Chapter 12: Aggregate Expenditure and Output in the Short Run

Yulei Luo

SEF of HKU

February 28, 2016 Learning Objectives

1. Understand how macroeconomic equilibrium is determined in the aggregate expenditure model. 2. Discuss the determinants of the four components of aggregate expenditure and de…ne the marginal propensity to consume and the marginal propensity to save.

3. Use a 45 line diagram to illustrate macroeconomic equilibrium. 4. De…ne the multiplier e¤ect and use it to calculate changes in equilibrium GDP. 5. Understand the relationship between the aggregate demand curve and aggregate expenditure. Output and Expenditure in the Short Run

I In this chapter, we explore the causes of the business cycle by examining the e¤ect of ‡uctuations in total spending (i.e., aggregate expenditure) on real GDP (total production).

I Aggregate expenditure (AE) The total amount of spending in the economy: the sum of consumption, planned investment, government purchases, and net exports. I (Conti.) During some years, AE increases about as much as does the production of goods and services:

I Most …rms sell about what they expected to sell and they will remain production and employment unchanged.

I During other years, AE increases more than the production:

I Firms will increase production and hire more workers.

I However, during some year, AE didn’tincrease as much as total production:

I Firms cut back on production and laid o¤ workers. The Aggregate Expenditure Model

I Aggregate expenditure model A macroeconomic model that focuses on the relationship between total spending and real GDP, assuming the price level is constant.

I It is used to study the business cycle involving the interaction of many economic variables.

I The key idea of AE model: In any particular year, the level of GDP is determined mainly by the level of AE that have several components.

I Economists began to study the relationship bw ‡uctuations in AE and ‡uctuations in GDP during the Great depression of the 1930s:

I In 1936, John M. Keynes systematically analyzed this relationship in his famous book (“The general theory of Employment, Interest, and Money”) and identi…ed four categories of AE that together equal to GDP (these are the same four categories). Aggregate Expenditure

I AE = C + I + G + NX (1)

1. Consumption (C): Spending by HHs on G&S such as furniture, food, etc. 2. Planned Investment (I ): Planned spending by …rms on capital goods, such as machinery, buildings, etc. or by HHs on new houses. 3. Government Purchases (G): Spending by local, state, and federal governments on G&S, such as building airport, highway, and salaries of gov. employees. 4. Net Exports (NX ): Spending by foreign …rms and hhs on G&S produced in the US minus spending by US …rms and HHs on G&S produced in other countries. The Di¤erence between Planned Investment and Actual Investment

I Notice that planned investment spending, rather than actual investment spending, is a component of aggregate expenditure.

I The amount of that …rms plan to spend on investment can be di¤erent from the amount they actually spend.

I The reason is that we need to consider inventories:

I Inventories: Goods that have been produced, but not yet sold.

I Changes in inventories are included as part of investment spending:

I Assume that the amount businesses plan to spend on inventories may be di¤erent from the amount they actually spend. I (Conti.) Changes in inventories depend on sales of goods, which …rms cannot always forecast with perfect accuracy.

I E.g., an auto company may produce 15, 000 cars and expect to sell them all. If it does sell all 15, 000, its inventories will be unchanged, but if it sells only 10, 000 it will have an unplanned increase in inventories.

I Hence, for the economy as a whole, we can say that actual investment spending (IS) will be greater (less) than planned IS when there is an unplanned increase (decrease) in inventories.

I Actual investment will equal planned investment only when there is no unplanned change in inventories. Macroeconomic Equilibrium

I Macroeconomic equilibrium is similar to microeconomic equilibrium (demand=supply of a product), in which the quantity of apples produced and sold will not change unless the demand or supply of this good changes.

I For the economy as a whole, macro equilibrium occurs where total spending equals to total production, that is,

Aggregate Expenditure = GDP Adjustments to Macro Equilibrium

I Increases and decreases in AE cause the year-to-year ‡uctuations in GDP.

I When AE is greater than GDP, inventories will decline, and GDP and total employment will increase.

I When AE is less than GDP, inventories will increase, and GDP and total employment will decrease.

I Only when AE equals GDP will the economy be in macroeconomic equilibrium. Adjustments to Macroeconomic Equilibrium

Just like markets for a particular product may not be in equilibrium (quantity supplied may not equal quantity demanded at the current price), the economy may not be in equilibrium.

