Econ 0110 1st Edition Lecture 22Current LectureSECTION 18:THE AUTONOMOUS SPENDING MULTIPLIERIN A MODEL WITH NO TAXESAUTONOMOUS SPENDINGAutonomous spending is any spending which is not induced by, or influenced by, thelevel of income or the size of the economy.INDUCED SPENDINGInduced spending is any increase in the level of spending that is related to an increase in thelevel of income or the size of the economy.Suppose autonomous spending increases in the economy. This could involve an increase inconsumption spending, investment spending, government spending, or foreign spending.EXAMPLES OF INCREASES IN AUTONOMOUS SPENDING:1. AN INCREASE IN AUTONOMOUS CONSUMPTION SPENDINGSuppose the stock market rises, so consumers decide to buy more cars.2. AN INCREASE IN AUTONOMOUS INVESTMENT SPENDINGThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Suppose interest rates decline so a corporation decides to borrow money and builds anew factory.3. AN INCREASE IN AUTONOMOUS GOVERNMENT SPENDINGSuppose the Federal government decides to build a new highway.4. AN INCREASE IN AUTONOMOUS EXPORT SPENDINGSuppose the Chinese economy booms and foreigners decide to buy more American carsor make more visits to Disneyland.EFFECT OF AN INCREASE IN AUTONOMOUS SPENDINGWhen autonomous spending increases, some sector of the economy is purchasing more than itdid 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. Thisis called INDUCED CONSUMPTION SPENDING.This induced consumption spending causes another increase in output and another increase inthe 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 MULTIPLIERThe multiplier is the change in equilibrium output divided by the change in autonomousspending that caused it.MULTIPLIER = DYe / D(AUTONOMOUS SPENDING)= (Change in equilibrium output)/(Change in autonomous spendingCALCULATION OF THE AUTONOMOUS SPENDING MULTIPLIEREXAMPLE:Let C = 100 + .75 YeLet I = 100 (All investment is autonomous.)Let G = 300 (All government spending is autonomous.)Let NX = 0 (Net export spending is autonomous.)SOLVE FOR Ye0Ye0 = [1/(1 – mpc)] x (C0 + I0 + G0 + NX0)Ye0 = [1/(1 - .75)] x (100 + 100 + 300 + 0)Ye0 = 4 x 500 = 2000Now suppose there is an autonomous increase in government spending. Assume G increases by100. Thus, the new level of government spending is 400, rather than 300. Thus, ∆G = 400 – 300= 100NEW SOLUTION FOR EQUILIBRIUMYe1 = [1/(1 – mpc)] x(C0 + I0 + G1 + NX0)Ye1 = [1/(1 - .75)] x (100 + 100 + 400 + 0)Ye1 = 4 x 600 = 2400Now let us calculate the value of the multiplier.DEFINITION:MULTIPLIER = DYe / D(AUTONOMOUS SPENDING)= DYe / DGDYe = 2400 – 2000 = 400DG = 400 – 300 = 100Multiplier = 400 / 100 = 4CONCLUSION: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 MULTIPLIERGENERAL SOLUTION:Let C = C0 + mpc YeC0 denotes autonomous consumptionLet I = I0Let G = G0Let NX = NX0Ye0 = C + I0 + G0 + NX0= C0 + mpc Ye + I0 + G0 + NX0Ye0 - mpc Ye0 = C0 + I0 + G0 + NX0 (1 – mpc)Ye0 = C0 + I0 + G0 + NX0Therefore, originally, we obtainYe0 = [1 / (1 – mpc)] x (C0 + I0 + G0 + NX0)Now suppose G increases to G1FIND THE NEW LEVEL OF EQUILIBRIUM:Ye1 = [1 / (1 – mpc)] x (C0 + I0 + G1 + NX0)MULTIPLIER = DYE / D(AUTONOMOUS SPENDING)= DYe / DGThe change in Ye isDYe = Ye1 – Ye0 = [1 / (1 – mpc)] x (G1 – G0)The change in autonomous spending isDG = G1 – G0The autonomous spending multiplier isMultiplier = [1 / (1 – mpc)] x (G1 – G0)/ (G1 – G0)= 1 / (1 – mpc)EXAMPLE:In the previous model, we hadmpc = .75We calculated the multiplier as Multiplier = DYe / DG = 400/100 = 4From our formula, we obtain the same result:Multiplier = 1 / (1 – mpc) = 1 / (1 - .75) = 4THE MULTIPLIER: AN ALTERNATIVE EXPLANATIONRound 1:Suppose G purchases increase by $100.Thus, output increases by $100 (and people’s incomes increase by $100). GDP increasesby $100.Round 2:Given that the mpc = .75, the $100 increase in income induces an additional $75increase in consumption spending.Thus, output increases by another $75 (and people’s incomes increase by $75). GDPincreases by the additional $75.Round 3:Given that the mpc = .75, the $75 increase in income induces an additional $56.25increase in consumption spending. Thus, output increases by $56.25 (and people’sincomes increase by $56.25). GDP increases by the additional $56.25.Round 4: GDP increases by $42.19Round 5: GDP increases by $31.16Round 6: GDP increases by $23.73Round 7: GDP increases by $17.80Round 8: GDP increases by $13.35And so forth.Total increase in GDP = 100 + 75 + 56.25 + ... = 400The $100 increase on autonomous spending induced a $400 increase in equilibrium output.Similarly, a $1 billion increase in autonomous spending would induce a $4 billion increase inequilibrium output.In each case, the multiplier is 4.FISCAL POLICY AND THE IMPORTANCE OF THE MULTIPLIER:Suppose the economy is operating far below full employment. Assume output is at level YUAssume output at full employment would be YFThat is, we have a GDP gap.GDP gap = YF - YUSUPPOSE WE WISH TO INCREASE GDP BY A CERTAIN AMOUNT TO ELIMINATE THE GDP GAPAN INCREASE IN C0, I0, or G0 CAN BRING ABOUT THE DESIRED RESULTQUESTION 1:Suppose we increase G by the amount DG.By how much will Ye increase?SOLUTION:Multiplier = DYe/ DG = 1/(1 – mpc)Thus,DYe = [1/(1 – mpc)] x DGEXAMPLESuppose we increase G by the amount DG = 100.By how much will Ye increase?(Assume mpc = .75)SOLUTION:DYe = [1/(1 – mpc)] x DG = [1/(1 - .75)] x 100 = 4 x 100 = 400FISCAL POLICY AND THE MULTIPLIERTo eliminate a GDP gap, we need to increase equilibrium output.Suppose the desired increase in Ye is DYe.By how much do we need to increase autonomous spending to achieve the desired increase inoutput?SOLUTION:The multiplier is given byMultiplier = DYe/ DG = 1/(1 – mpc)We obtain:DG = DYe x (1 – mpc)EXAMPLESuppose