Answer to Question #152463 in Macroeconomics for Joshua

Question

You are given data on the following variables in an economy:

Government spending = 300

Planned investment = 200

Net exports = 50

Autonomous taxes = 250

Income tax rate = 0.1

Marginal propensity to consume = 0.5

A. Consumption (C) is 600 when income (Y) is equal to 1500. Solve for autonomous consumption.

B. Solve for the equilibrium level of output in the following two scenarios:

I. There is an income tax = 0.1

ii. There is no income tax in the economy. Denote these two variables by Y*w and Y*wo, respectively

C. In the economy with an income tax of 10% what is the budget balance of the government?

D. Solve for the change in net exports that would bring the equilibrium output level in the economy with the income tax to the level of Y*wo that you found in part B. Specity both the magnitude of the change and whether it is an increase or a decrease. What wlike be the new level of net exports after this change?

Answer 1

A. autonomous consumption:

C=c+MPC(Y-t)

C=600

MPC=0.5

Y=1500

t=0.1

$600=c+0.5(1500-250)$

c=25

B

I.

$Y=C+MPC(Y-0.1\times Y)+I+G+Nx=600+0.5(Y-0.1\times Y)+200+300+50=0.45Y+1150$

$Y-0.45\times Y=1150$

Y=2090.91

II.

$Y=C+MPC(Y)+I+G+Nx=600+0.5(Y)+200+300+50=0.5Y+1150$

Y=2300

C.

$BD=G-T=300-2300\times0.1=300-230=70$

surplus

D.

$Y=C+MPC(Y)+I+G+Nx$

$2300=600+0.5(2300)+200+300+NX$

2300-2250=Nx

Nx=50

50-50=0

it will remain at the same level