If . . . then . . . and . . . aggregate expenditure is the economy is in equal to GDP inventories are unchanged macroeconomic equilibrium. aggregate expenditure is GDP and employment less than GDP inventories rise decrease. aggregate expenditure is GDP and employment greater than GDP inventories fall increase.

Table 12.1 The relationship between aggregate expenditure and GDP © Pearson Education Limited 2015 8 of 62 Making the The Effect of Unplanned Changes in Inventories Connection Firms like Apple don’t want to keep too much inventory on hand. Not only is it expensive, but technology quickly becomes outdated.

Apple forecasts its sales each month, and plans to have adequate inventory to cover sales. If sales are stronger than expected, it initially covers the extra sales through falling inventories.

• The falling inventories signal to Apple that it should hire more workers in order to increase production.

© Pearson Education Limited 2015 9 of 62 I Economists forecast what will happen to each component of AE. If they forecast that AE will decline in the future, that is equivalent to forecasting that GDP will decline and that the economy will enter a recession.

I Individuals and …rms closely watch these forecasts because ‡uctuations in GDP can have dramatic e¤ects on wages, pro…ts, and employment.

I When economists forecast that AE is likely to decline and the economy is headed for a recession, the gov. may implement macro policies to head o¤ the decline in AE and avoid the recession. Components of Real Aggregate Expenditure

The table below shows the values of the components of expenditure in 2012, with prices in 2009 dollars. Real Expenditure Expenditure Category (billions of 2009 dollars) Consumption $10,518 Planned investment 2,436 Government purchases 2,963 Net exports −431

Table 12.2 Components of real aggregate expenditure, 2012 Clearly consumption is the largest portion, with investment and government expenditures being roughly similarly sized. Net exports were negative in 2012: the value of U.S. imports was greater than the value of U.S. exports. For the next several slides, we will examine each component in more detail.

Consumption tends to follow a relatively smooth, upward trend; its growth declines during periods of recession. What affects the level of consumption? • Current disposable income • Household wealth • Expected future income • The price level • The interest rate We will proceed by examining Figure 12.1 Real consumption how each of these affects the level of consumption.

The …ve most important variables that determine the level of consumption:

I Current disposable income is the most important determinant of consumption.

I Disposable income (DI) is the income remaining to HHs after paying the personal income tax and receiving gov. transfer payments. I For most HHs, the higher (lower) their DI, the more (the less) they spend. I Aggregate (macro) consumption is the total of the consumption of US HHs. The main reason for the general upward trend in consumption is that DI has followed a similar upward trend. I (Conti.) Household wealth is the value of its assets minus the value of its liabilities.

I Assets include home, stock and bond holdings, and bank accounts. I Liabilities include any loans that it owes. I When the wealth of HHs increases (decreases), consumption increases (decreases). I Since shares of stock are an important component of HHs’ wealth, consumption should increase with stock prices. I A recent estimate of the e¤ects of changes in wealth on consumption indicates a permanent one-dollar increase in wealth induces 4 5 cents increase in consumption. I (Conti.) Expected future income: Most people prefer to keep their consumption fairly stable and smooth over time, even if their income ‡uctuates signi…cantly. Both current income and expected future income need to be considered to determine current consumption.

I The price level: Changes in the price level a¤ect consumption mainly through their e¤ect on HHs’wealth. As the price level rises, the real value of HHs wealth declines and so will HHs consumption. I (Conti.) The interest rate: When the interest rate (IR) is high, the reward to saving is increased and HHs are likely to save more and spend less.

I Note that consumption depends on the real IR that corrects the nominal IR for the impact of in‡ation. I Spending on durable goods (such as autos, one category of consumption) is most likely to be a¤ected by the interest rate because a high real IR increases the cost of spending …nanced by borrowing. The Consumption Function

I Consumption function The relationship between consumption spending and disposable income.

I Marginal propensity to consume (MPC): The slope of the consumption function: the amount by which consumption spending increases when disposable income increases:

change in consumption ∆C MPC = = . (2) change in disposable income ∆YD

I We can also use the MPC to determine how much consumption will change as income changes:

∆C = MPC ∆YD. The Relationship between Consumption and National Income

I Shift to discuss the relationship between aggregate consumption spending and GDP, rather than disposable income because we are interested in using the AE model to explain ‡uctuations in real GDP.

