Lecture Seven Review: Short-run equilibrium Adding the government sector Lump sum tax and net tax

 Assumption: price is fixed in the short run  Aggregate expenditure is the planned total spending on final goods and services  AE = C + I (no government, no trade)  The equilibrium output is that out put which creates total spending just sufficient to produce that output (Y = AE)  Saving equals planned investment (S = I)  No unplanned changes in inventories 2Lecture 7

 AE = C + I  C = C 0 + cY  Consumption is a function of dispensable income  C0: autonomous consumption  c: marginal propensity to consume (MPC), c = ΔC/ ΔY  I = I g : Planned investment is not a function of GDP, investment is autonomous expenditure  AE = C 0 + cY + I g ; AE = Y  (C 0 + I g ) + cY = Y  Y e = (C 0 + I g )/(1-c); equilibrium output is equal to autonomous expenditure divided by (1 – MPC)  Similarly, ΔY e = Δ(C 0 + I g )/(1-c). (Δ means “changes in”) 3Lecture 7

 MPS and the multiplier are inversely related  Multiplier = 1/MPS = 1/(1-MPC)  Recall ΔY e = Δ(C 0 + I g )/(1-c)  Multiplier = change in equilibrium output/change in autonomous expenditure  Multiplier = ΔY e /ΔAE 4Lecture 7

 Simplifying Assumptions  Government purchases do not cause any shift in consumption or investment schedules  Lump sum tax: taxes do not vary with GDP  Government spending (G is autonomous expenditure  Taxes affect disposable income 5Lecture 7

 Increases in public spending shift the AE schedule upward and result in higher equilibrium GDP  Examples  suppose government add 40 billion of purchases  suppose government impose 40 billion of lump- sum tax 6Lecture 7

GDPTDICaCa SaSa IgIg NXGAE $370$40$330$ Equilibrium Levels of Employment, Output & Income Consumption spending is lower 7Lecture 7

GDPTDICaCa SaSa IgIg NXGAE $370$40$330$345$ - 15$20$35$ Equilibrium Levels of Employment, Output & Income 8Lecture 7

GDPTDICaCa SaSa IgIg NXGAE $370$40$330$345$ - 15$20$35$40$ Equilibrium Levels of Employment, Output & Income 9Lecture 7

o 45 o C + I g GDP (billions of dollars) C + I g + G G= $40 +$80 l Impact of $40 billion in government purchases on equilibrium GDP Aggregate expenditures (billions of dollars) 10Lecture 7

o 45 o GDP (billions of dollars) C + I g + G C a + I g + G l Equilibrium GDP reduced by $40 billion Aggregate expenditures (billions of dollars) Lecture 7

 C = Y,I = 15, G = 15  AE = C + I + G  AE = Y = Y  AE = Y at equilibrium  Y = Y  50 = 0.2Y  Y e = 50/0.2 = 250  Recall equilibrium output is equal to autonomous expenditure divided by (1 – MPC)  Autonomous expenditure = = 50, 1 – MPC = 1 – 0.8 = 0.2  Y e = 50/0.2 = Lecture 7

 T = 10, I = 20, G = 15  C = (Y-10)  AE = C + I + G  AE = (Y-15) = Y –  AE = Y  AE = Y at equilibrium  Y = Y  42 = 0.2Y  Y e = 42/0.2 = 210  Taxes affect disposable income, which affect consumption 13Lecture 7

 C = C 0 + c(Y-T), I = I g and G  AE = C + I + G  AE = C 0 + c(Y-T) + I g + G  Y = AE at equilibrium  Y = C 0 + c(Y-T) + I g + G  Y e = (C 0 - cT+ I g + G)/(1-c) 14Lecture 7

 Equilibrium GDP may or may not provide full employment  Recessionary Expenditure Gap  Increasing autonomous expenditure has a multiplier effect 15Lecture 7

Real GDP (billions of dollars) (C a + I g + G) 1 o 45 oRecessionary Gap = $20 billion (C a + I g + G) Aggregate expenditures (billions of dollars) Full Employment GDP20 Recessionary gap - When aggregate expenditures are inadequate to bring about full employment Recessionary gap - When aggregate expenditures are inadequate to bring about full employment 16Lecture 7

