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b△ G b2△ T 3 b 2△ G b3△ T …………………………………………………… . n bn1△ G bn△ T △ Y = ( 1 + b2 + b3 + … + bn1 ) △ G =[ 1/(1b)] △ G △ Y = ( b b2 b3 … bn ) △ T = ( b)( 1+b2+ b3 + … + bn1 ) △ T =[ b/(1b)] △ T Comparison of Tax with Purchases △ Y = ( 1 + b2 + b3 + … + bn1 ) △ G = [ 1/(1b)] △ G △ Y = ( b b2 b3 … bn ) △ T =[ b/(1b)] △ T = [ 1/(1b)] (b △ T) Government expenditure multiplier: △ Y/ △ G = [ 1/(1b)] the government expenditure Multiplier is the increase in GDP induced by an increase of $ 1 in government purchase. Tax multiplier: △ Y /△ T = [ b/(1b)] the Tax Multiplier is the increase in GDP induced by an increase of $ 1 in tax. CHAPTER 24 THE MULTIPLIER MODEL T = Tax Transfer Total tax multiplier △ TX △ DI = △ TX △ AD = b△ TX GDP declines DI falls ……………………… .. Transfer multiplier △ TR △ DI = △ TR △ AD = b△ TR GDP increases DI rises ……………………… .. (Net) Tax multiplier △ ( TXTR) △ DI = △ (TX – TR) △ AD = b △ (TX – TR) GDP changes DI changes … CHAPTER 24 THE MULTIPLIER MODEL Total tax multiplier △ Y = [b/(1b) ] △ TX △ Y /△ TX = [b/(1b) ] Transfer multiplier △ Y = [b/(1b) ] △ TR △ Y /△ TR = b/(1b) (Net) Tax multiplier △ Y = [b/(1b) ] △ (TX TR) △ Y /△ T = △ Y /△ (TX TR )= b/(1b) CHAPTER 24 THE MULTIPLIER MODEL Question 1: If tax and purchase increase simultaneously by the same amount, will GDP increase, decrease, or remain unchanged? (balancedbudget multiplier) Question 2: If GDP is levied a proportional ine tax, ., tax is dependent on GDP, is the multiplier we developed above any different? Summary of Multiplier Principle: ?GDP increases with the increase in AD ?GDP increases by the amount greater than the increase in autonomous expenditure such as investment and government purchase. (The increase in GDP is the multiple increase in investment or government purchase.) ?The multiplier depends on MPC (and tax rate) ?The multiplier may influence GDP in two directions: the increase in investment increases GDP by a multiplier and the decrease in investment also reduces GDP by the same multiplier. ?The multiplier holds for excess capacity. CHAPTER 24 THE MULTIPLIER MODEL Summary of Fiscal Policy ?Government purchase has the same effect on GDP as investment. ?Total Tax influences GDP negatively by less extent than government purchases. ?Transfer payments influence GDP positively by the same extent as total tax but lower extent than government purchases. ?Balanced budget has expansionary effect on GDP. CHAPTER 24 THE MULTIPLIER MODEL Different Multipliers: Autonomous Expenditure Multiplier Investment Multiplier Government Purchases multiplier Tax Multiplier Transfer Payment Multiplier Definition of Multiplier Multiplier is the number by which the change in expenditures or in fiscal policies must be multiplied to get the resulting change in GDP