I Note that GDP and national income are almost the same. I Note that

Disposable income = National income Net taxes (3) where Net taxes=taxes minus gov transfer payments. Or, rearranging the equation:

National income = GDP = Disposable income + Net taxes. (4) The Consumption Function

How strong is the relationship between Figure 12.2 The relationship income and consumption? between consumption and income: 1960-2012 As the graphs demonstrate, the answer is “very strong”. A straight line (called the consumption function) describes this relationship very well, suggesting that households spend a consistent fraction of each extra dollar of real disposable income on consumption. © Pearson Education Limited 2015 15 of 62 Marginal Propensity to Consume

The graphs showed that consumers seem to have a relatively constant marginal propensity to consume: the amount by which consumption spending changes when disposable income changes. This marginal propensity to consume (MPC) is the slope of the consumption function, the relationship between consumption spending and disposable income. We can therefore estimate the MPC by estimating the slope of the production function: Change in consumption = = Change in disposable income ∆𝐶𝐶 𝑀𝑀𝑀𝑀𝑀𝑀 For 2002-2003, we find: ∆𝑌𝑌𝑌𝑌 $259 billion = = 0.97 $266 billion ∆𝐶𝐶 So if incomes rose∆ 𝑌𝑌𝑌𝑌$10 billion, we estimate consumption would rise by $10 billion x 0.97 = $9.7 billion. © Pearson Education Limited 2015 16 of 62 The Relationship between Consumption and National Income

The table shows the relationship between consumption and national income for an imaginary economy, keeping net taxes constant. As national income rises by $2,000 billion… … consumption rises by $1,500 billion. So the marginal propensity to consume for this economy is: $1,500 billion = = = 0.75 $2,000 billion ∆𝐶𝐶 𝑀𝑀𝑀𝑀𝑀𝑀 ∆𝑌𝑌 Figure 12.3 The relationship between consumption and national income © Pearson Education Limited 2015 18 of 62 Income, Consumption, and Saving

By definition, disposable income not spent is saved. Therefore we can write: National income = Consumption + Saving + Taxes Y = C + S + T Any change in national income can be decomposed into changes in the items on the right hand side:

∆Y = ∆C + ∆S + ∆T We assume net taxes do not change, so ∆T = 0; then: ∆Y = ∆C + ∆S Now divide through by ∆Y: ∆Y ∆C ∆S = + ∆Y ∆Y ∆Y

I HHs either (1) spend their income, (2) save it, or (3) use it to pay taxes. For the economy as a whole,

National income = Consumption + Saving + Taxes, (5)

which means that

Change in national income = Change in consumption (6) +Change in saving + Change in taxes

I Using symbols, where Y represents national income (and GDP), C represents consumption, S represents saving, and T represents taxes,

Y = C + S + T and ∆Y = ∆C + ∆S + ∆T . (7) I (Conti.) To simplify, we can assume that taxes are always a constant amount, in which case ∆T = 0, so that:

∆Y = ∆C + ∆S.

I Marginal propensity to save (MPS) The change in saving divided by the change in income:

∆C ∆S 1 = + or 1 = MPC + MPS ∆Y ∆Y Planned Investment

Investment has increased over time, but unlike consumption, it has not increased smoothly, and recessions decrease investment more. What affects the level of investment? • Expectations of future profitability • Interest rate • Taxes • Cash flow We will proceed by examining Figure 12.4 Real investment how each of these affects the level of planned investment.

I Expectations on future pro…tability

I Investment goods (equipment, o¢ ce buildings) are long-lived. I A …rm is unlikely to make a new investment unless it is optimistic that the demand for its product will remain strong for several years. I The optimism or pessimism of …rms is an important determinant of investment. I (Conti.) The interest rate

I Borrowing takes the form of issuing corporate bonds or receiving loans from banks. A signi…cant fraction of investment is …nanced by borrowing. HHs also borrow to …nance most of their spending on new houses. I Because households and …rms are interested in the cost of borrowing after taking into account the e¤ects of in‡ation, investment spending depends on the real interest rate. I Holding the other factors that a¤ect investment spending constant, there is an inverse relationship between the real interest rate and investment spending: I A higher real interest rate results in less investment spending, and a lower real interest rate results in more investment spending. I (Conti.) Taxes

I Firms focus on the pro…ts that remain after paying taxes. I A reduction in the corporate income tax on the pro…ts increases the after-tax pro…tability of investment. I Investment tax incentives (it provides …rms with a tax reduction when they spend on new investment goods) also increase investment spending.

