Chapter 10 Textbook PDF

C h a p t e r 10 Basic Macroeconomic Relationships* Learning Objectives chapter begins that process by examining the basic rela-...

C h a p t e r 10 Basic Macroeconomic Relationships* Learning Objectives chapter begins that process by examining the basic rela- tionships that exist between three different pairs of eco- LO10.1 Describe how changes in income affect nomic ­aggregates. (Recall that to economists “aggregate” consumption (and saving). means “total” or “combined.”) Specifically, this chapter LO10.2 List and explain factors other than income looks at the relationships between: that can affect consumption. ∙ Income and consumption (and income and saving). LO10.3 Explain how changes in real interest rates ∙ The interest rate and investment. affect investment. ∙ Changes in spending and changes in output. LO10.4 Identify and explain factors other than the What explains the trends in consumption (consumer spend- real interest rate that can affect investment. ing) and saving reported in the news? How do changes in LO10.5 Illustrate how changes in investment (or one interest rates affect investment? How can initial changes in of the other components of total spending) spending ultimately produce multiplied changes in GDP? can increase or decrease real GDP by a The basic macroeconomic relationships discussed in this multiple amount. chapter answer these questions. In Chapter 9 we discussed the business cycle, unem- ployment, and inflation. Our eventual goal is to build eco- The Income-Consumption nomic models that can explain these phenomena. This and Income-Saving Relationships LO10.1 Describe how changes in income affect consumption *Note to the Instructor: If you wish to bypass the aggregate expendi- (and saving). tures model (Keynesian cross model) covered in full in Chapter 11 , as- The other-things-equal relationship between income and con- signing the present chapter will provide a seamless transition to the sumption is one of the best-established relationships in macro- AD-AS model of Chapter 12 and the chapters beyond. If you want to economics. In examining that relationship, we are also cover the aggregate expenditures model, this present chapter provides exploring the relationship between income and saving. Recall the necessary building blocks. that economists define personal saving as “not spending” or as 201 202 PART FOUR Macroeconomic Models and Fiscal Policy “that part of disposable (after-tax) income not consumed.” Sav- of the 45° line—(S = DI − C). For ­example, in 2005 dis- ing (S) equals disposable income (DI) minus consumption (C). posable income was $9,401 billion and consumption was Many factors determine a nation’s levels of consumption $9,158 billion, so saving was $243 billion. Observe that the and saving, but the most significant is disposable income. vertical distance between the 45° line and line C increases Consider some recent historical data for the United States. In as we move rightward along the horizontal axis and de- Figure 10.1 each dot represents consumption and disposable creases as we move leftward. Like consumption, saving income for 1 year since 1993. The line C that is loosely fitted typically varies directly with the level of disposable in- to these points shows that consumption is directly (positively) come. However, that historical pattern broke down some- related to disposable income; moreover, households spend what in several years preceding the recession of 2007–2009. most of their income. But we can say more. The 45°(degree) line is a refer- ence line. Because it bisects the 90° angle formed by the The Consumption Schedule two axes of the graph, each point on it is equidistant from The dots in Figure 10.1 represent historical data—the actual the two axes. At each point on the 45° line, consumption amounts of DI, C, and S in the United States over a period of would equal disposable income, or C = DI. Therefore, the years. But because we want to understand how the economy vertical distance between the 45° line and any point on the would behave under different possible scenarios, we need a horizontal axis measures either consumption or disposable schedule showing the various amounts that households would income. If we let it measure disposable income, the vertical plan to consume at each of the various levels of disposable distance between it and the consumption line labeled C rep- income that might prevail at some specific time. Columns 1 resents the amount of saving (S) in that year. Saving is the and 2 of Table 10.1, represented in Figure 10.2a (Key amount by which actual consumption in any year falls short Graph), show the hypothetical consumption schedule that we FIGURE 10.1 Consumption and disposable income, 1993–2015. Each dot in this figure shows consumption and disposable income in a specific year. The line C, which generalizes the relationship between consumption and disposable income, indicates a direct relationship and shows that households consume most of their after-tax incomes. $14,000 15 14 12,000 13 11 12 09 10 Consumption (billions of dollars) 08 10,000 Saving in 07 2005 06 05 45° reference line C = DI 04 C 8,000 03 02 01 00 99 Consumption 6,000 98 in 2005 97 96 95 94 93 4,000 45° 0 0 4,000 6,000 8,000 10,000 12,000 $14,000 Disposable income (billions of dollars) Source: Bureau of Economic Analysis, www.bea.gov.  CHAPTER 10 Basic Macroeconomic Relationships 203 TABLE 10.1 Consumption and Saving Schedules (in Billions) and Propensities to Consume and Save (1) (4) (5) (6) (7) Level of Average Average Marginal Marginal Output Propensity Propensity Propensity Propensity and (2) (3) to Consume to Save to Consume to Save Income Consumption Saving (S), (APC), (APS), (MPC), (MPS), (GDP = DI) (C) (1) − (2) (2)/(1) (3)/(1) Δ(2)/Δ(1)* Δ(3)/Δ(1)* (1) $370 $375 $−5 1.01 −.01.75.25 (2) 390 390 0 1.00.00.75.25 (3) 410 405 5.99.01.75.25 (4) 430 420 10.98.02.75.25 (5) 450 435 15.97.03.75.25 (6) 470 450 20.96.04.75.25 (7) 490 465 25.95.05.75.25 (8) 510 480 30.94.06.75.25 (9) 530 495 35.93.07.75.25 (10) 550 510 40.93.07 *The Greek letter Δ, delta, means “the change in.” require. This consumption schedule (or “consumption func- b­ elow the h­ orizontal axis. We have marked the dissaving at tion”) reflects the direct consumption–disposable income re- the $370 billion level of income in Figure 10.2a and 10.2b. lationship suggested by the data in Figure 10.1, and it is Both vertical distances measure the $5 billion of dissaving consistent with many household budget studies. In the aggre- that occurs at $370 billion of income. gate, households increase their spending as their disposable In our example, the break-even income is $390 billion income rises and spend a larger proportion of a small dispos- (row 2, Table 10.1). This is the income level at which house- able income than of a large disposable income. holds plan to consume their entire incomes (C = DI). Graphi- cally, the consumption schedule cuts the 45° line, and the The Saving Schedule saving schedule cuts the horizontal axis (saving is zero) at the break-even income level. It is relatively easy to derive a saving schedule (or “saving At all higher incomes, households