Macroeconomic Theory and Policy

ECO 209Y Macroeconomic Theory and Policy Lecture 3: Aggregate Expenditure and Equilibrium Income Gustavo Indart Slide 1

Assumptions We will assume that: There is no depreciation There are no indirect taxes Net payment to foreign factors of production is nil Therefore, GDP, Net Domestic Income, and Gross National Product are all equal In other words, output and income are assumed to be equal and we will use the notation Y to refer to both Gustavo Indart Slide 2

Graphical Representation of GDP = National Income (Y) GDP GDP = Y Slope = 1 45 Y Gustavo Indart Slide 3

Assumptions (cont d) We will also assume that the price level (P) is fixed Therefore, this model applies to a situation where the economy is in a deep recession characterized by excess capacity and high unemployment That is, we will consider the so-called short-run Keynesian model Gustavo Indart Slide 4

Aggregate Expenditure Aggregate Expenditure (AE) is the total desired or planned expenditure on goods and services in the economy, that is: AE = C + I + G + NX Using the expenditure approach, we have seen that GDP was equal to: Y = C + I + G + NX GDP is equal to the actual expenditure on domestically produced goods and services Therefore, actual expenditure on domestically produced goods and services is equal to income (Y) since GDP is equal to income by assumption Gustavo Indart Slide 5

Aggregate Expenditure (cont d) The Aggregate Expenditure function indicates the desired level of expenditure at each level of income (Y) The Aggregate Expenditure function is an increasing function of Y Therefore, there must be a level of income at which desired aggregate expenditure (AE) is equal to actual aggregate expenditure (GDP = Y) This level of income at which Y = AE is the equilibrium level of output or income (Y*) At Y* the goods market is in equilibrium Gustavo Indart Slide 6

Aggregate Expenditure (cont d) If Y AE, then the economy is not in equilibrium If Y > AE excess supply in the goods market If Y < AE excess demand in the goods market Since P is assumed fixed, then the implicit assumption is that aggregate expenditure determines the amount of goods produced in the economy That is, Y must change in order to restore equilibrium in the economy Y must increase to eliminate an excess demand Y must decrease to eliminate an excess supply Gustavo Indart Slide 7

A Simple Model Consider a simple model of an economy without government sector (G = 0) and without external sector (X = Q = 0) Therefore, AE = C + I How is equilibrium income (Y*) determined in this economy? Gustavo Indart Slide 8

The Planned (or Desired) Consumption Function The planned consumption function is a description of the total planned personal consumption expenditure by all households in the economy Planned consumption expenditure depends on variables such as: Disposable income Wealth Interest rates Expectations about the future Gustavo Indart Slide 9

The Planned Consumption Function With the exception of disposable income, all the variables that determine planned consumption will be assumed constant Therefore, planned consumption will be assumed to be a function of disposable income (YD): C = C + c YD This equation indicates that planned consumption is equal to some constant (C) plus another constant (c) times disposable income (YD) Gustavo Indart Slide 10

The Consumption Function (cont d) The constant C describes the elements of consumption which are independent of disposable income The constant C is called autonomous consumption and captures the impact on C of all the constant variables The constant c describes the rate of change of consumption as disposable income changes, that is, it indicates the increase in consumption per unit increase in disposable income: c = C YD The constant c is called the marginal propensity to consume out of disposable income (MPC YD ) Gustavo Indart Slide 11

Marginal Propensity to Consume Since we are assuming that there is no government sector, taxes (TA) and transfer payments (TR) are nil Therefore, YD = Y This means that consumption is assumed to depend on income (Y) alone: C = C + cy Note that since Y = YD, then MPC Y = MPC YD However, as we will soon see, when YD differs from Y, MPC Y also differs from MPC YD Gustavo Indart Slide 12