I Cash ‡ow

I The di¤erence between the cash revenues received by the …rm and the cash spending by the …rm. I Most …rms use their own funds to …nance investment goods instead of borrowing outside. I The largest contributor to CF is pro…t. The more pro…table a …rm is, the greater its CF and the greater its ability to …nance investment. Government Purchases

Real government purchases include purchases at all levels of government: federal, state, and local. • This category does not include transfer payments; only purchases for which the government receives some good or service. Government purchases have generally, though not consistently, increased over time; exceptions include the early 1990s (end of cold war) Figure 12.5 Real government and due to state and local purchases cutbacks after 2009.

I The price level in US relative to the price levels in other countries: If prices in US increase more slowly than the prices of other countries, the demand for US products increases relative to other countries.

I The growth rate of GDP in US relative to the growth rates of other countries: When incomes (GDP) rise faster in US than in other countries, US consumers’purchases of foreign G&S will increase faster than foreign consumers’purchases of US G&S.

I The exchange rate between the dollar and other currencies: An increase in the value of the US dollar will reduce exports and increase imports. Net Exports

Net exports equals exports minus imports. The value of net exports is affected by: • Price level in U.S. vs. the price level in other countries • U.S. growth rate vs. growth rate in other countries • U.S. dollar exchange rate U.S. net exports have been negative for the last few decades. The value typically becomes higher (less negative) during a recession, Figure 12.6 Real net exports as spending on imports falls.

U.S. Net Exports If… will… …because… …U.S. price level U.S. goods become more expensive rises faster than relative to foreign goods; so imports foreign price levels… decrease rise and exports fall. …slower… increase The opposite is true. …U.S. GDP grows faster than foreign U.S. demand for imports rises faster GDP… decrease than foreign demand for our exports. …slower… increase The opposite is true. …$US rises in value Imports are cheaper, and our relative to other exports are more expensive. currencies… decrease So imports rise and exports fall. …falls… increase The opposite is true.

© Pearson Education Limited 2015 27 of 62 Making the The iPhone Is Made in China… or Is It? Connection When an iPhone is shipped from China to the U.S., GDP statistics register a $275 import from China to the U.S..

But iPhones are only assembled in China; no Chinese firm makes any of the iPhone’s components. • Only 4% of the value of the iPhone should be attributed to the assembly, according to one study.

Pascal Lamy of the WTO: “The concept of country of origin for manufactured goods has gradually become obsolete.”

I Whenever aggregate expenditure is less than real GDP, some …rms will experience an unplanned increase in inventories.

I If …rms don’tcut back on their production promptly, they will accumulate excess inventories. As a result, even if spending quickly returns to its normal levels, …rms will have to sell their excess inventories before they can return to producing at normal levels.

I This possibility can explain why a brief decline in AE can result in a fairly long recession. Hence, e¢ cient systems of inventories control help make recessions shorter and less severe. The 45°-Line Diagram

Suppose in the whole economy there is a single product: Pepsi. For the economy to be in equilibrium, the amount of Pepsi produced must equal the amount of Pepsi sold. Then any point on the 45° line could be an equilibrium—like points A or B. At point C, the economy’s inventories of Pepsi are being depleted, and production must rise.

At point D, inventories of Pepsi are Figure 12.7 An example of a growing, so production must fall. 45°-line diagram

We can apply this model to a real economy, with real national income (GDP) on the x-axis, and real aggregate expenditure on the y-axis. This model is also known as the Keynesian cross, because it is based on the analysis of economist John Maynard Keynes. Only points on the 45° line can be a macroeconomic equilibrium, with planned aggregate expenditure Figure 12.8 The relationship between equal to GDP. planned aggregate expenditure and GDP on a 45°-line diagram © Pearson Education Limited 2015 31 of 62 Determining the Macroeconomic Equilibrium

Any point on the 45° line could be an equilibrium; but how do we know which one will be the equilibrium in a given year? • To determine this, recall that when they receive additional income, households consume some of it, and save some of it. • The resulting consumption function tells us how much consumers will spend (real expenditure) when they have a particular income (real GDP). This will determine Consumption (C) in the equation Y = C + I + G + NX Macroeconomic equilibrium simply means the left side (real GDP) must equal the right side (planned aggregate expenditure). • The trick is to find the “right” level of C. For that, we use the 45° line diagram.