plan to save part of function”). Because saving equals disposable income less con- their incomes. Graphically, the vertical distance between the sumption (S = DI − C), we need only subtract consumption consumption schedule and the 45° line measures this saving (Table 10.1, column 2) from disposable income (column 1) to (see Figure 10.2a), as does the vertical distance between the find the amount saved (column 3) at each DI. Thus, columns 1 saving schedule and the horizontal axis (see Figure 10.2b). and 3 in Table 10.1 are the saving schedule, represented in Fig- For example, at the $410 billion level of income (row 3, Ta- ure 10.2b. The graph shows that there is a direct relationship ble 10.1), both these distances indicate $5 billion of saving. between saving and DI but that saving is a smaller proportion of a small DI than of a large DI. If households consume a smaller and smaller proportion of DI as DI increases, then they Average and Marginal Propensities must be saving a larger and larger proportion. Columns 4 to 7 in Table 10.1 show additional characteristics Remembering that at each point on the 45° line consump- of the consumption and saving schedules. tion equals DI, we see that dissaving (consuming in excess of after-tax income) will occur at relatively low DIs. For exam- APC and APS The fraction, or percentage, of total income ple, at $370 billion (row 1, Table 10.1), consumption is that is consumed is the average propensity to consume $375 billion. Households can consume more than their cur- (APC). The fraction of total income that is saved is the aver- rent incomes by liquidating (selling for cash) accumulated age propensity to save (APS). That is, wealth or by borrowing. Graphically, dissaving is shown as the vertical distance of the consumption schedule above the consumption APC = 45° line or as the vertical distance of the saving schedule income  KEY GRAPH FIGURE 10.2 Consumption and saving schedules. The two parts of this C figure show the income-consumption and 500 income-saving relationships in Table 10.1 graphically. (a) Consumption rises as income increases. Saving is negative (dissaving occurs) when the consumption 475 schedule is above the 45° line, and saving is positive when the consumption Consumption (billions of dollars) schedule is below the 45° line. (b) Like 450 consumption, saving increases as income Consumption goes up. The saving schedule is found by schedule subtracting the consumption schedule in 425 the top graph vertically from the 45° line. For these hypothetical data, saving is −$5 billion at $370 billion of income, zero at Saving $5 billion $390 billion of income, and $5 billion at 400 $410 billion of income. Saving is zero where consumption equals disposable income. 375 Dissaving $5 billion 45° 0 370 390 410 430 450 470 490 510 530 550 Disposable income (billions of dollars) (a) Consumption schedule Saving (billions of dollars) 50 Saving schedule S 25 Dissaving $5 billion Saving $5 billion 0 390 410 430 450 470 490 510 530 550 Disposable income (billions of dollars) (b) Saving schedule QUICK QUIZ FOR FIGURE 10.2 1. The slope of the consumption schedule in this figure is 0.75. 3. In this figure: Thus, the: a. the marginal propensity to consume is constant at all levels of a. slope of the saving schedule is 1.33. ­income. b. marginal propensity to consume is 0.75. b. the marginal propensity to save rises as disposable income rises. c. average propensity to consume is 0.25. c. consumption is inversely (negatively) related to disposable income. d. slope of the saving schedule is also 0.75. c. saving is inversely (negatively) related to disposable income. 2. In this figure, when consumption is a positive amount, saving: 4. When consumption equals disposable income: a. must be a negative amount. a. the marginal propensity to consume is zero. b. must also be a positive amount. b. the average propensity to consume is zero. c. can be either a positive or a negative amount. c. consumption and saving must be equal. d. is zero. d. saving must be zero. Answers: 1. b; 2. c; 3. a; 4. d 204  CHAPTER 10 Basic Macroeconomic Relationships 205 and saving GLOBAL PERSPECTIVE 10.1 APS = income Average Propensities to Consume, For example, at $470 billion of income (row 6, Table 10.1), the Selected Nations APC is 450 45 There are surprisingly large differences in average propen- 470 = 47 , or about 0.96 (= 96 percent), while the APS is 20 2 sities to consume (APCs) among nations. In 2014, Canada, 470 = 47 , or about 0.04 (= 4 percent). Columns 4 and 5 in Table the United States, Korea, and the Netherlands in particular 10.1 show the APC and APS at each of the 10 levels of DI. As had substantially higher APCs, and thus lower APSs, than implied by our previous discussion, the APC falls as DI several other advanced economies. ­increases, while the APS rises as DI goes up. Because disposable income is either consumed or saved, Average Propensity the fraction of any DI consumed plus the fraction saved (not to Consume, 2014 consumed) must exhaust that income. Mathematically, APC + 80 85 90 95 100 APS = 1 at any level of disposable income, as columns 4 and Canada 5 in Table 10.1 illustrate. So if 0.96 of the $470 billion of United States ­income in row 6 in consumed, 0.04 must be saved. That is why APC + APS = 1. Korea Global Perspective 10.1 shows APCs for several Netherlands ­countries. Australia Germany MPC and MPS The fact that households consume a cer- Sweden 45 tain proportion of a particular total income, for example, of 47 Switzerland a $470 billion disposable income, does not guarantee they Source: Organization for Economic Cooperation and Development, OECD, will consume the same proportion of any change in income www.oecd.org. Derived from OECD household saving rates as percent- they might receive. The proportion, or fraction, of any change ages of disposable income. Econ Outlook 98, Annex Table 23, extracted in income consumed is called the marginal propensity to April 2016. consume (MPC), “marginal” meaning “extra” or “a change in.” Equivalently, the MPC is the ratio of a change in con- sumption to a change in the income that caused the consump- saved. The fraction consumed (MPC) plus the fraction saved tion change: (MPS) must exhaust the whole change in income: MPC + MPS = 1 change in consumption MPC = change in income In our example, 0.75 plus 0.25 equals 1. Similarly, the fraction of any change in income saved is the MPC and MPS as Slopes The MPC is the numerical marginal propensity to save (MPS). The MPS is the ratio of value of the slope of the consumption schedule, and the a change in saving to the change in income that brought it MPS is the numerical value of the slope of the saving about: schedule. We know from the appendix to Chapter 1 that the change in saving slope of any line is the ratio of the vertical change to the MPS = horizontal change occasioned in moving from one point to change in income another on that line. If disposable income is $470 billion (row 6 horizontally in Figure 10.3 measures the slopes of the consumption and Table 10.1) and household income rises by $20 billion to saving lines, using enlarged portions of Figure 10.2a and $490 