Answer to Question #282120 in Macroeconomics for ABEX

Question

3. Consider an economy with the following aggregates:

Consumption function: C = 50 + 0:8Yd, where Yd is disposable income

Autonomous investment: I¯ = 70

Government expenditure: G¯ = 200

Government transfer: TR = 100

Tax rate: t = 0:20

(a) Calculate the equilibrium level of income, the multiplier, and the

budget surplus in this model.

(b) Suppose that the marginal propensity to consume increased permanently to 0.9. What is the impact of this increase on the level

of equilibrium income and the multiplier?

(c) Suppose that the tax rate t increases to 0.25. Calculate the new

equilibrium level of income, the budget surplus, and the multiplier.

Answer 1

Solution:

a.). At equilibrium: Y = AD

Y = C + I + G

C = 50 + 0.80Yd = 50 + 0.80 (Y – T) = 50 + 0.80 (Y – 0.20Y)

Y = 50 + 0.80 (Y – 0.20Y) + 70 + 200

Y = 50 + 0.64Y + 270

Y – 0.64Y = 320

0.36Y = 320

Y = 888.89

The equilibrium level of income (Y) = 889

Multiplier = $\frac{1}{(1 - MPC)}$

MPC = 0.80

= $\frac{1}{(1 - 0.80)} = \frac{1}{0.20} = 5$

The multiplier = 5

 

Budget surplus = T – G

T = 0.20Y = 0.20(889) = 178

G = 200

Budget surplus = 178 – 200 = (22)

Budget deficit = (22)

 

b.). Y = C + I + G

C = 50 + 0.90Yd = 50 + 0.90 (Y – T) = 50 + 0.90 (Y – 0.20Y)

Y = 50 + 0.90 (Y – 0.20Y) + 70 + 200

Y = 50 + 0.72Y + 270

Y – 0.72Y = 320

0.28Y = 320

Y = 1,142.86

The equilibrium level of income (Y) = 1,143

Multiplier = $\frac{1}{(1 - MPC)}$

MPC = 0.90

= $\frac{1}{(1 - 0.90)} = \frac{1}{0.10} = 10$

The multiplier = 10

 

c.). Y = C + I + G

C = 50 + 0.80Yd = 50 + 0.80 (Y – T) = 50 + 0.80 (Y – 0.25Y)

Y = 50 + 0.80 (Y – 0.25Y) + 70 + 200

Y = 50 + 0.6Y + 270

Y – 0.6Y = 320

0.4Y = 320

Y = 800

The equilibrium level of income (Y) = 800

Multiplier = $\frac{1}{(1 - MPC)}$

MPC = 0.80

= $\frac{1}{(1 - 0.80)} = \frac{1}{0.20} = 5$

The multiplier = 5

 

Budget surplus = T – G

T = 0.25Y = 0.25(800) = 200

G = 200

Budget surplus = 200 – 200 = 0

Budget surplus = 0