We start by placing the consumption function on the diagram. If there was no other expenditure in the economy, then the macroeconomic equilibrium would be where the consumption function crossed the 45° line; there, income (GDP) equals expenditure.

Figure 12.9 Macroeconomic equilibrium on the 45°-line diagram © Pearson Education Limited 2015 33 of 62 Finding Macroeconomic Equilibrium—part 2

But there are other expenditures. We will assume they are not affected by income; that they are predetermined. Then we add the other expenditures: planned investment… … government purchases… … and net exports. These are vertical shifts in real expenditure, because their values do not depend on real GDP. Figure 12.9 Macroeconomic equilibrium on the 45°-line diagram © Pearson Education Limited 2015 34 of 62 Finding Macroeconomic Equilibrium—part 3

At last, we have macroeconomic equilibrium: the point at which 1. Income equals expenditure, i.e. Y = C + I + G + NX 2. The level of consumption is consistent with the level of income, according to the consumption function. We call this top-most line the aggregate expenditure function. Figure 12.9 Macroeconomic equilibrium on the 45°-line diagram © Pearson Education Limited 2015 35 of 62 Adjustment to Macroeconomic Equilibrium In this economy, macroeconomic equilibrium occurs at $10 trillion. What if real GDP were lower, say $8 trillion? • Aggregate expenditure would be higher than GDP, so inventories would fall. • This would signal firms to increase production, increasing GDP. The reverse would occur if real GDP were above $10 trillion. Figure 12.10 Macroeconomic equilibrium © Pearson Education Limited 2015 36 of 62 Recession on the 45°-Line Diagram

Macroeconomic equilibrium can occur anywhere on the 45° line. Ideally, we would like it to occur at the level of potential GD P. If equilibrium occurs at this level, unemployment will be low—at the natural rate of unemployment, or the full employment level. But for various reasons, this might not occur. For example, maybe firms are pessimistic and reduce investment spending. • Then the equilibrium will occur below potential GDP—a Figure 12.11 Showing a recession recession. on the 45°-line diagram © Pearson Education Limited 2015 37 of 62 A Numerical Example of Macroeconomic Equilibrium

The table below shows several hypothetical combinations of real GDP and planned aggregate expenditure. Planned Real Planned Government Net Aggregate Unplanned GDP Consumption Investment Purchases Exports Expenditure Change in Real GDP (Y) (C) (I) (G) (NX) (AE) Inventories Will … $8,000 $6,200 $1,500 $1,500 − $500 $8,700 −$700 increase 9,000 6,850 1,500 1,500 −500 9,350 −350 increase be in 10,000 7,500 1,500 1,500 −500 10,000 0 equilibrium 11,000 8,150 1,500 1,500 −500 10,650 +350 decrease 12,000 8,800 1,500 1,500 −500 11,300 +700 decrease Note: The values are in billions of 2009 dollars Table 12.3 Macroeconomic equilibrium As real GDP changes, consumption changes but planned investment, government purchases, and net exports stay constant. Macroeconomic equilibrium can occur only at $10,000 billion; otherwise, the unplanned change in inventories will cause firms to change production and real GDP will change. © Pearson Education Limited 2015 39 of 62 The Multiplier E¤ect

I Autonomous expenditure: Expenditure that does not depend on the level of GDP.

I Planned investment, gov. spending, and net exports are all autonomous expenditures. I Note that consumption also includes an autonomous component. E.g., if HHs decide to spend more of their incomes and save less at every level of income there will be an autonomous increase in consumption.

I Multiplier: The increase in equilibrium real GDP divided by the increase in autonomous expenditure.

I Multiplier e¤ect: The process by which an increase in autonomous expenditure leads to a larger increase in real GDP. Summarizing the Multiplier E¤ect

I The multiplier e¤ect occurs both when autonomous expenditure increases and when it decreases.

I For example, with an MPC of 0.75, a decrease in planned investment of $100 billion will lead to a decrease in equilibrium income of $400 billion.

I The multiplier e¤ect makes the economy more sensitive to changes in autonomous expenditure than it would otherwise be.

I Because of the multiplier e¤ect, a decline in spending and production in one sector of the economy can lead to declines in spending and production in many other sectors of the economy.