billion (row 7), households will consume 15 3 20 , or 4 , and 10.2b. Observe that consumption changes by $15 billion 5 1 save 20 , or 4 , of that increase in income. In other words, the (the vertical change) for each $20 billion change in dispos- MPC is 34 or 0.75, and the MPS is 14 or 0.25, as shown in col- able income (the horizontal change). The slope of the con- umns 6 and 7. sumption line is thus 0.75 (= $15/$20), which is the value The sum of the MPC and the MPS for any change in dis- of the MPC. Saving changes by $5 billion (shown as posable income must always be 1. Consuming or saving out the vertical change) for every $20 billion change in dispos- of extra income is an either-or proposition; the fraction of any able income (shown as the horizontal change). The slope of change in income not consumed is, by definition, saved. If the saving line therefore is 0.25 (= $5/$20), which is the 0.75 of extra disposable income is consumed, 0.25 must be value of the MPS. 206 PART FOUR Macroeconomic Models and Fiscal Policy FIGURE 10.3 The marginal propensity to consume and the marginal Events sometimes suddenly boost the value of propensity to save. In the two parts of this figure, the Greek letter delta (Δ) existing wealth. When this happens, households tend to means “the change in.” (a) The MPC is the slope (ΔC/ΔDI) of the consumption increase their spending and reduce their saving. This schedule. (b) The MPS is the slope (ΔS/ΔDI) of the saving schedule. so-called wealth effect shifts the consumption schedule upward and the saving schedule downward. They move C in response to households taking advantage of the increased consumption possibilities afforded by the MPC = 15 =.75 sudden increase in wealth. Examples: In the late 1990s, 20 skyrocketing U.S. stock values expanded the value of Consumption ΔC ($15) household wealth by increasing the value of household assets. Predictably, households spent more and saved ΔDI ($20) less. In contrast, a strong “reverse wealth effect” occurred in 2008. Plunging real estate and stock market prices joined together to erase $11.2 trillion (yes, trillion) of household wealth. Consumers quickly reacted by reducing their consumption spending. The consumption schedule shifted downward. 0 Disposable income ∙ Borrowing Household borrowing also affects consumption. When a household borrows, it can increase current consumption beyond what would be possible if its spending were limited to its disposable income. By allowing households to spend more, borrowing shifts the 5 MPS = 20 =.25 current consumption schedule upward. S But note that there is no “free lunch.” While Saving ΔS ($5) borrowing in the present allows for higher consumption ΔDI ($20) in the present, it necessitates lower consumption in the future when the debts that are incurred due to the borrowing must be repaid. Stated a bit differently, increased borrowing increases debt (liabilities), which 0 Disposable income in turn reduces household wealth (since wealth = assets − liabilities). This reduction in wealth reduces future consumption possibilities in much the same way that a Nonincome Determinants decline in asset values would. But note that the term “reverse wealth effect” is reserved for situations in of Consumption and Saving which wealth unexpectedly changes because asset LO10.2 List and explain factors other than income that can values unexpectedly change. It is not used to refer to affect consumption. situations such as the one being discussed here where The amount of disposable income is the basic determinant of wealth is intentionally reduced by households through the amounts households will consume and save. But certain borrowing and piling up debt to increase current determinants other than income might prompt households to consumption. consume more or less at each possible level of income and thereby change the locations of the consumption and saving ∙ Expectations Household expectations about future prices schedules. Those other determinants are wealth, borrowing, and income may affect current spending and saving. For expectations, and interest rates. example, the expectation of higher prices tomorrow may cause households to buy more today while prices are still ∙ Wealth A household’s wealth is the dollar amount of low. Thus, the current consumption schedule shifts up and all the assets that it owns minus the dollar amount of its the current saving schedule shifts down. Or expectations liabilities (all the debt that it owes). Households build of a recession and thus lower income in the future may wealth by saving money out of current income. The lead households to reduce consumption and save more point of building wealth is to increase consumption today. Their greater present saving will help build wealth possibilities. The larger the stock of wealth that a that will help them ride out the expected bad times. The household can build up, the larger will be its present consumption schedule therefore will shift down and the and future consumption possibilities. saving schedule will shift up.  CHAPTER 10 Basic Macroeconomic Relationships 207 ∙ Real interest rates When real interest rates (those ∙ Taxation In contrast, a change in taxes shifts the adjusted for inflation) fall, households tend to borrow consumption and saving schedules in the same direction. more, consume more, and save less. A lower interest Taxes are paid partly at the expense of consumption and rate, for example, decreases monthly loan payments and partly at the expense of saving. So an increase in taxes induces consumers to purchase automobiles and other will reduce both consumption and saving, shifting the goods bought on credit. A lower interest rate also consumption schedule in Figure 10.4a and the saving diminishes the incentive to save because of the reduced schedule in Figure 10.4b downward. Conversely, interest “payment” to the saver. These effects on households will partly consume and partly save any consumption and saving, however, are very modest. decrease in taxes. Both the consumption schedule and They mainly shift consumption toward some products saving schedule will shift upward. (those bought on credit) and away from others. At best, ∙ Stability The consumption and saving schedules usually lower interest rates shift the consumption schedule are relatively stable unless altered by major tax increases slightly upward and the saving schedule slightly or decreases. Their stability may be because consumption- downward. Higher interest rates do the opposite. saving decisions are strongly influenced by long-term considerations such as saving to meet emergencies or saving for retirement. It may also be because changes in Other Important Considerations the nonincome determinants frequently work in opposite There are several additional important points regarding the directions and therefore may be self-canceling. consumption and saving schedules: ∙ Switching to real GDP When developing macroeconomic FIGURE 10.4 Shifts of the (a) consumption and (b) saving schedules. models, economists change their focus from the Normally, if households consume more at each level of real GDP, they are necessarily saving less. Graphically