theory, Keynes tried to explain how economies can remain at low levels of output and employment for protracted periods. He stressed a number of factors, most notably that aggregate spending may be too low to permit full employment during such periods. Keynes recommended increases in government spending as the most effective way to increase aggregate spending and restore full employment.

The General Theory is a difficult book, reflecting Keynes’s own struggle to understand the complex causes of the Depression. In retrospect, some of The General Theory’s arguments seem unclear or even inconsistent. Yet the book is full of fertile ideas, many of which had a worldwide impact and eventually led to what has been called the Keynesian revolution. Over the years, many economists have added to or modified Keynes’s conception, to the point that Keynes himself, were he alive today, probably would not recognize much of what is now called Keynesian economics. But the ideas that insufficient aggregate spending can lead to recession and that government policies can help to restore full employment are still critical to Keynesian theory.

The goal of this chapter is to present a theory, or model, of how recessions and expansions may arise from fluctuations in aggregate spending, along the lines first suggested by Keynes. This model, which we call the basic Keynesian model, is also known as the Keynesian cross, after the diagram that is used to illustrate the theory. In the body of the chapter, we will emphasize a numerical and graphical approach to the basic Keynesian model . Appendix A to this chapter provides a more general algebraic analysis.

We begin with a brief discussion of the key assumptions of the basic Keynesian model. We then turn to the important concept of total, or aggregate, planned spending in the economy. We show how, in the short run, the rate of aggregate spending helps to determine the level of output, which can be greater than or less than potential output. In other words, depending on the level of spending, the economy may develop an output gap. “Too little” spending leads to a recessionary output gap, while “too much” creates an expansionary output gap.

An implication of the basic Keynesian model is that government policies that affect the level of spending can be used to reduce or eliminate output gaps. Policies used in this way are called stabilization policies. Keynes himself argued for the active use of fiscal policy—policy relating to government spending and taxes—to eliminate output gaps and stabilize the economy. In the latter part of this chapter, we’ll show why Keynes thought fiscal policy could help to stabilize the economy and discuss the usefulness of fiscal policy as a stabilization tool.

The basic Keynesian model is not a complete or entirely realistic model of the economy since it applies only to the relatively short period during which firms do not adjust their prices but, instead, meet the demand forthcoming at preset prices. Furthermore, by treating prices as fixed, the basic Keynesian model presented in this chapter does not address the determination of inflation. Nevertheless, this model is an essential building block of leading current theories of short-run economic fluctuations and stabilization policies. In subsequent chapters, we will extend the basic Keynesian model to incorporate monetary policy, inflation, and other important features of the economy.

THE KEYNESIAN MODEL’S CRUCIAL ASSUMPTION: FIRMS MEET DEMAND AT PRESET PRICES

The basic Keynesian model is built on a key assumption: In the short run, firms meet the demand for their products at preset prices. Firms do not respond to every change in the demand for their products by changing their prices. Instead, they typically set a price for some period and then meet the demand at that price. By “meeting the demand,” we mean that firms produce just enough to satisfy their customers at the prices that have been set.² As we will see, the assumption that firms vary their production in order to meet demand at preset prices implies that fluctuations in spending will have powerful effects on the nation’s real GDP.

The assumption that, over short periods of time, firms meet the demand for their products at preset prices is generally realistic. Think of the stores where you shop. The price of a pair of jeans does not fluctuate from moment to moment according to the number of customers who enter the store or the latest news about the price of denim. Instead, the store posts a price and sells jeans to any customer who wants to buy at that price, at least until the store runs out of stock. Similarly, the corner pizza restaurant may leave the price of its large pie unchanged for months or longer, allowing its pizza production to be determined by the number of customers who want to buy at the preset price.

Firms do not normally change their prices frequently because doing so would be costly. Economists refer to the costs of changing prices as menu costs. In the case of the pizza restaurant, the menu cost is literally just that—the cost of printing up a new menu when prices change. Similarly, the clothing store faces the cost of remarking all its merchandise if the manager changes prices. But menu costs also may include other kinds of costs—for example, the cost of doing a market survey to determine what price to charge and the cost of informing customers about price changes. The Economic Naturalist 25.1 discusses how technology may affect menu costs in the future.

Menu costs will not prevent firms from changing their prices indefinitely. As we saw in the case of Al’s ice cream store (in Chapter 24, Short-Term Economic Fluctuations: An Introduction), too great an imbalance between demand and supply, as reflected by a difference between sales and potential output, will eventually lead firms to change their prices. If no one is buying jeans, for example, at some point the clothing store will mark down its jeans prices. Or if the pizza restaurant becomes the local hot spot, with a line of customers stretching out the door, eventually the manager will raise the price of a large pie.

Cost-Benefit

Like many other economic decisions, the decision to change prices reflects a cost-benefit comparison: Prices should be changed if the benefit of doing so—the fact that sales will be brought more nearly in line with the firm’s normal production capacity—outweighs the menu costs associated with making the change. As we have stressed, the basic Keynesian model developed in this chapter ignores the fact that prices will eventually adjust and, therefore, should be interpreted as applying to the short run.

The Economic Naturalist 25.1

Will new technologies eliminate menu costs?

Thanks to new technologies, changing prices and informing customers about price changes is becoming increasingly less costly. Will technology eliminate menu costs as a factor in price setting?

Keynesian theory is based on the assumption that costs of changing prices, which economists refer to as menu costs, are sufficiently large to prevent firms from adjusting prices immediately in response to changing market conditions. However, in many industries, new technologies have eliminated or greatly reduced the direct costs of changing prices. For example, the use of bar codes to identify individual products, together with scanner technologies, allows a grocery store manager to change prices with just a few keystrokes, without having to change the price label on each can of soup or loaf of bread. Airlines use sophisticated computer software to implement complex pricing strategies, under which two travelers on the same flight to Milwaukee may pay very different fares, depending on whether they are business or vacation travelers and on how far in advance their flights were booked. Online retailers have the ability to vary their prices by type of customer and even by individual customer, while other Internet-based companies, such as eBay, allow for negotiation over the price of each individual purchase. On-demand ride services such as Uber and Lyft evaluate, in real time, customers’ demand for rides and drivers’ supply of rides; their pricing systems estimate the market-clearing price, and when supply does not meet demand, they send a notification of instant price increases that customers view on their phones and have to accept before they are connected to a driver.

Will these reductions in the direct costs of changing prices make the Keynesian theory, which assumes that firms meet demand at preset prices, less relevant to the real world? This is certainly a possibility that macroeconomists must take into account. However, it is unlikely that new technologies will completely eliminate the costs of changing prices any time soon. In many sectors of the economy, gathering the information about market conditions needed to set the profit-maximizing price—including the prices charged by competitors, the costs of producing the good or service, and the likely demand for the product—will remain costly for firms. Another cost of changing prices is the use of valuable managerial time and attention needed to make informed pricing decisions. A more subtle cost of changing prices—particularly raising prices—is that doing so may lead regular customers to rethink their choice of suppliers and decide to search for a better deal elsewhere.

PLANNED AGGREGATE EXPENDITURE

In the simple Keynesian model, output at each point in time is determined by the amount that people throughout the economy want to spend—what we will refer to as planned aggregate expenditure. Specifically, planned aggregate expenditure (PAE) is total planned spending on final goods and servic es.

The four components of spending on final goods and services were introduced in Chapter 17, Measuring Economic Activity: GDP and Unemployment:

· 1.Consumption expenditure, or simply consumption (C), is spending by households on final goods and services. Examples of consumption expenditure are spending on food, clothes, and entertainment and on consumer durable goods like automobiles and furniture.

· 2.Investment (I) is spending by domestic firms on new capital goods, such as office buildings, factories, and equipment. Spending on new houses and apartment buildings (residential investment) and increases in inventories (inventory investment) also are included in investment.³

· 3.Government purchases (G) are purchases by federal, state, and local governments of final goods and services. Examples of government purchases include new schools and hospitals; military hardware; equipment for the space program; and the services of government employees such as soldiers, police, and government office workers. Recall from Chapter 17, Measuring Economic Activity: GDP and Unemployment, that transfer payments such as Social Security benefits and unemployment insurance and interest on the government debt are not included in government purchases. Transfer payments and interest contribute to aggregate expenditure only at the point when they are spent by their recipients (for example, when a recipient of a Social Security check uses the funds to buy food, clothing, or other consumption goods).

· 4.Net exports (NX) equal exports minus imports. Exports are sales of domestically produced goods and services to foreigners. Imports are purchases by domestic residents of goods and services produced abroad that have been included in C, I, and G but must now be subtracted because they do not represent domestic production. Net exports therefore represent the net demand for domestic goods and services by foreigners.

Together, these four types of spending—by households, firms, the government, and the rest of the world—sum to total, or aggregate, spending.

PLANNED SPENDING VERSUS ACTUAL SPENDING

In the Keynesian model, output is determined by planned aggregate expenditure, or planned spending, for short. Could planned spending ever differ from actual spending? The answer is yes. The most important case is that of a firm that sells either less or more of its product than expected. Note that additions to the stocks of goods sitting in a firm’s warehouse are treated in official government statistics as inventory investment by the firm. In effect, government statisticians assume that the firm buys its unsold output from itself; they then count those purchases as part of the firm’s investment spending.⁴

Suppose, then, that a firm’s actual sales are less than expected, so that part of what it had planned to sell remains in the warehouse. In this case, the firm’s actual investment, including the unexpected increases in its inventory, is greater than its planned investment, which did not include the added inventory. Suppose we agree to let I^p equal the firm’s planned investment, including planned inventory investment. A firm that sells less of its output than planned, and therefore adds more to its inventory than planned, will find that its actual investment (including unplanned inventory investment) exceeds its planned investment, so that I > I^p.

What about a firm that sells more of its output than expected? In that case, the firm will add less to its inventory than it planned, so actual investment will be less than planned investment, that is, I < I^p. The following example gives a numerical illustration.

EXAMPLE 25.1Planned versus Actual Investment

What is the difference between planned investment and actual investment?

Fly-by-Night Kite Co. produces $5,000,000 worth of kites during the year. It expects sales of $4,800,000 for the year, leaving $200,000 worth of kites to be stored in the warehouse for future sale. During the year, Fly-by-Night adds $1,000,000 in new production equipment as part of an expansion plan. Find Fly-by-Night’s actual investment, I, and its planned investment, I^p, if actual kite sales turn out to be $4,600,000. What if sales are $4,800,000? What if they are $5,000,000?

Fly-by-Night’s planned investment, I^p, equals its purchases of new production equipment ($1,000,000) plus its planned additions to inventory ($200,000), for a total of $1,200,000 in planned investment. The company’s planned investment does not depend on how much it actually sells.