I The larger the MPC, the larger the value of the multiplier. 1 I The formula for the multiplier, 1 MPC , is oversimpli…ed because it ignores some real world complications, such as the e¤ect that an increasing GDP can have on imports, in‡ation, and interest rates. These e¤ects combine to cause the simple formula to overstate the true value of the multiplier. Autonomous and Induced Expenditures

You may have noticed that a small change in planned aggregate expenditure causes a larger change in equilibrium real GDP. In our model, planned investment, government purchases, and net exports are autonomous expenditures: their level does not depend on the level of GDP. • But consumption has both an autonomous and induced effect. So its level does depend on the level of GDP, and this produces the upward-sloping AE line. Figure 12.12 The multiplier effect

An increase in an autonomous expenditure shifts the aggregate expenditure line upward. When this happens, real GDP increases by more than the change in autonomous expenditures; this is the multiplier effect. • The value of the increase in equilibrium real GDP divided by the increase in autonomous expenditures is the

multiplier. Figure 12.12 The multiplier effect

Initially, real GDP Additional Additional Total Additional rises by the amount Autonomous Induced Expenditure = Expenditure Expenditure Total Additional of the increase in (investment) (consumption) GDP autonomous Round 1 $100 billion $0 $100 billion Round 2 0 75 billion 175 billion expenditure. This Round 3 0 56 billion 231 billion causes an increase Round 4 0 42 billion 273 billion Round 5 0 32 billion 305 billion in real GDP, which ...... causes an increase . . . . Round 0 8 billion 377 billion in production, which 10 . . . . causes an increase . . . . in real GDP… . . . . Round 0 2 billion 395 billion 15 ...... Table 12.4 Round 0 1 billion 398 billion 19 The multiplier effect in . . . . action ...... Round n 0 0 $400 billion

We cannot say how long this adjustment to macroeconomic equilibrium will take—how many “rounds”, back and forth. But we can calculate the value of the multiplier, as the eventual change in real GDP divided by the change in autonomous expenditures (planned investment, in this case):

∆Y Change in real GDP $400 billion = = = 4 ∆I Change in investment spending $100 billion

With a multiplier of 4, each $1 increase in planned investment (or any other autonomous expenditure) eventually increases equilibrium real GDP by $4.

© Pearson Education Limited 2015 44 of 62 Making the The Multiplier in Reverse: the Great Depression Connection The multiplier can work in reverse too, like it did during the Great Depression of the 1930s. Several events, including the stock market crash of October 1929, led to reductions in investments by firms. Real GDP fell, so consumers cut back on spending, prompting firms to reduce production more, so consumers spent even less…

Year Consumption Investment Exports Real GDP Unemployment Rate 1929 $781 billion $124 billion $40 billion $1,056 billion 2.9% 1933 $638 billion $27 billion $22 billion $778 billion 20.9% Note: The values are in 2009 dollars.

© Pearson Education Limited 2015 45 of 62 Making the The Multiplier in Reverse—continued Connection The 45°-line diagram can help to illustrate this process. • Aggregate expenditures fell initially, due to the decrease in investment. • This prompted a multiplied effect on equilibrium real GDP. Recovery from the Great Depression took many years; unemployment remained above 10% until the U.S. entered World War II in 1941.

How can we know the eventual value of the multiplier? • In each “round”, the additional income prompts households to consume some fraction (the marginal propensity to consume). The total change in equilibrium real GDP equals:

The initial increase in planned investment spending = $100 billion Plus the first induced increase in consumption = MPC × $100 billion Plus the second induced increase in consumption = MPC × (MPC × $100 billion) = MPC2 × $100 billion Plus the third induced increase in consumption = MPC × (MPC2 × $100 billion) = MPC3 × $100 billion Plus the fourth induced increase in consumption = MPC × (MPC3 × $100 billion) = MPC4 × $100 billion And so on …

This becomes the infinite sum: Total change in GDP = $100 billion + MPC × $100 billion + MPC2 × $100 billion + MPC3 × $100 billion + MPC4 × $100 billion + …) Which we can rewrite as: Total change in GDP = $100 billion × (1 + MPC + MPC2 + MPC3 + MPC4 + …) by factoring out the initial $100 billion increase in investment. Since MPC is less than 1, the expression in parentheses is: 1 1− MPC In our case, MPC = 0.75; so the multiplier is 1/(1-0.75) = 4. A $100 billion increase in investment eventually results in a $400 billion increase in equilibrium real GDP. The general formula for the multiplier is: Change in equilibrium real GDP 1 Multiplier = = Change in autonomous expenditur e 1− MPC

I In discussing the AE model, John Maynard Keynes argued that if many households decide at the same time to increase their saving and reduce their spending, they may make themselves worse o¤ by causing aggregate expenditure to fall, thereby pushing the economy into a recession.