this means that an upward shift of the relationship between consumption (and saving) and consumption schedule (C0 to C1  ) entails a downward shift of the saving schedule disposable income to the relationship between (S0 to S1  ). If households consume less at each level of real GDP, they are saving consumption (and saving) and real domestic output (real more. A downward shift of the consumption schedule (C0 to C2) is reflected in an GDP). This modification is reflected in Figure 10.4a and upward shift of the saving schedule (S0 to S2). This pattern breaks down, 10.4b, where the horizontal axes measure real GDP. however, when taxes change; then the consumption and saving schedules move in the same direction—opposite to the direction of the tax change. ∙ Changes along schedules The movement from one point to another on a consumption schedule (for C1 example, from a to b on C0 in Figure 10.4a) is a change C0 in the amount consumed and is solely caused by a (billions of dollars) change in real GDP. On the other hand, an upward or C2 Consumption downward shift of the entire schedule, for example, a shift from C0 to C1 or C2 in Figure 10.4a, is a shift of the consumption schedule and is caused by changes in any one or more of the nonincome determinants of b consumption just discussed. a A similar distinction in terminology applies to the 45° saving schedule in Figure 10.4b. ∙ Simultaneous shifts Changes in wealth, expectations, 0 Real GDP (billions of dollars) interest rates, and household debt will shift the (a) consumption schedule in one direction and the saving Consumption schedule schedule in the opposite direction. If households decide S2 to consume more at each possible level of real GDP, they (billions of dollars) must save less, and vice versa. (Even when they spend S0 more by borrowing, they are, in effect, reducing their + Saving S1 current saving by the amount borrowed since borrowing 0 is, effectively, “negative saving.”) Graphically, if the consumption schedule shifts upward from C0 to C1 in – Figure 10.4a, the saving schedule shifts downward, from S0 to S1 in Figure 10.4b. Similarly, a downward shift of Real GDP (billions of dollars) the consumption schedule from C0 to C2 means an (b) upward shift of the saving schedule from S0 to S2. Saving schedule 208 PART FOUR Macroeconomic Models and Fiscal Policy CONSIDER THIS... QUICK REVIEW 10.1 ✓ Both consumption spending and saving rise when dis- The Great posable income increases; both fall when disposable Recession income decreases. and the Paradox ✓ The average propensity to consume (APC) is the frac- of Thrift tion of any specific level of disposable income that is spent on consumer goods; the average propensity to The Great Recession save (APS) is the fraction of any specific level of dis- of 2007–2009 al- posable income that is saved. The APC falls and the tered the prior con- APS rises as disposable income increases. sumption and saving ✓ The marginal propensity to consume (MPC) is the behavior in the econ- omy. Concerned about fraction of a change in disposable income that is con- reduced wealth, high sumed and it is the slope of the consumption sched- debt, and potential job ule; the marginal propensity to save (MPS) is the losses, households in- fraction of a change in disposable income that is creased their saving saved and it is the slope of the saving schedule. and reduced their con- ✓ Changes in consumer wealth, consumer expectations, sumption at each level interest rates, household debt, and taxes can shift the of after-tax income (or consumption and saving schedules (as they relate to each level of GDP). In real GDP). Source: © Digital Vision/Getty Images RF Figure 10.4, this out- come is illustrated as the downward shift of the consumption schedule in the top graph and the upward shift of the saving schedule in the lower graph. The Interest-Rate–Investment This change of behavior illustrates the so-called para- dox of thrift, which refers to the possibility that a reces- Relationship sion can be made worse when households become more LO10.3 Explain how changes in real interest rates affect thrifty and save in response to the downturn. The para- investment. dox of thrift rests on two major ironies. One irony is that In our consideration of major macro relationships, we next saving more is good for the economy in the long run, as turn to the relationship between the real interest rate and in- noted in Chapter 1 and Chapter 6. It finances invest- vestment. Recall that investment consists of expenditures on ment and therefore fuels subsequent economic growth. new plants, capital equipment, machinery, inventories, and so But saving more can be bad for the economy during a on. The investment decision is a marginal-benefit–marginal- recession. Because firms are pessimistic about future cost decision: The marginal benefit from investment is the sales, the increased saving is not likely to be matched by an equal amount of added investment. The extra saving expected rate of return businesses hope to realize. The mar- simply reduces spending on currently produced goods ginal cost is the interest rate that must be paid for borrowed and services. That means that even more businesses suf- funds. Businesses will invest in all projects for which the ex- fer, more layoffs occur, and people’s incomes decline pected rate of return exceeds the interest rate. Expected re- even more. turns (profits) and the interest rate therefore are the two basic The paradox of thrift has a second irony related to the determinants of investment spending. fallacy of composition (Chapter 1, Last Word): Households as a group may inadvertently end up saving less when each individual household tries to save more during a recession. Expected Rate of Return This is because each household’s attempt to save more im- Investment spending is guided by the profit motive; businesses plies that it is also attempting to spend less. Across all buy capital goods only when they think such purchases will be households, that collective reduction in total spending in profitable. Suppose the owner of a small cabinetmaking shop the economy creates additional job losses and further is considering whether to invest in a new sanding machine that drives down total income. The decline in total income re- costs $1,000 and has a useful life of only 1 year. (Extending the duces the ability of households as a group to save as much life of the machine beyond 1 year complicates the economic as they did before their spending reduction and subse- decision but does not change the fundamental analysis. We dis- quent income decline. cuss the valuation of returns beyond 1 year in Chapter 17.) The new machine will increase the firm’s output and sales revenue. Suppose the net expected revenue from the machine (that is,  CHAPTER 10 Basic Macroeconomic Relationships 209 after such operating costs as power, lumber, labor, and certain constant price level ensures that all our data, including the taxes have been subtracted) is $1,100. Then, after the $1,000 interest rate, are in real terms. cost of the machine is subtracted from the net expected revenue But what if inflation is occurring? Suppose a $1,000 