If Fly-by-Night sells only $4,600,000 worth of kites, it will add $400,000 in kites to its inventory instead of the $200,000 worth originally planned. In this case, actual investment equals the $1,000,000 in new equipment plus the $400,000 in inventory investment, so I = $1,400,000. We see that, when the firm sells less output than planned, actual investment exceeds planned investment (I > I^p).

If Fly-by-Night has $4,800,000 in sales, then it will add $200,000 in kites to inventory, just as planned. In this case, actual and planned investment are the same:

I = I ^p = $1,200,000.

Finally, if Fly-by-Night sells $5,000,000 worth of kites, it will have no output to add to inventory. Its inventory investment will be zero, and its total actual investment (including the new equipment) will equal $1,000,000, which is less than its planned investment of $1,200,000 (I < I^p).

Because firms that are meeting the demand for their product or service at preset prices cannot control how much they sell, their actual investment (including inventory investment) may well differ from their planned investment. However, for households, the government, and foreign purchasers, we may reasonably assume that actual spending and planned spending are the same. Thus, from now on we will assume that, for consumption, government purchases, and net exports, actual spending equals planned spending.

With these assumptions, we can define planned aggregate expenditure by the following equation:

PAE = C + I^p + G + NX.(25.1)

Equation 25.1 says that planned aggregate expenditure is the sum of planned spending by households, firms, governments, and foreigners. We use a superscript p to distinguish planned investment spending by firms, I^p, from actual investment spending, I. However, because planned spending equals actual spending for households, the government, and foreigners, we do not need to use superscripts for consumption, government purchases, or net exports.

CONSUMER SPENDING AND THE ECONOMY

In the U.S. economy, the largest component of planned aggregate expenditure is consumption spending, C. As already mentioned, consumer spending includes household purchases of goods such as groceries and clothing; services such as health care, concerts, and college tuition; and consumer durables such as cars, furniture, and computers. Thus, consumers’ willingness to spend affects sales and profitability in a wide range of industries. (Households’ purchases of new homes are classified as investment, rather than consumption, but home purchases represent another channel through which household decisions affect total spending.)

What factors determine how much people plan to spend on consumer goods and services in a given period? While many factors are relevant, a particularly important determinant of the amount people plan to consume is their after-tax, or disposable, income. All else being equal, households and individuals with higher disposable incomes will consume more than those with lower disposable incomes. Keynes himself stressed the importance of disposable income in determining household consumption decisions, claiming a “psychological law” that people would tie their spending closely to their incomes.

Figure 25.1 shows the relationship between aggregate real consumption expenditures and real disposable income in the United States for the period 1960–2016. Each point on the graph corresponds to a year between 1960 and 2012 (selected years are indicated in the figure). The position of each point is determined by the combination of consumption (on the vertical axis) and disposable income (on the horizontal axis) associated with that year. As you can see, there is indeed a close relationship between aggregate consumption and disposable income: Higher disposable income is associated with higher consumption.

FIGURE 25.1 The U.S. Consumption Function, 1960–2016.Each point on this figure represents a combination of aggregate real consumption and aggregate real disposable income for a specific year between 1960 and 2016. Note the strong positive relationship between consumption and disposable income.Source: U.S. Bureau of Economic Analysis, Real Disposable Personal Income [DSPIC96] and Real Personal Consumption Expenditures [PCECCA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DSPIC96, November 2, 2017.

Recall from Chapter 21, Saving and Capital Formation, that the disposable income of the private sector is the total production of the economy, Y, less net taxes (taxes minus transfers), or T. So we will assume that consumption spending (C) increases as disposable income (Y − T) increases. As already mentioned, other factors may also affect consumption, such as the real interest rate, also discussed in Chapter 21, Saving and Capital Formation. We return to some of these other factors shortly.

We can write this relationship between consumption and disposable income as a linear equation⁵

(25.2)

This equation, which we will dissect in a moment, is known as the consumption function. The consumption function relates consumption spending (C) to its determinants, in particular, disposable (after-tax) income (Y − T).

Let’s look at the consumption function, Equation 25.2, more carefully. The right side of the equation contains two terms, and (mpc)(Y − T). The amount of consumption represented by is called autonomous consumption since it is consumption that is not related to (i.e., autonomous from) changes in disposable income. For example, suppose consumers became more optimistic about the future, so that they wanted to consume more and save less at any given level of their current disposable income. In this case, will increase and consumption will increase even though disposable income has not changed.

We can imagine other factors that could affect autonomous consumption. Suppose, for example, that there is a boom in the stock market or a sharp increase in home prices, making consumers feel wealthier, and hence more inclined to spend, for a given level of current disposable income. This effect could be captured by assuming that increases. Likewise, a fall in home prices or stock prices that made consumers feel poorer and less inclined to spend would be represented by a decrease in . Economists refer to the effects of changes in asset prices on households’ wealth and hence their consumption spending as the wealth effect of changes in asset prices.

Finally, autonomous consumption also takes account of the effects that real interest rates have on consumption. In particular, higher real interest rates will make it more expensive to buy consumer durables on credit and so households may consume less and save more. would thus decrease and consumption will fall even though disposable income has not changed. The opposite is also true: A decline in real interest rates will lower borrowing costs and the opportunity cost of saving, and so households may increase their autonomous consumption and therefore their total consumption spending.

The Economic Naturalist 25.2

How did the decline in U.S. stock market values from 2000–2002 affect consumption spending?

From March 2000 to October 2002, the U.S. stock market suffered a 49 percent drop in value as measured by the Standard & Poor’s 500 stock index, a widely referenced benchmark of U.S. stock performance. According to MIT economist James Poterba, U.S. households owned roughly $13.3 trillion of corporate stock in 2000.⁶ If households’ stock market holdings reflect those of the Standard & Poor’s stock index, the 49 percent drop in the value of the stock market wiped out approximately $6.5 trillion of household wealth in two years. According to economic models based on historical experience, a dollar’s decrease in household wealth reduces consumer spending by 3 to 7 cents per year, so the reduction in stock market wealth had the potential to reduce overall consumer spending by $195 billion to $455 billion, a drop of approximately 3 to 7 percent. Yet, real consumption spending continued to rise from 2000 through 2002. Why did this happen?

Despite the start of a recession in March 2001, overall consumption spending remained strong during 2000–2002 for a variety of reasons. First, consumers’ real after-tax income continued to grow into the fall of 2001, helping to maintain strong consumer spending despite the drop in the stock market. Furthermore, throughout 2001 and into early 2002, the Federal Reserve significantly reduced interest rates; we’ll discuss how the Federal Reserve does this in another chapter. As we discussed, a reduction in interest rates helps to promote consumer spending, especially on durable goods such as automobiles, by reducing consumers’ borrowing costs. Finally, housing prices rose dramatically during this period, increasing consumers’ housing wealth and partially offsetting their decline in stock-related wealth. Data on repeat house sales that measure the price of individual houses that are sold and resold over time indicate that housing prices rose by 20.1 percent between the first quarter of 2000 and the third quarter of 2002.⁷ The total market value of household real estate was about $12 trillion in 2000, so house price appreciation added about $2.4 trillion to household wealth, offsetting about 37 percent of the decline in stock market wealth during this period.⁸

Overall, while the drop in stock market values clearly had a negative effect on consumer wealth, other offsetting factors helped to keep the 2000–2002 stock market decline from dampening consumption spending during this period.

The second term on the right side of Equation 25.2, (mpc)(Y − T), measures the effect of disposable income, Y − T, on consumption. The marginal propensity to consume (mpc), a fixed number, is the amount by which consumption rises when current disposable income rises by one dollar. The intuition behind the marginal propensity to consume is straightforward: If people receive an extra dollar of income, they will consume part of the dollar and save the rest. That is, their consumption will increase, but by less than the full dollar of extra income. It is therefore realistic to assume that the marginal propensity to consume is greater than 0 (an increase in income leads to an increase in consumption) but less than 1 (the increase in consumption will be less than the full increase in income). Mathematically, we can summarize these assumptions as 0 < mpc < 1.

Figure 25.2 shows a hypothetical consumption function, with consumption spending (C) on the vertical axis and disposable income (Y − T) on the horizontal axis. The intercept of the consumption function on the vertical axis equals autonomous consumption (), and the slope of the consumption function equals the marginal propensity to consume (mpc).

FIGURE 25.2 A Consumption Function.The consumption function relates consumption spending (C) to disposable income, (Y − T). The vertical intercept of the consumption function is autonomous consumption (), and the slope of the line equals the marginal propensity to consume (mpc).

PLANNED AGGREGATE EXPENDITURE AND OUTPUT

Thinking back to Grandma’s reminiscences, recall that an important element of her story involved the links among production, income, and spending. As the shoe factories in Grandma’s town reduced production, the incomes of both factory workers and factory owners fell. Workers’ incomes fell as the number of hours of work per week were reduced (a common practice during the Depression), as workers were laid off, or as wages were cut. Factory owners’ income fell as profits declined. Reduced incomes, in turn, forced both workers and factory owners to curtail their spending—which led to still lower production and further reductions in income. This vicious circle led the economy further and further into recession.

The logic of Grandma’s story has two key elements: (1) declines in production (which imply declines in the income received by producers) lead to reduced spending and (2) reductions in spending lead to declines in production and income. In this section, we look at the first part of the story, the effects of production and income on spending. We return later in this chapter to the effects of spending on production and income.

Why do changes in production and income affect planned aggregate spending? The consumption function, which relates consumption to disposable income, is the basic source of this relationship. Because consumption spending C is a large part of planned aggregate spending, and because consumption depends on output Y, aggregate spending as a whole depends on output.

Let’s examine the link between planned aggregate expenditure and output in two ways. We will begin by working with a specific numerical example so that you can see the relationship clearly. Next, we will plot the relationship on a graph so that you can see its general shape and start working with these concepts using graphs.

EXAMPLE 25.2Linking Planned Aggregate Expenditure to Output

What is the relationship between planned aggregate expenditure and output?

In a particular economy, the consumption function is

C = 620 + 0.8(Y − T),

so that the intercept term in the consumption function equals 620 and the marginal propensity to consume mpc equals 0.8. Also, suppose that we are given that planned investment spending I^p = 220, government purchases G = 300, net exports NX = 20, and taxes T = 250.

Write a numerical equation linking planned aggregate expenditure PAE to output Y. How does planned spending change when output and hence income change?

Recall the definition of planned aggregate expenditure, Equation 25.1:

PAE = C + I^p + G + NX.

