Chapter 11 Part 2 Basic Keynesian Model Expenditure and Tax Multipliers

Transcription

1 2/23/208 Chapter Part 2 Basic Keynesian Model Expenditure and Tax Multipliers What Happens When Things Change - When autonomous spending changes, the equilibrium level of real GDP changes. But the change in the equilibrium level of real GDP is larger than the change in autonomous expenditure. This is called the multiplier effect Spending Multiplier = Y Spending The Basic Idea of the Multiplier An increase in investment (or any other autonomous expenditure) increases aggregate expenditure and real GDP directly by that amount - If investment (I) increases by $, real GDP increases by $ If government (G) increases by $, real GDP increases by $ The increase in real GDP then leads to an increase in induced consumption expenditure as YD increases. The increase in induced expenditure leads to a further increase in aggregate expenditure and real GDP. Real GDP increases by more than the initial increase in autonomous expenditure.

2 2/23/208 Simple Multiplier Example No taxes (T), no imports (M), MPC = Autonomous Investment (I) spending increases by 00. Change Autonomous Investment Spending (I) Change in GDP(Y) Change in C Cumulative Change in Total Spending Round Round 2 Round 3 Round Round N +400 Spending Multiplier = Spending Multiplier = Y Spending = 4 Multiplier Exercise: MPC =.80 Change in I Change in Y Change in C Cumulative Change Total Spending Round Round 2 Round 3 Round 4 Round N 2

3 2/23/208 Multiplier Exercise: MPC =.80 Change in I Change in Y Change in C Cumulative Change Total Spending Round Round 2 Round 3 Round Round N +500 Y The spending multiplier = Spending = = 5 Spending Multiplier = Y Spending = MPC Spending Multiplier = = 5 = 0.8 The Size of the Multiplier With no Taxes (T) or Imports (M), The multiplier formula is: MPC If the MPC = 0.75, the multiplier would be: MPC = 0.75 = 4 9 of 38 3

4 2/23/208 Business Cycle Turning Points Turning points in the business cycle - peaks and troughs - occur when autonomous expenditure such as investment changes. A decrease in autonomous investment expenditure brings an unplanned increase in inventories, which triggers a recession. An increase in autonomous expenditure brings an unplanned decrease in inventories, which triggers an expansion. Skip pages for now Go to Mathematical Note, PP , the algebra of the Keynesian model Model Variables: () AE = aggregate expenditure = C + I + G + X M (2) Y is real GDP, C is consumption, I is investment, G is government spending, X is exports and M is imports, T is net taxes and YD is disposable income. (3) a is autonomous consumption, the intercept of the consumption function. (4) b is the MPC, slope of the consumption function (5) m is the MPM (6) T a is autonomous taxes (7) t is the marginal income tax rate Model Math from Chapter Mathematical Note, PP The Model: () AE = C + I + G + X M. (2) C = a + b (YD) (consumption function) (3) YD = Y T (definition) (4) C = a + b(y T) (substitute (3) into (2)) (5) T = T a + t(y) (tax equation, taxes depend on Y. T a is autonomous taxes, not related to income) (6) C = a + b(y (T a + ty)) (substitute (5) into (4)) (7) C = a - bt a + b(-t)y (multiply through) (8) M = my (import function) 4

5 2/23/208 Model Math from Chapter, Mathematical Note, PP Substitute and solve for AE: (9) AE = a - bt a + b(-t)y + I + G + X my [substitute (7) and (8) into ()] (0) AE = (a - bt a + I + G + X) + [b(-t) m]y [collect terms] ()A = (a - bt a + I + G + X) [autonomous expenditure] (2) AE = A + [b(-t) m]y [ this is just (0) in terms of autonomous expenditure and Y] AE Curve is just a straight line Intercept = A = a - bt a + I + G + X Slope = b(-t) m Planned AE AE Autonomous Expenditure = a - bt a + I + G + X Slope = b(-t) m Y (Real GDP) Equilibrium () Y = AE (equilibrium condition) (2) Y = A + [b(-t) m]y (3) Y - [b(-t) m] Y = A (bring Y to LHS) (4) Y = A (solve for Y) [b( t) m] 5

6 2/23/208 AE Curve Planned AE 45 0 line AE Autonomous Expenditure = a - bt a + I + G + X Slope = b(-t) m Y = AE Y - Real GDP Multiplier Formula () Y = A (Equilibrium Y) [b( t) m] (2) ΔY = [b( t) m] (3) Multiplier = DY DA = [b( t) m] b = MPC t = marginal tax rate m = MPM ΔA (change in Y due to change in autonomous spending) Multiplier Multiplier = DY DA = [b( t) m] If: b = MPC = 0.75 t = marginal tax rate = 0.2 m = MPM = 0. Multiplier = [.75(.2).] = 0.5 = 2 The multiplier is larger: Greater the MPC Smaller t Smaller m 6

7 2/23/208 Oodles of Multipliers Government Spending and Investment Multiplier ΔY = [b( t) m] ΔA A = (a - bt a + I + G + X) ΔA is equal to the change in any variable in the bracket ΔA = ΔG, if the change in autonomous spending is ΔG ΔY = [b( t) m] ΔG Gov t spending multiplier = ΔY ΔG = [b( t) m] Oodles of Multipliers Government Spending and Investment Multiplier ΔY = [b( t) m] ΔA A = (a - bt a + I + G + X) ΔA is equal to the change in any variable in the bracket ΔA = ΔI, if the change in autonomous spending is ΔI Inv t spending multiplier = ΔY ΔI = [b( t) m] Oodles of Multipliers Government Spending and Investment Multiplier ΔY = [b( t) m] ΔA A = (a - bt a + I + G + X) ΔA is equal to the change in any variable in the bracket Inv t spending multiplier = ΔY ΔI = [b( t) m] ΔY G = ΔY ΔI = ΔY ΔX = ΔY Δa = [b( t) m] 7

8 2/23/208 Autonomous Tax Multiplier A = (a - bt a + I + G + X) ΔA is equal to the change in any variable in the bracket ΔA = -ΔT a b ΔY = [b( t) m] ΔT a Autonomous tax multiplier = ΔY b = ΔT a [b( t) m] Balanced Budget Multiplier Model Math from Chapter Mathematical Note The country of Zambonia is described by the following equations: () Y = AE = C + I + G + X M (equilibrium condition) (2) C = YD (consumption function) (3) T = Y (tax equation) (4) I = 00 (5) G = 00 (6) X = 00 (7) M = 0.Y (import function) Solve for the equilibrium level of income. What is the size of the government spending multiplier? If the level of full employment potential GDP is,00, must government spending be increased of decreased to get to full employment and by what amount? 8