Question

1. a) In reality, tax revenues are not exogenous, but move positively with income (GDP). Suppose that T = ?̅ + tY, where t is an exogenous tax rate.

Use this tax revenue function to derive the government spending multiplier in the following simple model:

C = c + c1(Y – T) I = ?̅ G = ?̅
NX = NX0 -mY

b) Derive the IS curve for the economy in the above exercise, with I = ?̅ – 20i. Plot it in (Y, i) space.

TYPED ANSWER

Answer 1

AE = C + G + I + NX

AE = c + c​​​​​​t(Y-T- tY)+ I + G+ NX​​​0 - mY

So AE = c +I + G + NX​​​​​0 - c​​​​​​t​​​​​*T + Y(c​t*(1-t)-m)

Thus at eqm

Y = AE

so Y = A​​​​​​0 + Y(c​​​​​​t*(1-t)-m)

so Y [1-ct*(1-t)+m] = A​​​​​​0

thus govt spending multiplier = 1/[1-ct*(1-t)+m]

B)  IS curve,graph between i & Y

so as I = I – 20i

so from AE eqn

AE = c +I -20i + G + NX​​​​​0 - c​​​​​​t​​​​​*T + Y(c​t*(1-t)-m)

AE = A0 + Y(c_{​​​​​​t}*(1-t)-m) - 20i

thus at equilibrium, Y= AE

thus , Y = A_{​​​​​​0} + Y(c_{​​​​​​t}*(1-t)-m) -20i

20i = A0 - Y[ 1- c_{​​​​​​t}*(1-t)+m ]

i = A0/20 - Y/20*_g

_g = govt spending multiplier

Now graph :

Inverse shape curve between i & Y,

Y is on horizontal axis

Interest rate is on vertical axis

​​​​​​​