The Consumption Curve C C = C + cyd C C Slope = c YD Gustavo Indart Slide 13

Canada: Per Capita Consumption and Disposable Income, 1981-2005 26000 24000 22000 20000 18000 16000 2005 Dollars 1981 1986 1991 1996 2001 14000 Real Per Capita Disposable Income Real Per Capita Expenditure Gustavo Indart Slide 14

Marginal Propensity to Save The MPC YD is positive but less than 1, thus implying that a $1 increase in disposable income does not increase consumption by $1 A fraction c is spent on consumption and the rest is saved (i.e., a fraction s = 1 c is saved) The constant s is the marginal propensity to save out of disposable income (MPS YD ) Therefore, c + s = 1 Gustavo Indart Slide 15

The Planned Saving Function Since YD = C + S, the saving function is given by: S = YD C = YD (C + cyd) = C + (1 c)yd = C + syd Note that the MPS YD is also positive and less than 1 since s = 1 c The saving function is sort of the mirror image of the consumption function Gustavo Indart Slide 16

Consumption and Saving Functions C C C = C + c YD S = C + (1 c) YD C 0 = YD 0 C When YD = 0, then C = C and S = C S 45 YD 0 S YD At the level of YD at which the C curve intersects the 45º line, C = YD and thus S = 0. C YD 0 YD For YD < YD 0, C > YD and thus S < 0. For YD > YD 0, C < YD and thus S > 0. Gustavo Indart Slide 17

The Planned Investment Function The investment function is a description of the total (desired or planned) investment expenditure by all private economic agents in the economy In general, planned investment expenditure depends on: The real rate of interest The level of economic activity (Y) Businesses expectations about the behaviour of these variables during the lifetime of the investment Gustavo Indart Slide 18

The Planned Investment Function For simplicity, we will assume that the rate of interest and expectations about the future are constant Also for simplicity, we will further assume that planned investment is independent of the level of income (Y) Therefore, planned investment will not change as the level of income (Y) changes I is equal to autonomous investment: I = I Gustavo Indart Slide 19

The Investment Function (cont d) I I = I I I Y Gustavo Indart Slide 20

The Aggregate Expenditure Function In this very simple model, the aggregate expenditure function is: AE = C + I = (C + cy) + I = (C + I) + cy = AE + cy where AE = C + I is autonomous aggregate expenditure and cy is induced aggregate expenditure AE is the vertical intercept of the AE function, and c is the slope of the AE function (or the marginal propensity to spend) Gustavo Indart Slide 21

Aggregate Expenditure Function AE CI AE C = C + cy I = I AE = AE + cy AE = C + I I C Slope = c I I C Y Gustavo Indart Slide 22

Equilibrium Income and Output We have seen that in equilibrium, output (GDP) or income (Y) is equal to aggregate expenditure (AE): Y = AE = AE + cy Therefore, Y cy = AE (1 c)y = AE and equilibrium income is: 1 Y* = AE 1 c Gustavo Indart Slide 23

Aggregate Expenditure Function AE GDP AE AE = AE + cy Slope = c Actual Expenditure AE At Y = Y*, Y = AE and thus actual investment is equal to desired investment There is no involuntary change in inventories. At Y = Y 1, Y > AE and thus actual investment is greater than desired investment There is an involuntary increase in inventories. 45 Y 2 Y* Y 1 Y At Y = Y 2, Y < AE and thus actual investment is smaller than desired investment There is an involuntary decrease in inventories. Gustavo Indart Slide 24

Consumption and Saving The implicit assumption is that actual consumption is always equal to desired consumption as a result of involuntary changes in inventory If AE > Y, there is an involuntary decrease in inventory to satisfy the level of desired consumption If AE < Y, there is an involuntary increase in inventory because desired consumption is not enough (i.e., saving is too large) Therefore, since actual consumption and desired consumption are always equal, then actual saving and desired saving are always equal as well Gustavo Indart Slide 25

