Multiplier

Closing the recessionary gap Classical Theory  In the Classical Economics, a recessionary gap is only temporary.  Because the surplus in the labor market will depress the wage rate  Then cost of production falls  Price of products will also fall.  Through wealth effect, consumption will go up  In the income-expenditure diagram, the AE schedule will shift up.  Hence the recessionary gap will be closed automatically at reasonable speed.

Closing the recessionary gap Keynesian Theory  Prices and wage rates are rigid to go downward  When the firms and consumers remain pessimistic, even the wage rates and product prices fall, they do not increase employment or consumption  So the recessionary gap remains for long time. Recession is prolonged

Recessionary Gap 0 Y Y* AE AE=Y $ YpYp Recessionary gap

Close Recessionary Gap  Increase total spending AE  AE = C + I + G + (X - IM)  C, I and X-IM are not controllable  G can be controlled by the government  Keynes suggests to increase G thus AE to create more demand

Closing the Recessionary Gap 0 Y Y* AE AE=Y $ YpYp Recessionary gap AE’ GG

How much should G increase to close the gap  A smaller increase in G leads to larger increase in Y*  Graphically illustration

Closing the Recessionary Gap 0 Y Y* AE AE=Y $ YpYp Larger increase in Y* AE’ Initial increase in G

Numerical illustration  The model economy  C = DI  T = 0  I = 150  G = 200  X - IM = -50  Solved: Y* = 4000  Suppose: Yp = 5000

Numerical illustration  AE = Y  Equilibrium Y: Y* = 1/(1-0.9) X 400 = 10 X 400 = 4000  Potential GDP: Yp = 5000  The recessionary gap Yp - Y* = = 1000

Numerical illustration  Suppose G rises by 100, from 200 to 300, what happens to Y*?  AE = C + I + G + (X - IM) = Y = Y  The new equilibrium Y* Y** = 1/(1-0.9) X 500 = 10 X 500 = 5000

Numerical illustration  Increase in Y*  Y* = = $1000  G = $100  Y* = $1000  An increase in G by 100 leads to an increase in Y* by  Ten times large.

Expenditure Multiplier  Expenditure multiplier  Also called “income multiplier” Increase in Y* Increase in Y*  Expenditure Multiplier = Increase in G  Y*  Y*   E =  G  G

Expenditure Multiplier  Y* 1000  Y* 1000  E = = = 10  G 100  G 100

Expenditure Multiplier  Y* Y* Y* Y* Y* Y* Y* Y*  E = = ---- = ---- = G C I X-IM G C I X-IM

Economic insight of the multiplier  The trickling down effect –The multiplier is greater than 1 because one person’s spending is another person’s income. – spending   income –A portion of the increase in income is spent on consumption, creating more income, which in turn creates more consumption spending, and so on

Insight of multiplier  Suppose the government increases G by 100 (b$)  1st round, government spending: G = AE = 100 G = AE = 100  2nd round, contracted firms: C = AE = DI X 0.9 = 100 X MPC C = AE = DI X 0.9 = 100 X MPC = 100 X 0.9 = 90  3rd round, the shopkeepers, C = AE = DI X 0.9 = 90 X MPC = 90 X 0.9 = 81

How the Multiplier Builds Copyright © 2003 South-Western/Thomson Learning. All rights reserved. Spending Round Cumulative Spending Total $

Insight of Multiplier Round Number Increase in Spending in this round (b$) Cumulative total (b$) Infinity 0 1,000

Insight of multiplier  Cumulative increase in Y*: = X X (0.9) X (0.9) X (0.9) = 100 X ( ) 1 = 100 X = 100 X 10 = 1000

Geometric Progression and solution  1 + x + x 2 + x 3 + x = ( x < 1 ) = ( x < 1 ) 1 - x 1 - x

Expenditure multiplier 1   E = – MPC 1 – MPC  "oversimplified multiplier" formula  Larger MPC, larger  E

Autonomous changes in AE  Autonomous increase in C, I, or X-IM refers to an increase in C, I, or X - IM, which is independent of income Y.  In graph, an autonomous increase shifts the AE schedule up.  Any autonomous increase generates a multiplier effect on Y*

Induced changes in AE  Induced increase in C, I, or X – IM  refers to an increase in C, I or X - IM due to an increase in income Y.  In graph, an induced increase produces a movement along the AE schedule.

Autonomous and induced changes 0 Y Y* AE AE=Y $ YpYp Autonomous change AE’ Induced change

The Paradox of Thrift  If everyone tries to save more in recession  Then C falls  Then causes a multiple decrease in Y*  Then each individual ends up with less saving in absolute term.

The Paradox of Thrift Saving GDP before recession GDP in recession