in- of $1,100, the firm will have an expected profit of $100. Divid- vestment is expected to yield a real (inflation-adjusted) rate ing this $100 profit by the $1,000 cost of the machine, we find of return of 10 percent and the nominal interest rate is 15 per- that the expected rate of return, r, on the machine is 10 per- cent. At first, we would say the investment would be unprofit- cent (= $100/$1,000). It is important to note that this is an able. But assume there is ongoing inflation of 10 percent per ­expected rate of return, not a guaranteed rate of return. The year. This means the investing firm will pay back dollars with investment may or may not generate as much revenue or as approximately 10 percent less in purchasing power. While the much profit as anticipated. Investment involves risk. nominal interest rate is 15 percent, the real rate is only 5 per- cent (= 15 percent − 10 percent). By comparing this 5 per- cent real interest rate with the 10 percent expected real rate of The Real Interest Rate return, we find that the investment is potentially profitable One important cost associated with investing that our exam- and should be undertaken. ple has ignored is interest, which is the financial cost of bor- rowing the $1,000 of money “capital” to purchase the $1,000 of real capital (the sanding machine). Investment Demand Curve The interest cost of the investment is computed by multi- We now move from a single firm’s investment decision to total plying the interest rate, i, by the $1,000 borrowed to buy the demand for investment goods by the entire business sector. As- machine. If the interest rate is, say, 7 percent, the total interest sume that every firm has estimated the expected rates of return cost will be $70. This compares favorably with the net ex- from all investment projects and has recorded those data. We can pected return of $100, which produced the 10 percent ex- cumulate (successively sum) these data by asking: How many pected rate of return. If the investment works out as expected, dollars’ worth of investment projects have an expected rate of it will add $30 to the firm’s profit. return of, say, 16 percent or more? How many have 14 percent or We can generalize as follows: If the expected rate of return more? How many have 12 percent or more? And so on. (10 percent) exceeds the interest rate (here, 7 percent), the in- Suppose no prospective investments yield an expected re- vestment should be undertaken. The firm expects the invest- turn of 16 percent or more. But suppose there are $5 billion ment to be profitable. But if the interest rate (say, 12 percent) of investment opportunities with expected rates of return be- exceeds the expected rate of return (10 percent), the investment tween 14 and 16 percent; an additional $5 billion yielding should not be undertaken. The firm expects the investment to between 12 and 14 percent; still an additional $5 billion be unprofitable. The firm should undertake all investment proj- yielding between 10 and 12 percent; and an additional $5 bil- ects it thinks will be profitable. This means that the firm should lion in each successive 2 percent range of yield down to and array its prospective investment projects from the highest ex- including the 0 to 2 percent range. pected rate of return, r, downward and then invest in all proj- To cumulate these figures for each rate of return, r, we add ects for which r exceeds i. The firm therefore should invest to the amounts of investment that will yield each particular rate the point where r = i because then it will have undertaken all of return r or higher. This provides the data in the table in investments for which r is greater than i. Figure 10.5 (Key Graph). The data are shown graphically in This guideline applies even if a firm finances the invest- Figure 10.5. In the table, the number opposite 12 percent, for ment internally out of funds saved from past profit rather than example, means there are $10 billion of investment opportuni- borrowing the funds. The role of the interest rate in the in- ties that will yield an expected rate of return of 12 percent or vestment decision does not change. When the firm uses more. The $10 billion includes the $5 billion of investment money from savings to invest in the sander, it incurs an op- expected to yield a return of 14 percent or more plus the portunity cost because it forgoes the interest income it could $5 billion expected to yield between 12 and 14 percent. have earned by lending the funds to someone else. That inter- We know from our example of the sanding machine that est cost, converted to percentage terms, needs to be weighed an investment project will be undertaken if its expected rate against the expected rate of return. of return, r, exceeds the real interest rate, i. Let’s first suppose The real rate of interest, rather than the nominal rate, is i is 12 percent. Businesses will undertake all investments for crucial in making investment decisions. Recall from Chapter which r exceeds 12 percent. That is, they will invest until the 9 that the nominal interest rate is expressed in dollars of cur- 12 percent rate of return equals the 12 percent interest rate. rent value, while the real interest rate is stated in dollars of Figure 10.5 reveals that $10 billion of investment spending constant or inflation-adjusted value. Recall that the real inter- will be undertaken at a 12 percent interest rate; that means est rate is the nominal rate less the rate of inflation. In our $10 billion of investment projects have an expected rate of sanding machine illustration, our implicit assumption of a return of 12 percent or more.  KEY GRAPH FIGURE 10.5 The investment demand curve. The investment demand curve is constructed by arraying all potential investment projects in descending order of their expected rates of return. The curve slopes downward, reflecting an inverse relationship between the real interest rate (the financial “price” of each dollar of investing) and the quantity of investment demanded. Cumulative Amount of 16 Investment Having this Real Interest Rate (i) and Rate of Return or Higher, and real interest rate, i (percents) 14 Expected Rate of Return (r) Billions per Year Expected rate of return, r, 16% $ 0 12 Investment 14 5 10 demand 12 10 curve 10 15 8 8 20 6 25 6 4 30 4 2 35 0 40 2 ID 0 5 10 15 20 25 30 35 40 Investment (billions of dollars) QUICK QUIZ FOR FIGURE 10.5 1. The investment demand curve: 3. In this figure, if the real interest rate falls from 6 to 4 percent: a. reflects a direct (positive) relationship between the real interest a. investment will increase from 0 to $30 billion. rate and investment. b. investment will decrease by $5 billion. b. reflects an inverse (negative) relationship between the real inter- c. the expected rate of return will rise by $5 billion. est rate and investment. d. investment will increase from $25 billion to $30 billion. c. shifts to the right when the real interest rate rises. 