To find a numerical equation for planned aggregate expenditure, we need to find numerical expressions for each of its four components. The first component of spending, consumption, is defined by the consumption function, C = 620 + 0.8(Y − T). Since taxes T = 250, we can substitute for T to write the consumption function as C = 620 + 0.8(Y − 250). Now plug this expression for C into the definition of planned aggregate expenditure above to get

PAE = [620 + 0.8(Y − 250)] + I^p + G + NX,

where we have just replaced C by its value as determined by the consumption function. Similarly, we can substitute the given numerical values of planned investment I^p, government purchases G, and net exports NX into the definition of planned aggregate expenditure to get

PAE = [620 + 0.8(Y − 250)] + 220 + 300 + 20.

To simplify this equation, first note that 0.8(Y − 250) = 0.8Y − 200, and then add together all the terms that don’t depend on output Y. The result is

The final expression shows the relationship between planned aggregate expenditure and output in this numerical example. Note that, according to this equation, a $1 increase in Y leads to an increase in PAE of (0.8)($1 ), or 80 cents. The reason for this is that the marginal propensity to consume, mpc, in this example is 0.8. Hence, a $1 increase in income raises consumption spending by 80 cents. Since consumption is a component of total planned spending, total spending rises by 80 cents as well.

The solution to Example 25.2 illustrates a general point: Planned aggregate expenditure can be divided into two parts, a part that depends on output (Y) and a part that is independent of output. The portion of planned aggregate expenditure that is independent of output is called autonomous expenditure. In the equation above, autonomous expenditure is the constant term and is equal to 960. This portion of planned spending, being a fixed number, does not vary when output varies. By contrast, the portion of planned aggregate expenditure that depends on output (Y) is called induced expenditure. In the equation above, induced expenditure equals 0.8Y, the second term in the expression for planned aggregate expenditure. Note that the numerical value of induced expenditure depends, by definition, on the numerical value taken by output. Autonomous expenditure and induced expenditure together equal planned aggregate expenditure.

Figure 25.3 is a graph of the equation PAE = 960 + 0.8Y, which is a straight line with a vertical intercept of 960 and a slope of 0.8. This line, which shows the relationship between planned aggregate expenditure and output graphically, is called the expenditure line.

FIGURE 25.3 The Expenditure Line.The line PAE = 960 + 0.8Y, referred to as the expenditure line, shows the relationship of planned aggregate expenditure to output.

There are three properties of the expenditure line that are important to note. First, the slope of this line is equal to the marginal propensity to consume for our specific numerical example. This point holds in general: The slope of the expenditure line is equal to the marginal propensity to consume. Second, the vertical intercept is equal to autonomous expenditure for our example. This point also holds more generally: The vertical intercept of the expenditure line equals the level of autonomous expenditure. Third, changes in autonomous expenditure will shift the expenditure line: Increases in autonomous expenditure will shift the expenditure line up while decreases will shift the line down. We will apply all three of these properties in the rest of the chapter.

RECAP

PLANNED AGGREGATE EXPENDITURE

· Planned aggregate expenditure (PAE) is total planned spending on final goods and services. The four components of planned spending are consumer expenditure (C), planned investment (I^p), government purchases (G), and net exports (NX). Planned investment differs from actual investment when firms’ sales are different from what they expected, so that additions to inventory (a component of investment) are different from what firms anticipated.

· In the U.S. economy, the largest component of aggregate expenditure is consumer expenditure, or simply consumption. Consumption depends on disposable, or after-tax, income, according to a relationship known as the consumption function, stated algebraically as

· The constant term in the consumption function, , captures factors other than disposable income that affect consumer spending. For example, an increase in housing or stock prices that makes households wealthier and thus more willing to spend—an effect called the wealth effect—could be captured by an increase in . The slope of the consumption function equals the marginal propensity to consume, mpc, where 0 < mpc < 1. This is the amount by which consumption rises when disposable income rises by one dollar.

· Increases in output Y, which imply equal increases in income, cause consumption to rise. As consumption is part of planned aggregate expenditure, planned spending depends on output as well. The portion of planned aggregate expenditure that depends on output is called induced expenditure. The portion of planned aggregate expenditure that is independent of output is autonomous expenditure.

SHORT-RUN EQUILIBRIUM OUTPUT

Now that we have defined planned aggregate expenditure and seen how it is related to output, the next task is to see how output itself is determined. Recall the assumption of the basic Keynesian model: In the short run, producers leave prices at preset levels and simply meet the demand that is forthcoming at those prices. In other words, during the short-run period in which prices are preset, firms produce an amount that is equal to planned aggregate expenditure. Accordingly, we define short-run equilibrium output as the level of output at which output Y equals planned aggregate expenditure PAE:

Y = PAE.(25.3)

Short-run equilibrium output is the level of output that prevails during the period in which prices are predetermined.

We can find the short-run equilibrium output for the economy described in Example 25.2. There are two approaches to doing this, and we will demonstrate both. First, we can take a numerical approach, and find where Y = PAE either by using a table or by solving the equations directly. (We will again demonstrate both methods, as each method illustrates an important point about the basic Keynesian model.) Second, we can add a line to our graph of the expenditure line to find short-run equilibrium output. The resulting graph is called the Keynesian cross since it involves two lines intersecting. This approach will help us in generalizing the ideas we develop using the numerical approach.

FINDING SHORT-RUN EQUILIBRIUM OUTPUT: NUMERICAL APPROACH

Recall that in Example 25.2, planned spending is determined by the equation

PAE = 960 + 0.8Y.

Thus, for instance, when Y = 4,000, PAE = 960 + 0.8(4,000) = 4,160. Table 25.1 shows the results of similar calculations for different levels of output; column 1 shows various levels of output (Y), and column 2 lists the levels of planned aggregate expenditure (PAE) for the different levels of output given in column 1.

In Table 25.1, notice that since consumption rises with output, total planned spending (which includes consumption) rises also. But if you compare columns 1 and 2, you will see that every time output rises by 200, planned spending rises by only 160. That is because the marginal propensity to consume in this economy is 0.8 so that each dollar in added income raises consumption and planned spending by 80 cents.

Again, short-run equilibrium output is the level of output at which Y = PAE, or, equivalently, Y − PAE = 0. At this level of output, actual investment will equal planned investment, and there will be no tendency for output to change. Looking at Table 25.1, we can see there is only one level of output that satisfies that condition, Y = 4,800. At that level, output and planned aggregate expenditure are precisely equal, so that producers are just meeting the demand for their goods and services.

In this economy, what would happen if output differed from its equilibrium value of 4,800? Suppose, for example, that output were 4,000. Looking at the second column of Table 25.1, you can see that, when output is 4,000, planned aggregate expenditure equals 960 + 0.8(4,000), or 4,160. Thus, if output is 4,000, firms are not producing enough to meet the demand. They will find that, as sales exceed the amounts they are producing, their inventories of finished goods are being depleted by 160 per year, and that actual investment (including inventory investment) is less than planned investment. Under the assumption that firms are committed to meeting their customers’ demand, firms will respond by expanding their production.

Would expanding production to 4,160, the level of planned spending firms faced when output was 4,000, be enough? The answer is no because of induced expenditure. That is, as firms expand their output, aggregate income (wages and profits) rises with it, which in turn leads to higher levels of consumption. Indeed, if output expands to 4,160, planned spending will increase as well, to 960 + 0.8(4,160), or 4,288. So an output level of 4,160 will still be insufficient to meet demand. As Table 25.1 shows, output will not be sufficient to meet planned aggregate expenditure until it expands to its short-run equilibrium value of 4,800.

What if output were initially greater than its equilibrium value—say, 5,000? From Table 25.1, we can see that when output equals 5,000, planned spending equals only 4,960—less than what firms are producing. So at an output level of 5,000, firms will not sell all they produce, and they will find that their merchandise is piling up on store shelves and in warehouses (actual investment, including inventory investment, is greater than planned investment). In response, firms will cut their production runs. As Table 25.1 shows, they will have to reduce production to its equilibrium value of 4,800 before output just matches planned spending.

We can also find short-run equilibrium output directly by using the equation for planned aggregate expenditure:

PAE = 960 + 0.8Y.

By definition, an economy is in short-run equilibrium when

Y = PAE.

So, using our equation for planned aggregate expenditure, we have

Y = 960 + 0.8Y.

Solving for Y, we have Y = 4,800, the same result we obtained using Table 25.1.

CONCEPT CHECK 25.1

Construct a table like Table 25.1 for an economy like the one we have been working with, assuming that the consumption function is C = 820 + 0.7(Y − T) and that I^p = 600, G = 600, NX = 200, and T = 600.

What is short-run equilibrium output in this economy? (Hint: Try using values for output above 5,000.) Check your answer by finding short-run equilibrium output directly using the equation for planned aggregate expenditure.

FINDING SHORT-RUN EQUILIBRIUM OUTPUT: GRAPHICAL APPROACH

Figure 25.4 shows the graphical determination of short-run equilibrium output for the economy we analyzed numerically above. Output (Y) is plotted on the horizontal axis and planned aggregate expenditure (PAE) on the vertical axis.

FIGURE 25.4 Determination of Short-Run Equilibrium Output (Keynesian Cross).The 45° line represents the short-run equilibrium condition Y = PAE. The line PAE = 960 + 0.8Y, referred to as the expenditure line, shows the relationship of planned aggregate expenditure to output. Short-run equilibrium output (4,800) is determined at point E, the intersection of the expenditure line and the equilibrium condition (Y = PAE). This type of diagram is known as a Keynesian cross.

The figure contains two lines. The blue line is the expenditure line, which we discussed earlier. It shows how planned spending depends on output. The red dashed line is a 45° line extending from the origin. In general, a 45° line from the origin includes the points at which the variable on the vertical axis equals the variable on the horizontal axis. Hence, in this case, the 45° line shows all of the points at which PAE equals Y. Since an economy is in short-run equilibrium when Y = PAE, the short-run equilibrium for our example must be somewhere along this line.

At which particular point on the Y = PAE line will the economy be in short-run equilibrium? Only one point in the figure is on both the Y = PAE line and the expenditure line: point E, where the two lines intersect. At point E, short-run equilibrium output equals 4,800, which is the same value that we obtained with the numerical approach either by using Table 25.1 or by solving the equation directly.

What if the economy is above or below point E? At levels of output higher than 4,800, output exceeds planned aggregate expenditure. Hence, firms will be producing more than they can sell, which will lead them to reduce their rate of production. They will continue to reduce their production until output reaches 4,800, where output equals planned aggregate expenditure. By contrast, at levels of output below 4,800, planned aggregate expenditure exceeds output. In that region, firms will not be producing enough to meet demand, and they will tend to increase their production. Only at point E, where output equals 4,800, will firms be producing enough to just satisfy planned spending on goods and services.

The diagram in Figure 25.4 is called the Keynesian cross due to the fact that it is a crosslike, graphical model of Keynes’s basic ideas. The Keynesian cross shows graphically how short-run equilibrium output is determined in a world in which producers meet demand at predetermined prices.

