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Section 18 Notes.doc

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ECON 0110

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SECTION 18: THE AUTONOMOUS SPENDING MULTIPLIER IN A MODEL WITH NO TAXES DEFINITION: AUTONOMOUS SPENDING Autonomous spending is any spending which is not induced by, or influenced by, the level of income or the size of the economy. INDUCED SPENDING Induced spending is any increase in the level of spending that is related to an increase in the level of income or the size of the economy. Suppose autonomous spending increases in the economy. This could involve an increase in consumption spending, investment spending, government spending, or foreign spending. EXAMPLES: AN INCREASE IN AUTONOMOUS CONSUMPTION SPENDING Suppose the stock market rises, so consumers decide to buy more cars. AN INCREASE IN AUTONOMOUS INVESTMENT SPENDING Suppose interest rates decline so a corporation decides to borrow money and builds a new factory. AN INCREASE IN AUTONOMOUS GOVERNMENT SPENDING Suppose the Federal government decides to build a new highway. AN INCREASE IN AUTONOMOUS EXPORT SPENDING Suppose the Chinese economy booms and foreigners decide to buy more American cars or make more visits to Disneyland. EFFECT OF AN INCREASE IN AUTONOMOUS SPENDING When autonomous spending increases, some sector of the economy is purchasing more than it did before, and this causes an increase in output. This increase in output causes an increase in the incomes of the workers producing the output. This increase in income causes an increase in the consumption spending of the producers. This is called induced consumption spending. This induced consumption spending causes another increase in output and another increase in the incomes of the producers. This causes additional induced consumption spending. This process repeats itself over and over. CONCLUSION: Any increase in autonomous spending (from any sector) leads to a multiple increase in output. THE AUTONOMOUS SPENDING MULTIPLIER The multiplier is the change in equilibrium output divided by the change in autonomous spending that caused it. MULTIPLIER = ΔY / Δ(eUTONOMOUS SPENDING) = (Change in equilibrium output)/(Change in autonomous spending) CALCULATION OF THE AUTONOMOUS SPENDING MULTIPLIER EXAMPLE: Let C = 100 + .75 Y e Let I = 100 (All investment is autonomous.) Let G = 300 (All government spending is autonomous.) Let NX = 0 (Net export spending is autonomous.) SOLVE FOR Y e0 Y e0[1/(1 – mpc)] x (C 0 I 0 G + 0X ) 0 Y = [1/(1 - .75)] x (100 + 100 + 300 + 0) e0 Y = 4 x 500 = 2000 e0 Now suppose there is an autonomous increase in government spending. Assume G increases by 100. Thus, the new level of government spending is 400, rather than 300. Thus, ∆G = 400 – 300 = 100 NEW SOLUTION FOR EQUILIBRIUM Y e1[1/(1 – mpc)] x(C + 0 + 0 + NX1) 0 Y e1[1/(1 - .75)] x (100 + 100 + 400 + 0) Y e 4 x 600 = 2400 Now let us calculate the value of the multiplier. DEFINITION: MULTIPLIER = ΔY / Δ(AeTONOMOUS SPENDING) = ΔY e ΔG ΔY e 2400 – 2000 = 400 ΔG = 400 – 300 = 100 Multiplier = 400 / 100 = 4 CONCLUSION: The $100 in additional government spending led to a $400 increase in eventual output. Thus, each $1 of additional autonomous government spending caused a $4 increase in total output. Thus, the multiplier is 4. THE AUTONOMOUS SPENDING MULTIPLIER GENERAL SOLUTION: Let C = C 0 mpc Y e C 0enotes autonomous consumption Let I = 0 Let G = G 0 Let NX = NX 0 Y e0C + I + G0+ NX 0 0 = C 0 mpc Y + I e G +0NX 0 0 Y e0mpc Y = C e0I + G0+ N0 0 0 (1 – mpc)Y = e0+ I +0G + 0X 0 0 Therefore, originally, we obtain Y e0[1/(1 – mpc)] x (C + I +0G +0NX ) 0 0 Now suppose G increases to G 1 FIND THE NEW LEVEL OF EQUILIBRIUM: Y e1[1/(1 – mpc)] x (C + I +0G +0NX ) 1 0 MULTIPLIER = ΔY / Δ(AUTENOMOUS SPENDING) = ΔY /eΔG The change in Y is e ΔY e Y – e1= [1/e0 – mpc)] x (G – G ) 1 0 The change in autonomous spending is ΔG = G – 1 0 The autonomous spending multiplier
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