 Two different policies that a government might pursue to close a recessionary expenditure gap and achieve full employment:  1. Increase government spending  2. Lower taxes  Both work by increasing aggregate expenditures 17Lecture 7

 France is falling 2.0% above its targeted income of $18,000 and has a marginal propensity to consume of 0.6.  By using the multiplier model, what change in government expenditures would be needed to achieve this target?  Recall, Multiplier = ΔY e /ΔAE  Multiplier = 1/(1-MPC) = 1/(1-0.6) = 2.5  ΔY e = 2%*$18,000 =$360  ΔAE = $360 / 2.5 = $144  Government must increase its expenditure by $144 to close the output gap. Lecture 718

 Taxes and transfer payment affect consumption  Lump sum tax, DI = Y - T  Net tax, NT = tY, t net tax rate  DI = Y – NT = (1-t)Y 19Lecture 7

 Assume C = DI  T = 10  DI = Y-10  So C = (Y-10) C = Y – 8 = Y  Each dollar of lump sum tax reduces autonomous consumption by 0.8 dollar (80 cents) 20Lecture 7

 Assume C = DI  t = 10%  DI = (1-t)Y  So C = (1 – 0.10)Y C = Y  Each extra dollar of national income increase DI by $0.9 (90 cents), out of which household spend 72 cents and save 18 cents. 21Lecture 7

Real Consumption C Real GDP and Income Y C = Y, t = 0 C = (20-0.8*10) + 0.8Y Lecture 7 252

Real Consumption C Real GDP and Income Y C = Y, t = 0 C = Y, t = ΔC/ΔY = MPC(1-t) = 0.8 x 0.9 What about Multiplier? 23Lecture 7

 Government spending (G) shift AE vertically  Net tax (increasing tax rate) reduces DI, therefore lowers consumption, rotate AE to the right (slope of AE is reduced)  AE and C has the same slope MPC × (1-t)  Multiplier effect is given by the combination of the two  Multiplier = 1/(1-MPC x (1 –t))  The change of equilibrium GDP is given by G x multiplier. 24Lecture 7

YCIAE (a) No Government  AE = C + I  C = Y  I = 80  Autonomous Expenditure of 100  Multiplier = 5  Y e = 100 × 5 = 500 YCIAE Lecture 7

YCIGAE (b) T = 10, G = 50 AE = C + I + G  C = (Y-10)  C = Y  I = 80  G = 50  Autonomous Expenditure of 142  Multiplier = 5  Y e = 142 × 5 = 710 YCIGAE Lecture 7

YNTDICIGAE (c) Tax t = 0.10, G = 0  AE = C + I  C = (1-0.10)Y  C = Y  I = 80  Autonomous Expenditure of 100  Multiplier = 1/(1-0.8( ))= 3.57  Y e = 100 × 3.57 = Lecture 7

YNTDICIGAE (d) Tax t = 0.1, G = 50  AE = C + I + G  C = (1-0.1)Y  C = Y  I = 80, G =50  Autonomous expenditure =150  Multiplier = 1/(1-0.8(1- 0.1)) = 3.57  Y e = 150×3.57 = YNTDICIGAE Lecture 7

o 45 o GDP (billions of dollars) AE’ AE Autonomous expenditure is increased by 42 (intercept effect) AE shifts up Slope = 0.8, multiplier = 5, Y* = Aggregate expenditures (billions of dollars) Y = AE 710 G = 50, T = 10 29Lecture 7

o 45 o GDP (billions of dollars) AE’ AE Autonomous expenditure is increased by 50 (intercept effect) AE becomes flatter (t = 0.1, slope = 0.8 × (1-0.1) = 0.72; slope effect) 500 Aggregate expenditures (billions of dollars) Y = AE G = 50, t = Lecture 7

 Chapter 8.4 and 9 (exclude 9.3)  Understand how taxes and government spending affect equilibrium GDP  Homework 7 Lecture 731