CONCEPT CHECK 25.2

Use a Keynesian-cross diagram to show graphically the determination of short-run equilibrium output for the economy described in Concept Check 25.1. What are the intercept and the slope of the expenditure line?

RECAP

SHORT-RUN EQUILIBRIUM OUTPUT

· Short-run equilibrium output is the level of output at which output equals planned aggregate expenditure, or, in symbols, Y = PAE. For an example economy, short-run equilibrium output can be solved for numerically or graphically.

· The graphical solution is based on a diagram called the Keynesian cross. The Keynesian-cross diagram includes two lines: a 45° line that represents the condition Y = PAE, and the expenditure line, which shows the relationship of planned aggregate expenditure to output. Short-run equilibrium output is determined at the intersection of the two lines.

PLANNED SPENDING AND THE OUTPUT GAP

We’re now ready to use the basic Keynesian model to show how insufficient spending can lead to a recession. To illustrate the effects of spending changes on output, we will continue to work with the same example we’ve worked with throughout this chapter. We’ve shown that, in this economy, short-run equilibrium output equals 4,800. Let’s now make the additional assumption that potential output in this economy also equals 4,800, or Y* = 4,800, so that initially there is no output gap. Starting from this position of full employment, let’s analyze how a fall in planned aggregate expenditure can lead to a recession.

EXAMPLE 25.3A Fall in Planned Spending Leads to a Recession

Why does a fall in planned spending lead to a recession?

For the economy introduced in Example 25.2, we have found that short-run equilibrium output Y equals 4,800. Assume also that potential output Y* equals 4,800, so that the output gap Y* − Y equals zero.

Suppose, though, that consumers become more pessimistic about the future, so that they begin to spend less at every level of current disposable income. We can capture this change by assuming that , the constant term in the consumption function, falls to a lower level. To be specific, suppose that falls by 10 units, which in turn implies a decline in autonomous expenditure of 10 units. What is the effect of this reduction in planned spending on the economy?

We can see the effects of the decline in consumer spending on the economy using the Keynesian-cross diagram. Figure 25.5 shows the original short-run equilibrium point of the model (E), at the intersection of the 45° line, along which Y = PAE, and the original expenditure line, representing the equation PAE = 960 + 0.8Y. As before, the initial value of short-run equilibrium output is 4,800, which we have now assumed also corresponds to potential output Y*. But what happens if declines by 10 units, reducing autonomous expenditure by 10 units as well?

FIGURE 25.5 A Decline in Planned Spending Leads to a Recession.(1 ) A decline in consumers’ willingness to spend at any current level of disposable income reduces planned autonomous expenditure and shifts the expenditure line down; (2) the short-run equilibrium point moves from E to F; (3) equilibrium output falls from 4,800 to 4,750; a recessionary gap of 50 is created.

Originally, autonomous expenditure in this economy was 960, so a decline of 10 units causes it to fall to 950. Instead of the economy’s planned spending being described by the equation PAE = 960 + 0.8Y, as initially, it is now given by PAE = 950 + 0.8Y. What does this change imply for the graph in Figure 25.5? Since the intercept of the expenditure line (equal to autonomous expenditure) has decreased from 960 to 950, the effect of the decline in consumer spending will be to shift the expenditure line down in parallel fashion, by 10 units. Figure 25.5 indicates this downward shift in the expenditure line. The new short-run equilibrium point is at point F, where the new, lower expenditure line intersects the 45° line (or the Y = PAE line).

Point F is to the left of the original equilibrium point E, so we can see that output and spending have fallen from their initial levels. Since output at point F is lower than potential output, 4,800, we see that the fall in consumer spending has resulted in a recessionary gap in the economy. More generally, starting from a situation of full employment (where output equals potential output), any decline in autonomous expenditure leads to a recession.

Numerically, how large is the recessionary gap in Figure 25.5? To answer this question, we can use Table 25.2, which is in the same form as Table 25.1. The key difference is that in Table 25.2 planned aggregate expenditure is given by PAE = 950 + 0.8Y, rather than by PAE = 960 + 0.8Y, as in Table 25.1.

As in Table 25.1, the first column of the table shows alternative possible values of output Y, and the second column shows the levels of planned aggregate expenditure PAE implied by each value of output in the first column. Notice that 4,800, the value of short-run equilibrium output found in Table 25.1, is no longer an equilibrium; when output is 4,800, planned spending is 4,790, so output and planned spending are not equal. As the table shows, following the decline in planned aggregate expenditure, short-run equilibrium output is 4,750, the only value of output for which Y = PAE. (We can also find this short-run equilibrium output directly by solving the equation Y = 950 + 0.8Y.) Thus, a drop of 10 units in autonomous expenditure has led to a 50-unit decline in short-run equilibrium output. If full-employment output is 4,800, then the recessionary gap shown in Figure 25.5 is 4,800 − 4,750 = 50 units.

CONCEPT CHECK 25.3

In the economy described in Example 25.3, we found a recessionary gap of 50, relative to potential output of 4,800. Suppose that, in this economy, the natural rate of unemployment u* is 5 percent. What will the actual unemployment rate be after the recessionary gap appears? (Hint: Recall Okun’s law from Chapter 24, Short-Term Economic Fluctuations: An Introduction.)

The example that we just worked through showed that a decline in autonomous expenditure, arising from a decreased willingness of consumers to spend, causes short-run equilibrium output to fall and opens up a recessionary gap. The same conclusion applies to declines in autonomous expenditure arising from other sources. Suppose, for instance, that firms become disillusioned with new technologies and cut back their planned investment in new equipment. In terms of the model, this reluctance of firms to invest can be interpreted as a decline in planned investment spending I^p. Under our assumption that planned investment spending is given and does not depend on output, planned investment is part of autonomous expenditure. So a decline in planned investment spending depresses autonomous expenditure and output, in precisely the same way that a decline in the autonomous part of consumption spending does. Similar conclusions apply to declines in other components of autonomous expenditure, such as government purchases and net exports, as we will see in later applications.

CONCEPT CHECK 25.4

Repeat the analysis of Example 25.3, except assume that consumers become more rather than less confident about the future. As a result, rises by 10 units, which in turn raises autonomous expenditure by 10 units. Show graphically that this increase in consumers’ willingness to spend leads to an expansionary output gap. Find the numerical value of the expansionary output gap.

The Economic Naturalist 25.3

What caused the 2007–2009 recession in the United States?

The house price bubble that burst in summer 2006 is a primary cause of the 2007–2009 recession. The average price of American homes rose at a spectacular rate from the late 1990s until the summer of 2006; this phenomenon attracted both borrowers and lenders who wished to profit from the record real estate boom.

Figure 21.1 in Chapter 21, Saving and Capital Formation (see The Economic Naturalist 21.1), showed real house prices between 1975 and 2016. The highest average annual rate of increase in house prices previously was the spike of 1976 to 1979, when house prices rose 4.7 percent per year. By contrast, from 2001 to 2006, average house prices rose by an average of 8.2 percent per year. This number masks the fact that over the period the rate of increase itself rose, starting at 4 percent in 2001 and peaking at an annual rate of 12 percent in 2004–2005.

We can use the rule of 72, discussed in Chapter 19, Economic Growth, Productivity, an Living Standards, to put these numbers in context. At the growth rates experienced in the 1970s and 1980s, the average price of a house doubles in 15 to 19 years. By contrast, at the growth rates experienced in the house price boom in the 2000s, the average price of a house doubles in about 10 years, that is, between 50 percent and 100 percent faster than ever before.

The average home price peaked in July 2006. Prices at first fell gradually, declining by about 6 percent from July 2006 through May 2007. The decline accelerated, however, and between May 2007 and February 2009 the average home price dropped by more than 20 percent.

The bursting of the housing bubble and the financial market crisis it induced caused both businesses and households to cut back on their spending in two ways. First, the financial market disruptions made it difficult for businesses to borrow funds for investment spending and for consumers to borrow funds for purchasing housing and automobiles. Second, the financial crisis reduced household wealth and increased the le vel of uncertainty about the future, which led to a reduction in autonomous spending, or spending independent of output.

Analytically, this situation can be represented as a downward shift in the planned aggregate expenditure (PAE) line as shown in Figure 25.6. At point E, planned spending and output are both equal to potential output Y*. After the expenditure line shifts down, planned spending is less than actual output; the natural response of businesses is to reduce production until their output again meets demand (seen as the movement from point E to point F in Figure 25.6). At F, the economy is in a recession, with output below potential. Further, since output is below potential, Okun’s law tells us that unemployment has now risen above the natural rate.

FIGURE 25.6 The End of the House Price Bubble.

THE MULTIPLIER

In Example 25.3 and Table 25.2, we analyzed a case in which the initial decline in consumer spending (as measured by the fall in ), and hence in autonomous expenditure, was only 10 units, and yet short-run equilibrium output fell by 50 units. Why did a relatively modest initial decline in consumer spending lead to a much larger fall in output?

The reason the impact on output was greater than the initial change in spending is the “vicious circle” effect suggested by Grandma’s reminiscences about the Great Depression. Specifically, a fall in consumer spending not only reduces the sales of consumer goods directly; it also reduces the incomes of workers and owners in the industries that produce consumer goods. As their incomes fall, these workers and capital owners reduce their spending, which reduces the output and incomes of other producers in the economy. And these reductions in income lead to still further cuts in spending. Ultimately, these successive rounds of declines in spending and income may lead to a decrease in planned aggregate expenditure and output that is significantly greater than the change in spending that started the process.

The effect on short-run equilibrium output of a 1-unit increase in autonomous expenditure is called the income-expenditure multiplier, or the multiplier for short. In our example economy, the multiplier is 5. That is, each 1-unit change in autonomous expenditure leads to a 5-unit change in short-run equilibrium output in the same direction. The idea that a change in spending may lead to a significantly larger change in short-run equilibrium output is a key feature of the basic Keynesian model.

What determines how large the multiplier will be? An important factor is the marginal propensity to consume (mpc) out of disposable income. If the mpc is large, then falls in income will cause people to reduce their spending sharply, and the multiplier effect will then also be large. If the marginal propensity to consume is small, then people will not reduce spending so much when income falls, and the multiplier also will be small. Appendix B to this chapter provides more details on the multiplier in the basic Keynesian model, including a formula that allows us to calculate the value of the multiplier under specific assumptions about the economy.

RECAP

PLANNED SPENDING AND THE OUTPUT GAP

· If short-run equilibrium output differs from potential output, an output gap exists.

· Increases in autonomous expenditure shift the expenditure line upward, increasing short-run equilibrium output; decreases in autonomous expenditure shift the expenditure line downward, leading to declines in short-run equilibrium output. Decreases in autonomous expenditure that drive actual output below potential output are a source of recessions.