4. In this figure, investment will be: d. shifts to the left when the real interest rate rises. a. zero if the real interest rate is zero. 2. In this figure: b. $40 billion if the real interest rate is 16 percent. a. greater cumulative amounts of investment are associated with c. $30 billion if the real interest rate is 4 percent. lower real interest rates. d. $20 billion if the real interest rate is 12 percent. b. lesser cumulative amounts of investment are associated with lower expected rates of return on investment. c. higher interest rates are associated with higher expected rates of re- turn on investment, and therefore greater amounts of investment. d. interest rates and investment move in the same direction. Answers: 1. b; 2. a; 3. d; 4. c Put another way: At a financial “price” of 12 percent, d­ emanded at each “price” i (interest rate) of investment. The $10 billion of investment goods will be demanded. If the interest vertical axis in Figure 10.5 shows the various possible real rate is lower, say, 8 percent, the amount of investment for which interest rates, and the horizontal axis shows the correspond- r equals or exceeds i is $20 billion. Thus, firms will demand ing quantities of investment demanded. The inverse $20 billion of investment goods at an 8 percent real interest rate. (downsloping) relationship between the interest rate (price) At 6 percent, they will demand $25 billion of investment goods. and dollar quantity of investment demanded conforms to the By applying the marginal-benefit–marginal-cost rule that law of demand discussed in Chapter 3. The curve ID in Fig- investment projects should be undertaken up to the point ure 10.5 is the economy’s investment demand curve. It where r = i, we see that we can add the real interest rate to the shows the amount of investment forthcoming at each real in- vertical axis in Figure 10.5. The curve in Figure 10.5 not only terest rate. The level of investment depends on the expected shows rates of return; it shows the quantity of investment rate of return and the real interest rate. 210  CHAPTER 10 Basic Macroeconomic Relationships 211 Shifts of the Investment ∙ Technological change Technological progress—the development of new products, improvements in existing Demand Curve products, and the creation of new machinery and LO10.4 Identify and explain factors other than the real interest production processes—stimulates investment. The rate that can affect investment. development of a more efficient machine, for example, Figure 10.5 shows the relationship between the interest rate and lowers production costs or improves product quality and the amount of investment demanded, other things equal. When increases the expected rate of return from investing in other things change, the investment demand curve shifts. In the machine. Profitable new products (cholesterol general, any factor that leads businesses collectively to expect medications, Internet services, high-definition greater rates of return on their investments increases investment televisions, cellular phones, and so on) induce a flurry demand. That factor shifts the investment demand curve to the of investment as businesses tool up for expanded right, as from ID0 to ID1 in Figure 10.6. Any factor that leads production. A rapid rate of technological progress shifts businesses collectively to expect lower rates of return on their the investment demand curve to the right. investments shifts the curve to the left, as from ID0 to ID2. What ∙ Stock of capital goods on hand The stock of capital are those non-interest-rate determinants of investment demand? goods on hand, relative to output and sales, influences ∙ Acquisition, maintenance, and operating costs The investment decisions by firms. When the economy is initial costs of capital goods, and the estimated costs of overstocked with production facilities and when firms operating and maintaining those goods, affect the have excessive inventories of finished goods, the expected rate of return on investment. When these costs expected rate of return on new investment declines. rise, the expected rate of return from prospective Firms with excess production capacity have little investment projects falls and the investment demand incentive to invest in new capital. Therefore, less curve shifts to the left. Example: Higher electricity costs investment is forthcoming at each real interest rate; the associated with operating tools and machinery shifts the investment demand curve shifts leftward. investment demand curve to the left. Lower costs, in When the economy is understocked with production contrast, shift it to the right. facilities and when firms are selling their output as fast ∙ Business taxes When government is considered, firms as they can produce it, the expected rate of return on look to expected returns after taxes in making their new investment increases and the investment demand investment decisions. An increase in business taxes curve shifts rightward. lowers the expected profitability of investments and ∙ Planned inventory changes Recall from Chapter 7 that shifts the investment demand curve to the left; a the definition of investment includes changes in reduction of business taxes shifts it to the right. inventories of unsold goods. An increase in inventories is counted as positive investment while a decrease in FIGURE 10.6 Shifts of the investment demand curve. Increases in inventories is counted as negative investment. It is investment demand are shown as rightward shifts of the investment demand important to remember that some inventory changes are curve; decreases in investment demand are shown as leftward shifts of the planned, while others are unplanned. Since the investment investment demand curve. demand curve deals only with planned investment, it is only affected by planned changes that firms desire to make to their inventory levels. If firms are planning to Increase increase their inventories, the investment demand curve in investment shifts to the right. If firms are planning on decreasing their Expected rate of return, r, and real interest rate, i (percents) demand inventories, the investment demand curve shifts to the left. Firms make planned changes to their inventory levels mostly because they are expecting either faster or slower sales. A firm that expects its sales to double in the next year will want to keep more inventory in stock, thereby increasing its investment demand. By contrast, a firm that is expecting slower sales will plan on reducing its inventory, thereby reducing its overall investment Decrease in ID2 ID0 ID1 demand. But because life often does not turn out as investment expected, firms often find that the actual amount of demand inventory investment that they end up making is either 0 Investment (billions of dollars) more or less than what they had planned. The size of the 212 PART FOUR Macroeconomic Models and Fiscal Policy gap is, naturally, the dollar amount of their unplanned inventory changes. These unplanned inventory GLOBAL PERSPECTIVE 10.2 adjustments will play a large role in the aggregate Gross Investment Expenditures as a expenditures model studied in Chapter 11. ­Percentage of GDP, Selected Nations ∙ Expectations We noted that business investment is As a percentage of GDP, investment varies widely by nation. based on expected returns (expected additions to profit). These differences, of