Saving and Investment By definition, saving is equal to actual investment. Indeed, Output (GDP) is equal to income (Y) by assumption Income not spend on consumption is saved Output not used for consumption is used for investment Y = C + S and Y = C + actual I S = actual I In equilibrium, when Y = AE, there is no involuntary change in inventory Therefore, planned or desired investment is equal to actual investment in equilibrium Therefore, in a closed economy with no government sector, If Y = AE, then S = desired I If Y < AE, then S < desired I If Y > AE, then S > desired I Gustavo Indart Slide 26

Equilibrium Income Actual Expenditure AE GDP AE AE S = C + (1 c)y I = I AE = AE + cy S 45 Y* Y Y = AE at Y = Y*, and thus Y* is the equilibrium level of income. I C Y* S Y I S = I at Y = Y*, and thus Y* is the equilibrium level of income. Gustavo Indart Slide 27

Saving and Investment By definition, saving is always equal to actual investment Question: If high rates of investment are desirable, are high rates of saving also desirable? If saving determined productive investment, then high rates of saving might be desirable But high desired saving is the result of low desired consumption expenditure Therefore, actual investment will be large because firms will experience involuntary increases in inventory Therefore, higher desired saving does not translate into higher productive capacity of the economy But higher desired investment does translate into higher Y and thus into higher desired saving Gustavo Indart Slide 28

Saving and Investment (cont d) AE GDP AE AE S = C + (1 c)y I = I AE = AE + cy AE 1 AE 2 S I C 2 C 1 45 Y 2 Y 2 Y 1 Y 1 S S Y Y I Initially the economy is in equilibrium at Y 1. As desired saving increases to S and aggregate expenditure decreases to AE, Y > AE and Y falls. Gustavo Indart Slide 29

The Multiplier 1 Y* = AE 1 c How does a change in autonomous expenditure (AE) affect equilibrium income (Y*)? The equation for equilibrium income shows that a AE will affect Y* in the following way: Y* = The expression 1 1 c AE Y* 1 1 α AE = = = AE 1 c 1 slope of AE curve is called the autonomous expenditure multiplier or just the multiplier Gustavo Indart Slide 30

The Multiplier (cont d) A change in autonomous expenditure (ΔAE) causes equilibrium income (Y*) to change by the initial change in AE times the multiplier (α AE ) This change in Y*, α AE ΔAE, is the final result and does not show the process leading to it Let s have a look at the process leading to this final outcome Suppose that autonomous expenditure increases by AE Gustavo Indart Slide 31

Process of Adjustment Round AE this round Y this round Accumulated Y 1 AE AE AE 2 3 4 c AE c AE (1+c) AE c 2 AE c 2 AE (1+c+c 2 ) AE c 3 AE c 3 AE (1+c+c 2 +c 3 ) AE n [1/(1 c)] AE Gustavo Indart Slide 32

Process of Adjustment (cont d) After n rounds, the series 1 + c + c 2 + c 3 + converges to α AE = 1/(1 c) Let s call a = 1 + c + c 2 + c 3 + Multiply a by c ca = c + c 2 + c 3 + Now subtract ca from a: a ca = (1 + c + c 2 + c 3 + ) (c + c 2 + c 3 + ) = 1 Therefore, a (1 c) = 1 a = 1/(1 c) Gustavo Indart Slide 33

Introduction of the Government Sector Disposable income (YD) changes: Households pay taxes Households receive transfer payments Equation for AE changes: AE = C + I + G We will assume that government expenditure on goods and services is independent of the level of income, that is, G is fixed G = G Gustavo Indart Slide 34

Disposable Income and the Consumption Function We have seen that consumption is a function of disposable income (YD): C = C + cyd where C is autonomous consumption and c is the marginal propensity to consume out of disposable income (MPC YD ) Disposable income (YD) is equal to: YD = Y + TR TA where TR are government transfer payments and TA are direct taxes Gustavo Indart Slide 35