· Generally, a one-unit change in autonomous expenditure leads to a larger change in short-run equilibrium output, reflecting the working of the income-expenditure multiplier. The multiplier arises because a given initial increase in spending raises the incomes of producers, which leads them to spend more, raising the incomes and spending of other producers, and so on.

STABILIZING PLANNED SPENDING: THE ROLE OF FISCAL POLICY

According to the basic Keynesian model, inadequate spending is an important cause of recessions. To fight recessions—at least, those caused by insufficient demand rather than slow growth of potential output—policymakers must find ways to stimulate planned spending. Policies that are used to affect planned aggregate expenditure, with the objective of eliminating output gaps, are called stabilization policies. Policy actions intended to increase planned spending and output are called expansionary policies; expansionary policy actions are normally taken when the economy is in recession. It is also possible, as we have seen, for the economy to be “overheated,” with output greater than potential output (an expansionary gap). The risk of an expansionary gap, as we will see in more detail later, is that it may lead to an increase in inflation. To offset an expansionary gap, policymakers will try to reduce spending and output. Contractionary policies are policy actions intended to reduce planned spending and output.

The two major tools of stabilization policy are monetary policy and fiscal policy. Recall that monetary policy refers to decisions about the size of the money supply, whereas fiscal policy refers to decisions about the government’s budget—how much the government spends and how much tax revenue it collects. In the remainder of this chapter we will focus on how fiscal policy can be used to influence spending in the basic Keynesian model, as well as on some practical issues that arise in the use of fiscal policy in the real world. Monetary policy will be discussed in incoming chapters.

GOVERNMENT PURCHASES AND PLANNED SPENDING

Decisions about government spending represent one of the two main components of fiscal policy, the other being decisions about taxes and transfer payments. Keynes himself felt that changes in government purchases were probably the most effective tool for reducing or eliminating output gaps. His basic argument was straightforward: Government purchases of goods and services, being a component of planned aggregate expenditure, directly affect total spending. If output gaps are caused by too much or too little total spending, then the government can help to guide the economy toward full employment by changing its own level of spending. Keynes’s views seemed to be vindicated by the events of the 1930s, notably the fact that the Depression did not end until governments greatly increased their military spending in the latter part of the decade.

Example 25.4 shows how increased government purchases of goods and services can help to eliminate a recessionary gap. (The effects of government spending on transfer programs, such as unemployment benefits, are a bit different. We will return to that case shortly.)

EXAMPLE 25.4Recessionary Gap

How can the government eliminate an output gap by changing its purchases of goods and services?

In our example economy, we found that a drop of 10 units in consumer spending creates a recessionary gap of 50 units. How can the government eliminate the output gap and restore full employment by changing its purchases of goods and services G?

Planned aggregate expenditure was given by the equation PAE = 960 + 0.8Y, so that autonomous expenditure equaled 960. The 10-unit drop in implied a 10-unit drop in autonomous expenditure, to 950. Because the multiplier in that sample economy equaled 5, this 10-unit decline in autonomous expenditure resulted in turn in a 50-unit decline in short-run equilibrium output.

To offset the effects of the consumption decline, the government would have to restore autonomous expenditure to its original value, 960. Under our assumption that government purchases are simply given and do not depend on output, government purchases are part of autonomous expenditure, and changes in government purchases change autonomous expenditure one-for-one. Thus, to increase autonomous expenditure from 950 to 960, the government should simply increase its purchases by 10 units (for example, by increasing spending on military defense or road construction). According to the basic Keynesian model, this increase in government purchases should return autonomous expenditure and, hence, output to their original levels.

The effect of the increase in government purchases is shown graphically in Figure 25.7. After the 10-unit decline in the autonomous component of consumption spending , the economy is at point F, with a 50-unit recessionary gap. A 10-unit increase in government purchases raises autonomous expenditure by 10 units, raising the intercept of the expenditure line by 10 units and causing the expenditure line to shift upward in parallel fashion. The economy returns to point E, where short-run equilibrium output equals potential output (Y = Y* = 4,800) and the output gap has been eliminated.

FIGURE 25.7 An Increase in Government Purchases Eliminates a Recessionary Gap.After a 10-unit decline in the autonomous part of consumer spending , (1 ) the economy is initially at point F, with a recessionary gap of 50 (see Figure 25.5); (2) a 10-unit increase in government purchases raises autonomous expenditure by 10 units, shifting the expenditure line back to its original position and raising the equilibrium point from F to E; (3) the new equilibrium is at point E, where output equals potential output (Y − Y* = 4,800), the output gap has been eliminated.

CONCEPT CHECK 25.5

In Concept Check 25.4, you considered the case in which consumers become more rather than less confident, leading to an expansionary output gap. Discuss how a change in government purchases could be used to eliminate an expansionary gap. Show your analysis graphically.

To this point we have been considering the effect of fiscal policy on a hypothetical economy. The Economic Naturalist 25.4 illustrates the application of fiscal policy in a real economy.

The Economic Naturalist 25.4

Does military spending stimulate the economy?

An antiwar poster from the 1960s bore the message “War is good business,” referring to the uncomfortable fact that there are sectors in the economy that can do quite well during wars. War itself poses too many economic and human costs to be good business, but military spending could be a different matter. According to the basic Keynesian model, increases in aggregate expenditure resulting from stepped-up government purchases may help bring an economy out of a recession or depression. Does military spending stimulate aggregate demand?

Figure 25.8 shows U.S. military spending as a share of GDP from 1929 to 2016. The shaded areas in the figure correspond to periods of recession as shown earlier in Table 24.1. Note the spike that occurred during World War II (1941–1945), when military spending exceeded 43 percent of U.S. GDP, as well as the surge during the Korean War (1950–1953). Smaller increases in military spending relative to GDP occurred at the peak of the Vietnam War in 1967–1969, during the Reagan military buildup of the 1980s, and during the wars in Afghanistan and Iraq (which started in 2001 and 2003, respectively).

FIGURE 25.8 U.S. Military Expenditures as a Share of GDP, 1929–2016.Military expenditures as a share of GDP rose during World War II, the Korean War, the Vietnam War, the Reagan military buildup of the early 1980s, and during the wars in Afghanistan and Iraq. Increased military spending is often associated with an expanding economy and declining unemployment. The shaded areas indicate periods of recession.Source: Bureau of Economic Analysis, www.bea.gov

Figure 25.8 provides some support for the idea that expanded military spending tends to promote growth in aggregate demand. The clearest case is the World War II era, during which massive military spending helped the U.S. economy to recover from the Great Depression. The U.S. unemployment rate fell from 17.2 percent of the workforce in 1939 (when defense spending was less than 2 percent of GDP) to 1.2 percent in 1944 (when defense spending was greater than 43 percent of GDP). Two brief recessions, in 1945 and 1948–1949, followed the end of the war and the sharp decline in military spending. At the time, though, many people feared that the war’s end would bring a resumption of the Great Depression, so the relative mildness of the two postwar recessions was something of a relief.

Increases in defense spending during the post–World War II period were also associated with economic expansions. The Korean War of 1950–1953 occurred simultaneously with a strong expansion, during which the unemployment rate dropped from 5.9 percent in 1949 to 2.9 percent in 1953. A recession began in 1954, the year after the armistice was signed, though military spending had not yet declined much. Economic expansions also occurred during the Vietnam-era military buildup in the 1960s and the Reagan buildup of the 1980s. Finally, on a smaller scale, increased government spending for military purposes and homeland security probably contributed to the relative mildness of the U.S. recession that began in 2001. These episodes support the idea that increases in government purchases—in this case, of weapons, other military supplies, and the services of military personnel—can help to stimulate the economy.

TAXES, TRANSFERS, AND AGGREGATE SPENDING

Besides making decisions about government purchases of goods and services, fiscal policymakers also determine the level and types of taxes to be collected and transfer payments to be made. (Transfer payments, recall, are payments made by the government to the public, for which no current goods or services are received. Examples of transfer payments are unemployment insurance benefits, Social Security benefits, and income support payments to farmers. Once again, transfer payments are not included in government purchases of goods and services.) The basic Keynesian model implies that, like changes in government purchases, changes in the level of taxes or transfers can be used to affect planned aggregate expenditure and thus eliminate output gaps.

Unlike changes in government purchases, however, changes in taxes or transfers do not affect planned spending directly. Instead they work indirectly, by changing disposable income in the private sector. For example, either a tax cut or an increase in government transfer payments increases disposable income, equal to Y − T. According to the consumption function, when disposable income rises, households should spend more. Specifically, households should initially increase their expenditures by mpc times the increase in disposable income (Equation 25.2). Thus a tax cut or increase in transfers should increase planned aggregate expenditure. Likewise, an increase in taxes or a cut in transfers, by lowering households’ disposable income, will tend to lower planned spending. The following example illustrates the effects of a tax cut on spending and output.

EXAMPLE 25.5Using a Tax Cut to Close a Recessionary Gap

How can the government eliminate an output gap by cutting taxes?

In our hypothetical economy, an initial drop in consumer spending of 10 units creates a recessionary gap of 50 units. We showed that this recessionary gap could be eliminated by a 10-unit increase in government purchases. Suppose that, instead of increasing government purchases, fiscal policymakers decided to stimulate consumer spending by changing the level of tax collections. By how much should they change taxes to eliminate the output gap?

A common first guess to the answer to this problem is that policymakers should cut taxes by 10, but that guess is not correct. Let’s see why.

The source of the recessionary gap in Example 25.3 is the reduction that households made in their consumption spending by 10 units at each level of output Y—that is, the constant term in the consumption function is assumed to have fallen 10 units. To eliminate this recessionary gap, the change in taxes must induce households to increase their consumption spending by 10 units at each output level. However, if taxes T are cut by 10 units, raising disposable income Y − T by 10 units, consumption at each level of output Y will increase by only 8 units.

Why? The reason is that the marginal propensity to consume in our example is 0.8, so that consumption spending increases by only 0.8 times the amount of the tax cut. (The rest of the tax cut is saved.) An increase in autonomous expenditure of 8 units is not enough to return output to its full-employment level, in this example.

To raise consumption spending by 10 units at each level of output, fiscal policymakers must instead cut taxes by 12.5 units. This will raise the level of disposable income, Y − T, by 12.5 units at each level of output Y. Consequently, consumption will increase by the marginal propensity to consume times the increase in disposable income, or by 0.8(12.5) = 10. Thus, a tax cut of 12.5 will spur households to increase their consumption by 10 units at each level of output.

