GY=1C11

0<C1<1

The denominator is less than numerator therefore the multiplier is greater than 1.

Explanation:

C(Y,T)=C0+C1(YT)

I(r)=I0I1r

AE=C0+C1(YT)+I0I1r + G

Y=AE

Y=C0+C1(YT)+I0I1r + G

Y=C0+C1YC1T+I0I1r + G

YC1Y=C0C1T+I0I1r + G

Y(1C1)=AI1r,whereA=C0C1T+I0 + G

Y=1C11[AI1r]..........IS equation.

Y=1C11[C0C1T+I0I1r+G]

GY=1C11

0<C1<1

C₁ = marginal propensity to consume

Lets say C₁ = 0.5

Multiplier = 10.51

= 2

The denominator is less than numerator therefore the multiplier is greater than 1.

QUESTION

1) why are we only differentiating the expression 1/1-c_1 ? What about C_0 C _1 T+ I_0 I_1 r+G?

2) Why is (the absolute value) of the multiplier with respect to T less than with respect to G |dY/dT| < |dY/dG|?