I The lower incomes in the recession might mean that total saving does not increase, despite the attempts by many individuals to increase their own saving.

I Keynes referred to this outcome as the paradox of thrift because what appears to be something favorable to the long-run performance of the economy might be counterproductive in the short run. The Aggregate Demand Curve

I When demand for a product increases, …rms will usually respond by increasing production, but they are also likely to increase prices. So far, we have …xed the price level (PL).

I In fact, as we will see, increases (decreases) in the PL will cause AE decrease (rise). There are 3 reasons for this inverse relationship between changes in the PL and changes in AE. I 1. (Conti.) A rising PL decreases consumption by decreasing the real value of household wealth. 2. If the PL in US rises relative to the PLs in other countries, US exports will become relatively more expensive and foreign imports will become relatively less expensive, causing net exports to fall. 3. When prices rise, …rms and HHs need more money to …nance buying and selling. If the central bank doesn’tincrease money supply, the result will increase the IR and then reduce investment as …rms and HHs borrow less to build new factories, ect., and new houses, respectively.

I Aggregate demand curve (AD) A curve showing the relationship between the price level and the level of planned aggregate expenditure in the economy, holding constant all other factors that a¤ect aggregate expenditure. The Effect of a Change in Price Level on Real GDP

Figure 12.13 The effect of a change in the price level on real GDP The diagrams show the effects described on the previous slide: a. Increases in the price level cause AE and real GDP to fall. b. Decreases in the price level cause AE and real GDP to rise. © Pearson Education Limited 2015 54 of 62 The Aggregate Demand Curve

Consequently, there is an inverse relationship between the price level and real GDP.

This relationship is known as the aggregate demand curve.

Aggregate demand (AD) curve: A curve that shows the relationship between the price level and the level of planned aggregate expenditure in the economy, holding constant all other factors that affect aggregate expenditure. Figure 12.14 The aggregate demand curve © Pearson Education Limited 2015 55 of 62 Why Build a Numerical Model?

Graphical analysis of macroeconomic equilibrium can tell us the qualitative changes that take place. • But an equation-based model can allow us to make quantitative or numerical estimates of what will occur.

Economists in universities, firms, and the government rely on econometric models in which they statistically estimate the relationships between economic variables.

Based on the example in the text, we can generate the following equations (changing the MPC so as to generate different results):

1. C = 1,000 + 0.65Y Consumption function

2. I = 1,500 Planned investment function

3. G = 1,500 Government spending function

4. NX = −500 Net export function

5. Y = C + I + G + NX Equilibrium condition

In using the model, researchers would estimate the parameters of the model—like the MPC or the values of the autonomous expenditure components like planned investment—using statistical methods and years of observations of data.

The first four equations can be used to form the aggregate expenditure function—the right hand side of the fifth equation.

The fifth equation is the essential “equilibrium condition”, representing the effect of the 45°-line.

Substituting the first four equations into the fifth gives: Y = 1,000 + 0.65Y + 1,500 + 1,500 − 500 Subtracting 0.65Y from both sides gives: Y − 0.65Y = 1,000 + 1,500 + 1,500 − 500 Which simplifies to: 0.35Y = 3,500 3,500 Y = =10,000 0.35

More generally, we could allow the parameters of the model to be represented by letters. 1. C = C + MPC(Y ) Consumption function

2. I = I Planned investment function

3. G = G Government spending function

4. NX = NX Net export function

5. Y = C + I + G + NX Equilibrium condition

The letters with bars over them are parameters—fixed (autonomous) values. For example, C was 1000 in our example.

Solving now for equilibrium, we get Y = C + MPC(Y ) + I + G + NX

Y − MPC(Y ) = C + I + G + NX

Y (1− MPC) = C + I + G + NX

C + I + G + NX 1 Y = = (C + I + G + NX )× 1− MPC 1− MPC

The last equation makes clear that: Equilibrium GDP = Autonomous expenditure × Multiplier