These changes are illustrated in Table 25.3. Following the initial 10-unit drop in consumer spending, the equilibrium level of output fell to 4,750. When net taxes are equal to their initial level of 250, column 3 illustrates that disposable income equals 4,750 − 250 = 4,500. After the drop in consumer spending, the consumption function becomes C = 610 + 0.8(Y − T). Thus, when Y = 4,750 and T = 250, consumption will equal 610 + 0.8(4,750 − 250) = 610 + 0.8(4,500) = 4,210, as shown in column 4. If taxes are cut by 12.5 to 237.5, disposable income at that level of output will rise by 12.5 to 4,750 − 237.5 = 4,512.5. Consumption at that level of output will rise by 0.8(12.5) = 10 so that C = 610 + 0.8(4,750 − 237.5) = 4,220. This increase will just offset the initial 10-unit decrease in and will bring the economy back to full employment.

Note that, since T refers to net taxes, or taxes less transfers, the same result could be obtained by increasing transfer payments by 12.5 units. Because households spend 0.8 times any increase in transfer payments they receive, this policy also would raise consumption spending by 10 units at any level of output.

Graphically, the effect of the tax cut is identical to the effect of the increase in government purchases, shown in Figure 25.8. Because it leads to a 10-unit increase in consumption at any level of output, the tax cut shifts the expenditure line up by 10 units. Equilibrium is attained at point E in Figure 25.8, where output again equals potential output.

CONCEPT CHECK 25.6

In a particular economy, a 20-unit increase in planned investment moved the economy from an initial situation with no output gap to a situation with an expansionary gap. Describe two ways in which fiscal policy could be used to offset this expansionary gap. Assume the marginal propensity to consume equals 0.5.

The Economic Naturalist 25.5

Why did the federal government temporarily cut taxes in 2001 and 2009?

On May 25, 2001, Congress passed the Economic Growth and Tax Relief Reconciliation Act (EGTRRA) of 2001, which President George W. Bush signed on June 7. The EGTRRA made significant cuts in income tax rates and also provided for one-time tax rebate checks of up to $300 for individual taxpayers and up to $600 for married taxpayers filing a joint return. Millions of families received these checks in August and September of 2001, with payments totaling about $38 billion. Why did the federal government send out these checks?

Almost eight years later, in February 2009, Congress passed the American Recovery and Reinvestment Act (ARRA) of 2009, which President Barack Obama signed on February 17, 2009. Among its provisions, the ARRA included $288 of tax relief, including a new payroll tax credit of $400 for individuals and $800 for couples in 2009 and 2010. Why did the federal government make these tax cuts?

Although the 2001 recession was not officially “declared” until November 2001 (when the National Bureau of Economic Research announced that the recession had begun in March), there was clear evidence by the spring of 2001 that the economy was slowing. Congress and the president hoped that by sending tax rebate checks to households, they could stimulate spending and perhaps avoid recession. In retrospect, the timing of the tax rebate was quite good since the economy and consumer confidence were further buffeted by the terrorist attacks on New York City and Washington on September 11, 2001.

Did the 2001 tax rebates have their intended effect of stimulating consumer spending? It is difficult to know with any certainty, since we do not know how much households would have spent if they had not received these extra funds. In a study published in 2006, economists found that households spent about two-thirds of their rebates within six months of receiving them.⁹ This suggests that the rebate had a substantial effect on consumer spending, which held up remarkably well during the last quarter of 2001 and into 2002, assisting the economy’s recovery substantially. Most economists would agree that fiscal policy generally—including not only the tax rebates, but also significantly increased spending for the military and for domestic security following September 11—was an important reason that the 2001 recession was relatively short and mild.

In contrast with the 2001 recession, the 2007–2009 recession was the most severe recession since the end of World War II. By the time the ARRA was passed, not only had the beginning of the recession already been officially declared, but the recession’s effects were already widely felt. For example, unemployment had already increased by around 3 percent since December 2007. Congress and the president hoped that a large tax cut, in addition to about half a trillion dollars of direct government spending and increased transfer payments, would stimulate the economy and help it recover from the recession.

RECAP

FISCAL POLICY AND PLANNED SPENDING

· Fiscal policy consists of two tools for affecting total spending and eliminating output gaps: (1) changes in government purchases and (2) changes in taxes or transfer payments.

· An increase in government purchases increases autonomous expenditure by an equal amount. A reduction in taxes or an increase in transfer payments increases autonomous expenditure by an amount equal to the marginal propensity to consume times the reduction in taxes or increase in transfers.

· The ultimate effect of a fiscal policy change on short-run equilibrium output equals the change in autonomous expenditure times the multiplier. Accordingly, if the economy is in recession, an increase in government purchases, a cut in taxes, or an increase in transfers can be used to stimulate spending and eliminate the recessionary gap.

FISCAL POLICY AS A STABILIZATION TOOL: THREE QUALIFICATIONS

The basic Keynesian model might lead you to think that precise use of fiscal policy can eliminate output gaps. But as is often the case, the real world is more complicated than economic models suggest. We close the chapter with three qualifications about the use of fiscal policy as a stabilization tool.

FISCAL POLICY AND THE SUPPLY SIDE

We have focused so far on the use of fiscal policy to affect planned aggregate expenditure. However, most economists would agree that fiscal policy may affect potential output as well as planned aggregate expenditure. On the spending side, for example, investments in public capital, such as roads, airports, and schools, can play a major role in the growth of potential output, as we discussed in Chapter 19, Economic Growth, Productivity, and Living Standards. On the other side of the ledger, tax and transfer programs may well affect the incentives, and thus the economic behavior, of households and firms. For example, a high tax rate on interest income may reduce the willingness of people to save for the future, while a tax break on new investment may encourage firms to increase their rate of capital formation. Such changes in saving or investment will in turn affect potential output. Many other examples could be given of how taxes and transfers affect economic behavior and thus possibly affect potential output as well.

Some critics of the Keynesian theory have gone so far as to argue that the only effects of fiscal policy that matter are effects on potential output. This was essentially the view of the so-called supply-siders, a group of economists and journalists whose influence reached a high point during the first Reagan term (1981–1985). Supply-siders focused on the need for tax cuts, arguing that lower tax rates would lead people to work harder (because they would be allowed to keep a larger share of their earnings), to save more, and to be more willing to innovate and take risks. Through their arguments that lower taxes would substantially increase potential output, with no significant effect on spending, the supply-siders provided crucial support for the large tax cuts that took place under the Reagan administration. Supply-sider ideas also were used to support the long-term income tax cut passed under President George W. Bush in 2001.

A more balanced view is that fiscal policy affects both spending and potential output. Thus, in making fiscal policy, government officials should take into account not only the need to stabilize aggregate expenditure but also the likely effects of government spending, taxes, and transfers on the economy’s productive capacity.

THE PROBLEM OF DEFICITS

A second consideration for fiscal policymakers thinking about stabilization policies is the need to avoid large and persistent budget deficits. Recall from Chapter 21, Saving and Capital Formation, that the government’s budget deficit is the excess of government spending over tax collections. Sustained government deficits can be harmful because they reduce national saving, which in turn reduces investment in new capital goods—an important source of long-run economic growth. The need to keep deficits under control may make increasing spending or cutting taxes to fight a slowdown a less attractive option, both economically and politically.

Moreover, international lenders would not let a country run large and persistent deficits for too long even if at home deficits appeared politically attractive. As an extreme example, Greece’s government has for many years been running large budget deficits—estimated at more than 7 percent of GDP, on average, from 1995 to 2016. These large deficits eventually led in the past few years to a government-debt crisis. As international lenders question the Greek government’s ability to pay back any future loans, Greece’s government has been very limited in its ability to run further deficits to stimulate the economy and fight recessions. Indeed, in 2016, the Greek government was forced to run a small budget surplus in spite of no real GDP growth and a very high unemployment rate (more than 23 percent!).

THE RELATIVE INFLEXIBILITY OF FISCAL POLICY

The third qualification about the use of fiscal policy is that fiscal policy is not always flexible enough to be useful for stabilization. Our examples have implicitly assumed that the government can change spending or taxes relatively quickly in order to eliminate output gaps. In reality, changes in government spending or taxes must usually go through a lengthy legislative process, which reduces the ability of fiscal policy to respond in a timely way to economic conditions. For example, budget and tax changes proposed by the president must typically be submitted to Congress 18 months or more before they go into effect. Another factor that limits the flexibility of fiscal policy is that fiscal policymakers have many other objectives besides stabilizing aggregate spending, from ensuring an adequate national defense to providing income support to the poor. What happens if, say, the need to strengthen the national defense requires an increase in government spending, but the need to contain aggregate expenditure requires a decrease in government spending? Such conflicts can be difficult to resolve through the political process.

This lack of flexibility means that fiscal policy is less useful for stabilizing spending than the basic Keynesian model suggests. Nevertheless, most economists view fiscal policy as an important stabilizing force, for two reasons. The first is the presence of automatic stabilizers, provisions in the law that imply automatic increases in government spending or decreases in taxes when real output declines. For example, some government spending is earmarked as “recession aid”; it flows to communities automatically when the unemployment rate reac hes a certain level. Taxes and transfer payments also respond automatically to output gaps: When GDP declines, income tax collections fall (because households’ taxable incomes fall) while unemployment insurance payments and welfare benefits rise—all without any explicit action by Congress. These automatic changes in government spending and tax collections help to increase planned spending during recessions and reduce it during expansions, without the delays inherent in the legislative process.

The second reason that fiscal policy is an important stabilizing force is that although fiscal policy may be difficult to change quickly, it may still be useful for dealing with prolonged episodes of recession. The Great Depression of the 1930s, the Japanese slump of the 1990s, and the global recession of 2007–2009 are three cases in point. However, because of the relative lack of flexibility of fiscal policy, in modern economies aggregate spending is more usually stabilized through monetary policy. The stabilizing role of monetary policy is the subject of the next chapter.

RECAP

FISCAL POLICY AS A STABILIZATION TOOL: THREE QUALIFICATIONS

· Changes in taxes and transfer programs may affect the incentives and economic behavior of households and firms.

· Governments must weigh the short-run effects of fiscal policy against the possibility of large and persistent budget deficits.

· Changes in spending and taxation take time and thus fiscal policy can be relatively slow and inflexible.

