Consider an economy described by the following functions: C = 20 + 0.80Y, I = 30, G = 50, TR = 100 (a) Find the equilibrium level of income and the autonomous expenditure multiplier in the model. (b) If government expenditure increases by 30, what is the impact on equilibrium income? (c) If a lump-sum tax of 30 is added to pay for the increase in government purchases, how will equilibrium income change?

Given is

C = 20 + 0.80 Y (C = 20 & MPC = 0.8)

I = 30

c = 0.80

G = 50

TR = 100

(a) Equilibrium level of income = 1/(1-c) [C + cTR + I + G]

= 1/ (1 – 0.8) [ 20 + (0.8 X 100) + 30 + 50]

= 900

Autonomous expenditure multiplier = 1/1-c

= 1/1-0.8

= 5

(b) If government expenditure increases by 30, what is the impact on equilibrium income?

New level of equilibrium income = 1/(1-c) [C + cTR + I + G + ∆G], Where ∆G = 30

= 1050

Change in equilibrium income = 1050 – 900 = 150

c) Tax multiplier ∆Y/ ∆T = -c/1-c

= -0.8/0.2

= - 4

∆Y/ ∆T = - 4

∆Y = - 4 X ∆T

= - 4 X 30

= - 120

Y = 900 – 120 = 780

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