course, can change from year to year. Most capital goods are durable, with a life expectancy of Gross Investment as a 10 or 20 years. Thus, the expected rate of return on Percentage of GDP, 2014 capital investment depends on the firm’s expectations of 0 10 20 30 40 50 future sales, future operating costs, and future China profitability of the product that the capital helps produce. These expectations are based on forecasts of future Korea business conditions as well as on such elusive and Canada difficult-to-predict factors as changes in the domestic Mexico political climate, international relations, population France growth, and consumer tastes. If executives become more Japan optimistic about future sales, costs, and profits, the United States investment demand curve will shift to the right; a Germany pessimistic outlook will shift the curve to the left. United Kingdom Global Perspective 10.2 compares investment spending Italy relative to GDP for several nations in a recent year. Domestic real interest rates and investment demand determine the lev- Source: Gross fixed capital formation data from International Financial Statistics, International Monetary Fund, www.imf.org. els of investment relative to GDP. Instability of Investment course of the business cycle can be attributed to demand In contrast to consumption, investment is unstable; it rises shocks relating to unexpected increases and decreases in and falls quite often. Investment, in fact, is the most volatile ­investment. Figure 10.7 shows just how volatile investment in component of total spending—so much so that most of the the United States has been. Notice that the percentage swings fluctuations in output and employment that happen over the in investment in real terms are greater than the ­percentage 35 FIGURE 10.7 The volatility of investment, 1976–2015. Annual 30 Gross investment percentage changes in investment 25 spending are often several times greater than the percentage 20 changes in GDP. (Data are in real terms. Investment is gross private 15 domestic investment.) 10 Percentage change 5 0 GDP –5 –10 –15 –20 –25 –30 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015 Year Source: Bureau of Economic Analysis, www.bea.gov.  CHAPTER 10 Basic Macroeconomic Relationships 213 A less optimistic view, however, may lead to smaller CONSIDER THIS... amounts of investment as firms repair older facilities The Great Recession and and keep them in use. the Investment Riddle ∙ Irregularity of innovation New products and processes During the severe recession of stimulate investment. Major innovations such as 2007–2009, real interest rates railroads, electricity, airplanes, automobiles, computers, essentially declined to zero. Figure the Internet, and cell phones induce vast upsurges or 10.5 suggests that this drop in in- “waves” of investment spending that in time recede. But terest rates should have boosted such innovations occur quite irregularly, adding to the investment spending. But invest- volatility of investment. ment declined substantially during ∙ Variability of profits High current profits often this period. On an annual basis, it Source: © Stephanie Dalton declined by 9 percent in 2008 and generate optimism about the future profitability of new Cowan/Getty Images RF 26 percent in 2009. Does this investments, whereas low current profits or losses combination of lower real interest rates and reduced invest- spawn considerable doubt about the wisdom of new ment make Figure 10.5 irrelevant? investments. Additionally, firms often save a portion of Definitely not! The key to the investment riddle is that current profits as retained earnings and use these funds during the recession, the investment demand curve shifted (as well as borrowed funds) to finance new investments. inward, as from ID0 to ID2 in Figure 10.6. This inward shift So current profits affect both the incentive and ability to overwhelmed any investment-increasing effects of the de- invest. But profits themselves are highly variable from cline of real interest rates. The net result turned out to be year to year, contributing to the volatility of investment. less investment, not more. The leftward shift of the investment demand reflected a In terms of our previous analysis, we would represent volatility decline in the expected returns from investment. Firms envi- of investment as occasional and substantial unexpected shifts of sioned zero or negative returns on investment in new capital the investment demand curve (as in Figure 10.6), which cause because they were facing an overstock of existing capital significant changes in investment spending (as in Figure 10.7). relative to their current sales. Understandably, they there- These demand shocks can contribute to cyclical instability. fore were not inclined to invest. Also, firms were extremely pessimistic about when the economy would regain its strength. This pessimism also contributed to low expected QUICK REVIEW 10.2 rates of return on investment and thus to exceptionally weak investment demand. Further, even though the interest rate ✓ A specific investment will be undertaken if the ex- was so low, firms that wanted to borrow and invest found pected rate of return, r, equals or exceeds the real in- that lenders were reluctant to lend them money for fear that terest rate, i. they would not be able to pay back the loans. ✓ The investment demand curve shows the total mone- tary amounts that will be invested by an economy at various possible real interest rates. swings in real GDP. Several interrelated factors drawn from ✓ The investment demand curve shifts when changes our previous discussion explain the variability of investment. occur in (a) the costs of acquiring, operating, and maintaining capital goods, (b) business taxes, (c) tech- ∙ Variability of expectations Business expectations can nology, (d) the stock of capital goods on hand, and change quickly when some event suggests a significant (e) business expectations. possible change in future business conditions. Changes in exchange rates, trade barriers, legislative actions, stock market prices, government economic policies, the outlook for war or peace, court decisions in key labor or The Multiplier Effect* antitrust cases, and a host of similar considerations may LO10.5 Illustrate how changes in investment (or one of the cause substantial shifts in business expectations. other components of total spending) can increase or decrease real GDP by a multiple amount. ∙ Durability Because of their durability, capital goods A final basic relationship that requires discussion is the relation- have indefinite useful lifespans. Within limits, purchases ship between changes in spending and changes in real GDP. As- of capital goods are discretionary and therefore can be suming that the economy has room to expand—so that increases postponed. Firms can scrap or replace older equipment and buildings, or they can patch them up and use them *Instructors who cover the full aggregate expenditures (AE) model (Chapter for a few more years. Optimism about the future may 11) rather than moving directly to aggregate demand and aggregate supply prompt firms to replace their older