SUMMARY

· The basic Keynesian model shows how fluctuations in planned aggregate expenditure, or total planned spending, can cause actual output to differ from potential output. Too little spending leads to a recessionary output gap; too much spending creates an expansionary output gap. This model relies on the crucial assumption that firms do not respond to every change in demand by changing prices. Instead, they typically set a price for some period and then meet the demand forthcoming at that price. Firms do not change prices continually because changing prices entails costs, called menu costs. (LO1)

· Planned aggregate expenditure is total planned spending on final goods and services. The four components of total spending are consumption, investment, government purchases, and net exports. Planned and actual consumption, government purchases, and net exports are generally assumed to be the same. Actual investment may differ from planned investment because firms may sell a greater or lesser amount of their production than they expected. If firms sell less than they expected, for example, they are forced to add more goods to inventory than anticipated. And because additions to inventory are counted as part of investment, in this case actual investment (including inventory investment) is greater than planned investment. (LO2)

· Consumption is related to disposable, or after-tax, income by a relationship called the consumption function. The amount by which consumption rises when disposable income rises by one dollar is called the marginal propensity to consume (mpc). The marginal propensity to consume is always greater than zero but less than one (that is, 0 < mpc <1). (LO2)

· An increase in real output raises planned aggregate expenditure since higher output (and, equivalently, higher income) encourages households to consume more. Planned aggregate expenditure can be broken down into two components: autonomous expenditure and induced expenditure. Autonomous expenditure is the portion of planned spending that is independent of output; induced expenditure is the portion of spending that depends on output. (LO2)

· In the period in which prices are fixed, short-run equilibrium output is the level of output that just equals planned aggregate expenditure. Short-run equilibrium can be determined numerically by a table that compares alternative values of output and the planned spending implied by each level of output, or by directly manipulating the relevant equations. Short-run equilibrium output also can be determined graphically in a Keynesian-cross diagram. (LO3)

· Changes in autonomous expenditure will lead to changes in short-run equilibrium output. In particular, if the economy is initially at full employment, a fall in autonomous expenditure will create a recessionary gap and a rise in autonomous expenditure will create an expansionary gap. The amount by which a one-unit increase in autonomous expenditure raises short-run equilibrium output is called the multiplier. An increase in autonomous expenditure not only raises spending directly; it also raises the incomes of producers, who in turn increase their spending, and so on. Hence the multiplier is greater than one; that is, a one-dollar increase in autonomous expenditure tends to raise short-run equilibrium output by more than one dollar. (LO4)

· To eliminate output gaps and restore full employment, the government employs stabilization policies. The two major types of stabilization policy are monetary policy and fiscal policy. Stabilization policies work by changing planned aggregate expenditure and hence short-run equilibrium output. For example, an increase in government purchases raises autonomous expenditure directly, so it can be used to reduce or eliminate a recessionary gap. Similarly, a cut in taxes or an increase in transfer payments increases the public’s disposable income, raising consumption spending at each level of output by an amount equal to the marginal propensity to consume times the cut in taxes or increase in transfers. Higher consumer spending, in turn, raises short-run equilibrium output. (LO5)

· Three qualifications must be made to the use of fiscal policy as a stabilization tool. First, fiscal policy may affect potential output as well as aggregate spending. Second, large and persistent government budget deficits reduce national saving and growth; the need to keep deficits under control may limit the use of expansionary fiscal policies. Finally, because changes in fiscal policy must go through a lengthy legislative process, fiscal policy is not always flexible enough to be useful for short-run stabilization. However, automatic stabilizers—provisions in the law that imply automatic increases in government spending or reductions in taxes when output declines—can overcome the problem of legislative delays to some extent and contribute to economic stability. (LO6)

KEY TERMS

automatic stabilizers

autonomous consumption

autonomous expenditure

consumption function

contractionary policies

disposable income

expansionary policies

expenditure line

fiscal policy

income-expenditure multiplier

induced expenditure

marginal propensity to consume (mpc)

menu costs

planned aggregate expenditure (PAE)

short-run equilibrium output

stabilization policies

wealth effect

REVIEW QUESTIONS

1. 1.What is the key assumption of the basic Keynesian model? Explain why this assumption is needed if one is to accept the view that aggregate spending is a driving force behind short-term economic fluctuations. (LO1)

2. 2.Give an example of a good or service whose price changes very frequently and one whose price changes relatively infrequently. What accounts for the difference? (LO1)

3. 3.Define planned aggregate expenditure and list its components. Why does planned spending change when output changes? (LO2)

4. 4.Explain how planned spending and actual spending can differ. Illustrate with an example. (LO2)

5. 5.Sketch a graph of the consumption function, labeling the axes of the graph. Discuss the economic meaning of (a) a movement from left to right along the graph of the consumption function and (b) a parallel upward shift of the consumption function. Give an example of a factor that could lead to a parallel upward shift of the consumption function. (LO2)

6. 6.Sketch the Keynesian-cross diagram. Explain in words the economic significance of the two lines graphed in the diagram. Given only this diagram, how could you determine autonomous expenditure, induced expenditure, the marginal propensity to consume, and short-run equilibrium output? (LO3)

7. 7.Define the multiplier. In economic terms, why is the multiplier greater than one? (LO4)

8. 8.The government is considering two alternative policies, one involving increased government purchases of 50 units, the other involving a tax cut of 50 units. Which policy will stimulate planned aggregate expenditure by more? Why? (LO5)

9. 9.Discuss three reasons why the use of fiscal policy to stabilize the economy is more complicated than suggested by the basic Keynesian model. (LO6)

PROBLEMS

1. 1.Acme Manufacturing is producing $4,000,000 worth of goods this year and expects to sell its entire production. It also is planning to purchase $1,500,000 in new equipment during the year. At the beginning of the year, the company has $500,000 in inventory in its warehouse. Find actual investment and planned investment if Acme actually sells

a. $3,850,000 worth of goods.

b. $4,000,000 worth of goods.

c. $4,200,00 worth of goods.

2. Assuming that Acme’s situation is similar to that of other firms, in which of these three cases is output equal to short-run equilibrium output? (LO2, LO3)

3. 2.Data on before-tax income, taxes paid, and consumption spending for the Simpson family in various years are given below: (LO2)

a. Graph the Simpsons’ consumption function and find their household’s marginal propensity to consume.

b. How much would you expect the Simpsons to consume if their income was $32,000 and they paid taxes of $5,000?

c. Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption by $1,000 at each level of after-tax income. (“Income” does not include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume?

4. 3.An economy is described by the following equations: (LO2)

a. Find a numerical equation linking planned aggregate expenditure to output.

b. Find autonomous expenditure and induced expenditure in this economy.

5. 4.For the economy described in Problem 3: (LO3)

a. Construct a table like Table 25.1 to find short-run equilibrium output. Consider possible values for short-run equilibrium output ranging from 8,200 to 9,000.

b. Show the determination of short-run equilibrium output for this economy using the Keynesian-cross diagram.

c. What is the output gap for this economy? If the natural rate of unemployment is 4 percent, what is the actual unemployment rate for this economy? (Hint: Use Okun’s law.)

6. 5.For the economy described in Problems 3, take as given that the multiplier for this economy is 2.5. Find the effect on short-run equilibrium output of: (LO4)

a. An increase in government purchases from 1,500 to 1,600.

b. A decrease in tax collections from 1,500 to 1,400 (leaving government purchases at their original value).

c. A decrease in planned investment spending from 900 to 800.

7. 6.An economy is initially at full employment, but a decrease in planned investment spending (a component of autonomous expenditure) pushes the economy into recession. Assume that the mpc of this economy is 0.75 and that the multiplier is 4. (LO4, LO5)

a. How large is the recessionary gap after the fall in planned investment?

b. By how much would the government have to change its purchases to restore the economy to full employment?

c. Alternatively, by how much would the government have to change taxes?

d. * Suppose that the government’s budget is initially in balance, with government spending equal to taxes collected. A balanced-budget law forbids the government from running a deficit. Is there anything that fiscal policymakers could do to restore full employment in this economy, assuming they do not want to violate the balanced-budget law?

8. 7.An economy is described by the following equations:

The multiplier in this economy is 5. (LO4, LO5)

a. Find a numerical equation relating planned aggregate expenditure to output.

b. Construct a table to find the value of short-run equilibrium output. (Hint: The economy is fairly close to full employment.)

c. By how much would government purchases have to change in order to eliminate any output gap? By how much would taxes have to change? Show the effects of these fiscal policy changes in a Keynesian-cross diagram.

d. Repeat part c assuming that Y* = 630.

e. Show your results for parts b through d on a Keynesian- cross diagram.

9. 8.*An economy is described by the following equations: (LO3, LO4, LO5)

a. For this economy, find the following: autonomous expenditure, the multiplier, short-run equilibrium output, and the output gap.

b. Illustrate this economy’s short-run equilibrium on a Keynesian-cross diagram.

c. Calculate the amount by which autonomous expenditure would have to change to eliminate the output gap.

d. Suppose that the government decided to close the output gap by reducing taxes. By how much must taxes be reduced in order to do this?

10. 9.*An economy has zero net exports. Otherwise, it is identical to the economy described in Problem 7. (LO3, LO4, LO5)

a. Find short-run equilibrium output.

b. Economic recovery abroad increases the demand for the country’s exports; as a result, NX rises to 100. What happens to short-run equilibrium output?

c. Repeat part b, but this time assume that foreign economies are slowing, reducing the demand for the country’s exports, so that NX = −100. (A negative value of net exports means that exports are less than imports.)

d. How do your results help to explain the tendency of recessions and expansions to spread across countries?

ANSWERS TO CONCEPT CHECKS

1. 25.1First we need to find an equation that relates planned aggregate expenditure PAE to output Y. We start with the definition of planned aggregate expenditure and then substitute the numerical values given in the problem:

Using this relationship, we construct a table analogous to Table 25.1. Some trial and error is necessary to find an appropriate range of guesses for output (column 1).

