Income Determination and the Multiplier

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The presentation explaining macro economics talks about income determination , investment multiplier, and explains the same with the help of an example

MACROECONOMICS
Income Determination and the Multiplier

THE AUTONOMOUS INVESTMENT MULTIPLIER
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In a two sector economy, the National Income Identity is: Y=C+I Putting the value of C and I Y = Ca+ C(Y)+Ia+I(Y) dY= dCa+ C‘(DY)(dY-dT)+dIa+I‘(Y) dY Assuming that the level of Cais fixed and I does not respond to Y dY= c(dY)+dIa dY(1-c) = dIa dY = dIa/(1-c) This implies that an additional increase in the autonomous investment will result in an increase in Y by 1/(1-c) times the autonomous investment. Here 1/(1-c) is called as the multiplier (K). If an economy has c=0.8, then the value of multiplier will be 5. This implies: If Ia in the hypothetical economy is raised by Rs. 100, then the National Income will go up by Rs. 500

CONTINUE…
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However, if investment responds to Y, then the value of K is 1/(1-c-i), where i=MPI (This is called as the Accelerator ?) If investment responds to Y, then the value of K will be higher than other wise AD+I’(Y)+I AD=Y AD, I
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AD+I’(Y ) AD+Ia AD

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YI’(Y Y* YIa
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YI’(Y)+Ia

Y

CONTINUE…
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In a three sector economy, the National Income Identity is: Y = C + I+G Putting the value of C, I and G Y = Ca+ C(Y-T)+Ia+I(Y) +Ga+G(Y) dY= dCa+ C‘(DY)(dY-dT)+dIa+I‘(Y) dY+dGa+G‘(Y)dY

Assuming that level is T, Ca, Ia is fixed and I and G do not respond to Y
dY= c(dY)+dGa dY(1-c) = dGa dY = dGa/(1-c)
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This implies that an additional increase in the autonomous Govt. expenditure will result in an increase in Y by 1/(1-c) times the Govt. expenditure. Here 1/(1-c) is called as the Govt. expenditure multiplier (Kg). If an economy has c=0.8, then the value of Kg will be 5. This implies: If Ga in the hypothetical economy is raised by Rs. 100, then the National Income will go up by Rs. 500

CONTINUE…
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However, in a three sector economy, if the Govt. spends exactly the same amount as its Tax Revenue (T), then T=Ga (A case where the Govt. resorts to a Balanced Budget)

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Y = Ca+ C(Y-T)+Ia+I(Y) +Ga+G(Y)
dY= dCa+ C‘(DY)(dY-dT)+dIa+I‘(Y) dY+dGa+G‘(Y)dY Assuming that the level of Ca, Ia is fixed and I and G do not respond to Y dY= c(dY-dT)+dG a dY(1-c) = dGa-c(dT), (but dT = dGa, since T =Ga ) dY(1-c) = dGa-c(dGa) = dGa (1-c) dY/ dGa = (1-c)/(1-c)= 1 (Known as the Balanced Budget Multiplier)

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This implies that if the Govt. spends exactly the same amount as its Tax Revenue (T), or the Govt. resorts to a Balanced Budget, an additional increase in the autonomous Govt. expenditure will result in an exact amount of increase in Y This implies: If Ga in the hypothetical economy is raised by Rs. 100, then the National Income will go up by Rs. 100

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