Disposable Income and the Consumption Function (cont d) Let s assume that taxes are a function of income and that transfer payments are independent of income: TA = T + ty TR = TR Therefore, disposable income is equal to: YD = Y + TR (T + ty) = TR T + (1 t)y Gustavo Indart Slide 36

The Consumption Function as a Function of Income As a function of income, the consumption function is: C = C + cyd YD = TR T + (1 t)y = C + c [ TR T + (1 t)y ] = (C + ctr ct) + c(1 t)y That is, (C + ctr ct) is the vertical intercept and c(1 t) is the slope Note that c(1 t) is the marginal propensity to consume out of income (MPC Y ) Also note that MPC Y < MPC YD if t > 0 Gustavo Indart Slide 37

The Aggregate Expenditure Function The aggregate expenditure function is: AE = C + I + G = [ C + ctr ct + c(1 t)y ] + I + G = AE + c(1 t)y where AE = C + ctr ct + I + G The vertical intercept is AE and the slope is c(1 t) Recall that the slope of the AE curve is the marginal propensity to spend Gustavo Indart Slide 38

Equilibrium Output and Income Equilibrium income is determined where Y = AE: Y = AE + c (1 t)y [ 1 c (1 t) ] Y = AE Therefore, 1 Y* = AE 1 c (1 t) Gustavo Indart Slide 39

The Multiplier The autonomous expenditure multiplier becomes: 1 α AE = 1 c(1 t) Note that as before, the multiplier is equal to 1 over 1 minus the slope of the AE curve Also note that, as t increases, α AE becomes smaller (the AE curve becomes flatter) Gustavo Indart Slide 40

The Effect of a Change in G Recall that AE = AE + c(1 t)y where AE = C + ctr ct + I + G Therefore, a change in G will have an impact on AE and thus on the position of the AE curve It will not have any effect on the slope of the AE curve Therefore, the value of the multiplier will not be affected either Indeed, AE = G Therefore, Y = α AE AE = α AE G Note that if G > 0, then AE > 0 and the AE curve shifts up Gustavo Indart Slide 41

The Effect of an Increase in G AE GDP AE 2 AE 1 AE 2 AE = G AE 1 = AE 1 + c(1 t)y AE 1 Y = α AE AE AE 2 = AE 2 + c(1 t)y 45 Y 1 Y 2 Y Gustavo Indart Slide 42

Effect of a Change in Taxes A change in taxes (TA) will affect the level of disposable income (YD) and thus the level of consumption (C) In turn, since consumption (C) is one component of aggregate expenditure (AE), the change in taxes will have an impact on the level of equilibrium income (Y*) Let s consider two cases: The impact of a change in autonomous net taxes (T), i.e., autonomous taxes minus autonomous subsidies The impact of a change in the tax rate (t) Gustavo Indart Slide 43

The Effect of a Change in T Recall that AE = AE + c(1 t)y where AE = C + ctr ct + I + G Therefore, a change in T will have an impact on AE and thus on the position of the AE curve It will not have any effect on the slope of the AE curve Therefore, the value of the multiplier will not be affected either Indeed, AE = c T Therefore, Y = α AE AE = α AE c T Note that if T < 0, then AE > 0 and the AE curve shifts up Gustavo Indart Slide 44

The Effect of a Decrease in T AE GDP AE = C ct + ctr + I + G AE > Y AE 2 AE 1 AE 2 AE = c T AE 1 = AE 1 + c(1 t)y AE 1 Y = α AE AE AE 2 = AE 2 + c(1 t)y 45 Y 1 Y 2 Y Gustavo Indart Slide 45

The Effect of a Change in t Recall that AE = AE + c(1 t)y Therefore, a change in t will have an impact on the slope of the AE curve Therefore, the value of the multiplier will be affected It will not have, however, any effect on the vertical intercept of the AE curve Note that if t < 0, then AE curve becomes steeper Gustavo Indart Slide 46