Short-run equilibrium output equals 6,000, as that is the only level of output that satisfies the condition Y = PAE. Using the equation for planned aggregate expenditure, in equilibrium we have Y = 1,800 + 0.7Y. Solving for Y, we find that Y = 6,000, just as we found using the table. (LO3)

2. 25.2The graph shows the determination of short-run equilibrium output, Y = 6,000. The intercept of the expenditure line is 1,800 and its slope is 0.7. Notice that the intercept equals autonomous expenditure and the slope equals the marginal propensity to consume. (LO3)

3. 25.3This problem is an application of Okun’s law, introduced in Chapter 24, Short-Term Economic Fluctuations: An Introduction. The recessionary gap in this example is −50/4,800, or about −1.04 percent, of potential output. By Okun’s law, cyclical unemployment is one-half the percentage size of the output gap, or 0.52 percent. As the natural rate of unemployment is 5 percent, the total unemployment rate after the recessionary gap appears will be approximately 5.52 percent. (LO4)

4. 25.4This concept check is just the reverse of the analysis in the text. An increase in of 10 units raises autonomous expenditure and hence the intercept of the expenditure line by 10 units. The expenditure line shifts up, in parallel fashion, by 10 units, leading to an increase in output and an expansionary output gap. As output falls by 50 units in the text in Example 25.3, it rises by 50 units, to 4,850, in the case analyzed here. To verify that short-run equilibrium output equals 4,850, note that an increase of 10 units in autonomous expenditure implies that PAE rises from 960 + 0.8Y to 970 + 0.8Y. When Y = 4,850, then PAE = 970 + 0.8(4,850) = 4,850, so that we have Y = PAE. (LO4)

5. 25.5In Concept Check 25.4, we saw that a 10-unit increase in increases autonomous expenditure and hence the intercept of the expenditure line by 10 units. The expenditure line shifts upward, in parallel fashion, by 10 units, leading to an expansionary output gap. To offset this gap, the government should reduce its purchases by 10 units, returning autonomous expenditure to its original level. The expenditure line shifts back down to its original position, restoring output to its initial full-employment level. The graph is just the reverse of Figure 25.8, with the expenditure line being shifted up by the increase in consumption and down (back to point E) by the offsetting reduction in government purchases. (LO5)

6. 25.6The 20-unit increase in planned investment is a 20-unit increase in autonomous expenditure, which will lead to an even greater increase in short-run equilibrium output. To offset the 20-unit increase in autonomous expenditure by means of fiscal policy, the government can reduce its purchases by 20 units. Alternatively, it could raise taxes (or cut transfers) to reduce consumption spending. Since the mpc = 0.5, to reduce consumption spending by 20 units at each level of output, the government will need to increase taxes (or reduce transfers) by 40 units. At each level of output, a 40-unit tax increase will reduce disposable income by 40 units and cause consumers to reduce their spending by 0.5 × 40 = 20 units, as needed to eliminate the expansionary output gap. (LO5)

APPENDIX A

his chapter has shown how to solve the basic Keynesian model numerically and graphically, using the Keynesian cross diagram. In this appendix, we will show how to find a more general algebraic solution for short-run equilibrium output in the basic Keynesian model. This solution has the advantage of showing clearly the links between short-run equilibrium output, the multiplier, and autonomous expenditure. The general method can also be applied when we make changes to the basic Keynesian model, as we will see in following chapters.

The model we will work with is the same one presented in the main part of the chapter. Start with the definition of planned aggregate expenditure, Equation 25.1:

PAE = C + I^p + G + NX.(25.1)

Equation 25.1 says that planned aggregate expenditure is the sum of the four types of planned spending: consumption spending by households, C; planned investment spending by firms, I^p; government purchases, G; and net exports purchased by foreigners, NX.

The first component of planned aggregate expenditure, consumption spending, is determined by the consumption function, Equation 25.2. It is copied below, with one change: while in the body of this and the following chapters we use mpc for the marginal propensity to consume, in the appendices we will use just one letter, c. This will simplify the notation in our algebraic treatment.

(25.2)

The consumption function says that consumption spending increases when disposable (after-tax) income Y − T increases. Each dollar increase in disposable income raises consumption spending by c dollars, where c, the marginal propensity to consume, is a number between 0 and 1. Other factors affecting consumption spending are captured by the term . For example, a boom in the stock market that leads consumers to spend more at each level of disposable income (a wealth effect) would be represented as an increase in .

As in the body of the chapter, we assume that planned investment, government purchases, net exports, and net tax collections are simply given numbers. A variable whose value is fixed and given from outside the model is called an exogenous variable; so, in other words, we are assuming that planned investment, government purchases, net exports, and net tax collections are exogenous variables. Using an overbar to denote the given value of an exogenous variable, we can write this assumption as

So, for example, is the given value of planned investment spending, as determined outside the model. In our examples we will set and the other exogenous variables equal to some particular number.

Our goal is to solve algebraically for short-run equilibrium output, the level of output that prevails during the period in which prices are predetermined. The first step is to relate planned aggregate expenditure PAE to output Y. Starting with the definition of planned aggregate expenditure (Equation 25.1), use the consumption function (Equation 25.2) to substitute for consumption spending C and replace I^p, G, NX, and T with their exogenous values. With these substitutions, planned aggregate expenditure can be written as

Rearranging this equation to separate the terms that do and do not depend on output Y, we get

(25A.1)

Equation 25A.1 is an important equation because it shows the relationship between planned aggregate expenditure PAE and output Y. The bracketed term on the right side of the equation represents autonomous expenditure, the part of planned spending that does not depend on output. The term cY represents induced expenditure, the part of planned spending that does depend on output. Equation 25A.1 is also the equation that describes the expenditure line in the Keynesian cross diagram; it shows that the intercept of the expenditure line equals autonomous expenditure and the slope of the expenditure line equals the marginal propensity to consume.

We can illustrate how Equation 25A.1 works numerically by using Example 25.2 in the text. That example assumed the following numerical values: = 620, = 220, = 300, = 20, = 250, and c = 0.8. Plugging these values into Equation 25A.1 and simplifying, we get

PAE = 960 + 0.8Y,

which is the same answer we found in Example 25.2. Autonomous expenditure in this example equals 960, and induced expenditure equals 0.8Y.

The second step in solving for short-run equilibrium output begins with the definition of short-run equilibrium output (Equation 25.3):

Y = PAE.

Remember that short-run equilibrium output is the value of output at which output equals planned aggregate expenditure. Using Equation 25A.1 to substitute for PAE in the definition of short-run equilibrium output, we get

The value of Y that solves this equation is the value of short-run equilibrium output. To solve for Y, group all terms involving Y on the left side of the equation:

or

Dividing both sides of the equation by (1 − c) gives

(25A.2)

Equation 25A.2 gives short-run equilibrium output for our model economy in terms of the exogenous values , , , and and the marginal propensity to consume, c. We can use this formula to solve for short-run equilibrium output in specific numerical examples. For example, suppose that we onc e again plug in the numerical values assumed in Example 25.2: = 620, = 220, = 300, = 20, = 250, and c = 0.8. We get

which is the same answer we found more laboriously using Table 25.1.

CONCEPT CHECK 25A.1

Use Equation 25A.2 to find short-run equilibrium output for the economy described in Concept Check 25.1 in the text. What are the intercept and the slope of the expenditure line?

Equation 25A.2 shows clearly the relationship between autonomous expenditure and short-run equilibrium output. Autonomous expenditure is the first term on the right side of Equation 26A.1, equal to The equation shows that a one-unit increase in autonomous expenditure increases short-run equilibrium output by 1/(1 − c) units. In other words, we can see from Equation 25A.2 that the multiplier for this model equals 1/(1 − c). Further discussion of the multiplier is given in Appendix B to this chapter.

ANSWERS TO APPENDIX CONCEPT CHECKS

1. 25A.1 The equation describing short-run equilibrium output is

(25A.2)

Using data from Concept Check 25.1, set = 820, c = 0.7, = 600, = 600, = 200, and = 600. Plugging these values into Equation (25A.2) we get

which is the same result obtained in Concept Check 25.1.

APPENDIX B

his appendix builds on the example economy used throughout the chapter to give a more complete explanation of the income-expenditure multiplier in the basic Keynesian model. In the chapter, we saw that a drop in autonomous expenditure of 10 units caused a decline in short-run equilibrium output of 50 units, five times as great as the initial change in spending. Hence, the multiplier in this example is 5.

To see why this multiplier effect occurs, note that the initial decrease of 10 in consumer spending (more precisely, in the constant term of the consumption function, ) has two effects. First, the fall in consumer spending directly reduces planned aggregate expenditure by 10 units. Second, the fall in spending also reduces by 10 units the incomes of producers (workers and firm owners) of consumer goods. Since the marginal propensity to consume is 0.8, the producers of consumer goods will therefore reduce their consumption spending by 8, or 0.8 times their income loss of 10. This reduction in spending cuts the income of other producers by 8 units, leading them to reduce their spending by 6.4, or 0.8 times their income loss of 8. These income reductions of 6.4 lead still other producers to cut their spending by 5.12, or 0.8 times 6.4, and so on. In principle, this process continues indefinitely, although after many rounds of spending and income reductions, the effects become quite small.

When all these “rounds” of income and spending reductions are added, the total effect on planned spending of the initial reduction of 10 in consumer spending is

10 + 8 + 6.4 + 5.12 + ⋯.

The three dots indicate that the series of reductions continues indefinitely. The total effect of the initial decrease in consumption also can be written as

This expression highlights the fact that the spending that takes place in each round is 0.8 times the spending in the previous round (0.8) because that is the marginal propensity to consume out of the income generated by the previous round of spending.

A useful algebraic relationship, which applies to any number x greater than 0 but less than 1, is

If we set x = 0.8, this formula implies that the total effect of the decline in consumption spending on aggregate demand and output is

This answer is consistent with our earlier calculation, which showed that short-run equilibrium output fell by 50 units, from 4,800 to 4,750.

By a similar analysis, we also can find a general algebraic expression for the multiplier in the basic Keynesian model. Recalling that in the appendices, we use c for the marginal propensity to consume out of disposable income (in the body of the chapters we use mpc), we know that a one-unit increase in autonomous expenditure raises spending and income by one unit in the first round; by c × 1 = c units in the second round; by c × c = c² units in the third round; by c × c² = c³ units in the fourth round; and so on. Thus, the total effect on short-run equilibrium output of a one-unit increase in autonomous expenditure is given by

1 + c + c² + c³ + ⋯.

Applying the algebraic formula given above, and recalling that 0 < c < 1, we can rewrite this expression as 1/(1 − c). Thus, in a basic Keynesian model with a marginal propensity to consume of c, the multiplier equals 1/(1 − c). Note that if c = 0.8 then 1/(1 − c) = 1/(1 − 0.8) = 5, which is the same value of the multiplier we found numerically above.

¹A brief biography of Keynes is available at www.bbc.co.uk/history/historic_figures/keynes_john_maynard.shtml.

²Obviously, firms can meet the forthcoming demand only up to the point where they reach the limit of their capacity to produce. For that reason, the Keynesian analysis of this chapter is relevant only when producers have unused capacity.

³As we discussed earlier, we use “investment” here to mean spending on new capital goods such as factories, housing, and equipment, which is not the same as financial investment. This distinction is important to keep in mind.

⁴For the purposes of measuring GDP, treating unsold output as being purchased by its producer has the advantage of ensuring that actual production and actual expenditure are equal.

⁵You should review the material in the appendix to Chapter 1, Thinking Like an Economist, if you don’t regularly work with linear equations.

⁶See Table 1 in James M. Poterba, “Stock Market Wealth and Consumption,” Journal of Economic Perspectives 14 (Spring 2000), pp. 99–118.

⁷U.S. Federal Housing Finance Agency, “All-Transactions House Price Index for the United States [USSTHPI],” retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/USSTHPI, November 2, 2017. House prices continued to rise, peaking in 2007.

⁸Federal Reserve Board, “Flow of Funds Accounts of the United States,” www.federalreserve.gov.

⁹David S. Johnson, Jonathan A. Parker, and Nicholas S. Souleles, “Household Expenditure and the Income Tax Rebates of 2001,” American Economic Review, December 2006, pp. 1589–1610.

*Denotes more difficult problem.