facilities and such (Chapter 12) may choose to defer this discussion until after the analysis of modernizing will call for a high level of investment. equilibrium real GDP. 214 PART FOUR Macroeconomic Models and Fiscal Policy in spending do not lead to increases in prices—there is a direct neither the initial increase in spending nor any of the subse- relationship between these two aggregates. More spending re- quent increases in spending will cause prices to rise. sults in a higher GDP; less spending results in a lower GDP. But The initial $5 billion increase in investment generates an there is much more to this relationship. A change in spending, equal amount of wage, rent, interest, and profit income be- say, investment, ultimately changes output and income by more cause spending and receiving income are two sides of the than the initial change in investment spending. That surprising same transaction. How much consumption will be induced by result is called the multiplier effect: a change in a component of this $5 billion increase in the incomes of households? We total spending leads to a larger change in GDP. The multiplier find the answer by applying the marginal propensity to con- determines how much larger that change will be; it is the ratio of sume of 0.75 to this change in income. Thus, the $5 billion a change in GDP to the initial change in spending (in this case, increase in income initially raises consumption by $3.75 investment). Stated generally, (= 0.75 × $5) billion and saving by $1.25 (= 0.25 × $5) billion, change in real GDP as shown in columns 2 and 3 in the table. Multiplier = Other households receive as income (second round) the initial change in spending $3.75 billion of consumption spending. Those households By rearranging this equation, we can also say that Change in consume 0.75 of this $3.75 billion, or $2.81 billion, and save GDP = multiplier × initial change in spending. 0.25 of it, or $0.94 billion. The $2.81 billion that is consumed So if investment in an economy rises by $30 billion and flows to still other households as income to be spent or saved GDP increases by $90 billion as a result, we then know from (third round). And the process continues, with the added con- our first equation that the multiplier is 3 (= $90/$30). sumption and income becoming less in each round. The pro- Note these three points about the multiplier: cess ends when there is no more additional income to spend. The bar chart in Figure 10.8 shows several rounds of the ∙ The “initial change in spending” is usually associated multiplier process of the table graphically. As shown by with investment spending because of investment’s rounds 1 to 5, each round adds a smaller and smaller blue volatility. But changes in consumption (unrelated to block to national income and GDP. The process, of course, changes in income), net exports, and government continues beyond the five rounds shown (for convenience we purchases also lead to the multiplier effect. have simply cumulated the subsequent declining blocks into a ∙ The “initial change in spending” associated with single block labeled “All other”). The accumulation of the ad- investment spending results from a change in the real ditional income in each round—the sum of the blue blocks— interest rate and/or a shift of the investment demand curve. is the total change in income or GDP resulting from the initial ∙ Implicit in the preceding point is that the multiplier $5 billion change in spending. Because the spending and re- works in both directions. An increase in initial spending spending effects of the increase in investment diminish with will create a multiple increase in GDP, while a decrease each successive round of spending, the cumulative increase in in spending will create a multiple decrease in GDP. output and income eventually ends. In this case, the ending occurs when $20 billion of additional income accumulates. Rationale Thus, the multiplier is 4 (= $20 billion/$5 billion). The multiplier effect follows from two facts. First, the econ- omy supports repetitive, continuous flows of expenditures and income through which dollars spent by Smith are received as The Multiplier and the Marginal Propensities income by Chin and then spent by Chin and r­eceived as in- You may have sensed from the table in Figure 10.8 that the come by Gonzales, and so on. (This chapter’s Last Word fractions of an increase in income consumed (MPC) and ­presents this idea in a humorous way.) Second, any change in saved (MPS) determine the cumulative respending effects of income will change both consumption and saving in the same any initial change in spending and therefore determine the direction as, and by a fraction of, the change in income. size of the multiplier. The MPC and the multiplier are directly It follows that an initial change in spending will set off a related and the MPS and the multiplier are inversely related. spending chain throughout the economy. That chain of spend- The precise formulas are as shown in the next two equations: ing, although of diminishing importance at each successive 1 step, will cumulate to a multiple change in GDP. Initial Multiplier = changes in spending produce magnified changes in output 1 − MPC and income. Recall, too, that MPC + MPS = 1. Therefore MPS = 1 − MPC, The table in Figure 10.8 illustrates the rationale underly- which means we can also write the multiplier formula as ing the multiplier effect. Suppose that a $5 billion increase in investment spending occurs. We assume that the MPC is 1 Multiplier = 0.75, the MPS is 0.25, and prices remain constant. That is, MPC  CHAPTER 10 Basic Macroeconomic Relationships 215 (2) (3) FIGURE 10.8 The multiplier (1) Change in Change in process (MPC = 0.75). An initial Change in Consumption Saving change in investment spending of Income (MPC = 0.75) (MPS = 0.25) $5 billion creates an equal $5 billion of new income in round 1. Households Increase in investment of $5.00 $5.00 $ 3.75 $1.25 spend $3.75 (= 0.75 × $5) billion Second round 3.75 2.81 0.94 of this new income, creating Third round 2.81 2.11 0.70 $3.75 billion of added income in Fourth round 2.11 1.58 0.53 round 2. Of this $3.75 billion of new income, households spend Fifth round 1.58 1.19 0.39 $2.81 (= 0.75 × $3.75) billion, and All other rounds 4.75 3.56 1.19 income rises by that amount in Total $20.00 $15.00 $5.00 round 3. Such income increments over the entire process get successively smaller but eventually 20.00 produce a total change of income and GDP of $20 billion. The Cumulative income, GDP (billions of dollars) $4.75 multiplier therefore is 4 (= $20 billion/$5 billion). 15.25 $1.58 13.67 $2.11 $20 billion ΔGDP = 11.56 ΔI = $2.81 8.75 $5 billion $3.75 5.00 $5.00 1 2 3 4 5 All other Rounds of spending This latter formula is a quick way to determine the multiplier. If the MPS were 0.33 rather than 0.25, the successive in- All you need to know is the MPS. creases in consumption and income would be less than those The smaller the fraction of any change in income saved, in the table in Figure 10.8. We would discover that the pro- the greater the respending at each round and, therefore, the cess ended with a $15 billion in