The Effect of a Decrease in t AE GDP Suppose now that t decreases, i.e., t 2 < t 1 AE > Y AE 2 AE 1 AE 1 = AE + c(1 t 1 )Y AE Y AE 2 = AE + c(1 t 2 )Y 45 Y 1 Y 2 Y Gustavo Indart Slide 47

The Government Budget The budget surplus (BS) is defined as the difference between government revenues (taxes, TA) and the government total expenditures (expenditure on goods and services, G, plus transfer payments, TR) BS = TA (G + TR) The budget deficit (BD) is defined as the difference between government total expenditures and government revenues BD = (G + TR) TA Note that the budget deficit is the negative of the budget surplus BD = BS Gustavo Indart Slide 48

Budget Surplus Function Suppose that: TA = T + ty G = G TR = TR Therefore, BS = TA G TR = T + ty G TR = (T G TR) + ty = BS + ty BS = T G TR < 0 Gustavo Indart Slide 49

Budget Surplus Function BS BS = BS + ty BS = 0 if Y = Y 0 BS BS < 0 if Y < Y 0 Y 0 Y BS > 0 if Y > Y 0 BS Therefore, the size and sign of the BS are not determined exclusively by government policy. To a large extent, they depend on where the economy happens to be along the business cycle. Gustavo Indart Slide 50

An Increase in G and the BS An increase in G decreases the BS The decrease in BS, however, is not equal to the increase in G Since G causes Y to increase, revenues (TA) also increase when Y increases and thus the BS decreases by less than G Indeed, the G causes Y to increase by G times the multiplier: Y = α AE G Therefore, taxes increase by the Y times the tax rate (t): TA = t Y = t α AE G Gustavo Indart Slide 51

An Increase in G and the BS BS = TA G = t α AE G G = (t α AE 1) G t = [ 1] G 1 c(1 t) t [1 c(1 t)] = G 1 c(1 t) t 1 + c ct = G 1 c(1 t) (1 c)(1 t) = G < 0 1 c(1 t) α AE = 1 1 c(1 t) Gustavo Indart Slide 52

The Full-Employment Budget Surplus Depending on the level of Y, we could have a positive or negative budget surplus independently of the level of G Therefore, there is nothing intrinsically right or wrong with a positive or negative budget surplus per se To conclude that a positive or negative budget surplus is not desirable we must first estimate what the full-employment budget surplus would be The full-employment budget surplus measures the surplus at the full employment level of income (Y fe ) Given our equation for the budget surplus, the full-employment budget surplus (BS fe ) is: BS fe = ty fe G TR where Y fe is the full-employment level of income Gustavo Indart Slide 53

The Full-Employment Budget Surplus (cont d) BS BS As the diagram shows, there is a budget deficit at the initial level of equilibrium income. AE Y AE However, the diagram also shows that there would be a budget surplus if the level of equilibrium income were at the level of full-employment income. 45 Y* Y fe Y The diagram suggests that there is insufficient demand and thus G should be increased rather than decreased. Gustavo Indart Slide 54

Federal Budget Deficit (1960-2005) Source: P. Krugman, R. Wells and A. Myatt, Macroeconomics. Gustavo Indart Slide 55

Federal Budget Deficit and the Unemployment Rate Source: P. Krugman, R. Wells and A. Myatt, Macroeconomics. Gustavo Indart Slide 56

Are Canadians Over-Taxed? (2010) Country Taxes as % of GDP Country Taxes as % of GDP Australia n/a Korea 25.1 Austria 42.0 Mexico 18.1 Belgium 43.8 Netherlands n/a Canada 31.0 New Zealand 31.3 Czech Republic 34.9 Norway 42.8 Denmark 48.2 Poland n/a Finland 42.1 Portugal 31.3 France 42.9 Slovak Republic 28.4 Germany 36.3 Spain 31.7 Greece 30.9 Sweden 45.8 Hungary 37.6 Switzerland 29.8 Iceland 36.3 Turkey 26.0 Ireland 28.0 United Kingdom 35.0 Italy 43.0 United States 24.8 Japan n/a OECD average n/a Source: OECD Tax Statistics, 2011. Gustavo Indart Slide 57

Health Expenditure Per Capita (2011 or nearest year) Source: OECD, Health at Glance 2013 OECD Indicators, p. 155. Gustavo Indart Slide 58

Public Social Spending (% of GDP) Source: Mowat Centre based on OECD Social Expenditure Database. Gustavo Indart Slide 59

Competitiveness Ranking (2010) Country Rank Score Country Rank Score Switzerland 1 5.63 Hong Kong SAR 11 5.30 Sweden 2 5.56 United Kingdom 12 5.25 Singapore 3 5.48 Taiwan, China 13 5.21 United States 4 5.43 Norway 14 5.14 Germany 5 5.39 France 15 5.13 Japan 6 5.37 Australia 16 5.11 Finland 7 5.37 Qatar 17 5.10 Netherlands 8 5.33 Austria 18 5.09 Denmark 9 5.32 Belgium 19 5.07 Canada 10 5.30 Luxembourg 20 5.05 Source: World Economic Forum, The Global Competitiveness Report, 2013. Gustavo Indart Slide 60

Corruption Perceptions Index (2014) Country Rank Score Country Rank Score Denmark 1 92 Iceland 12 79 New Zealand 2 91 United Kingdom 14 78 Finland 3 89 Belgium 15 76 Sweden 4 87 Japan 15 76 Norway 5 86 Barbados 17 74 Switzerland 6 86 Hong Kong 17 74 Singapore 7 84 Ireland 17 74 Netherlands 8 83 United States 17 74 Luxembourg 9 82 Chile 21 73 Canada 10 81 Uruguay 21 73 Australia 11 80 Austria 23 72 Germany 12 79 Bahamas 24 71 Source: Transparency International. Gustavo Indart Slide 61

Happiness Ranking (2012) Country Rank Score Country Rank Score Denmark 1 7.693 Israel 11 7.301 Norway 2 7.655 Costa Rica 12 7.257 Switzerland 3 7.650 New Zealand 13 7.221 Netherlands 4 7.512 UAE 14 7.144 Sweden 5 7.480 Panama 15 7.143 Canada 6 7.477 Mexico 16 7.088 Finland 7 7.389 United States 17 7.082 Austria 8 7.369 Ireland 18 7.076 Iceland 9 7.355 Luxembourg 19 7.054 Australia 10 7.350 Venezuela 20 7.039 Source: United Nations, World Happiness Report, 2013. Gustavo Indart Slide 62

The Introduction of the Foreign Sector We will assume that the equations for exports (X) and imports (Q) are as follows: X = X Q = Q + my where m is the marginal propensity to import Therefore, the equation for net exports (NX) is: NX = X Q = X Q my Gustavo Indart Slide 63

The Equation for the AE Curve NX = X Q my In a closed economy, the equation for AE was: AE = C + I + G = AE + c(1 t)y where AE = C ct + ctr + I + G In an open economy, the equation for AE is: AE = C + I + G + NX = AE + [c(1 t) m]y where AE = C ct + ctr + I + G + X Q Gustavo Indart Slide 64

Equilibrium Income In equilibrium, Y = AE, that is, Y = AE + [c(1 t) m]y {1 [c(1 t) m]}y = AE Therefore, equilibrium income is: 1 Y* = AE 1 c(1 t) + m where AE = C ct + ctr + I + G + X Q Gustavo Indart Slide 65

The Multiplier The multiplier is: α AE = 1 1 c(1 t) + m 1 = 1 slope of the AE curve Where the slope of the AE curve (i.e., the marginal propensity to spend) is the fraction of each additional dollar of income which is spent on domestically produced goods Gustavo Indart Slide 66