5 Given the following variables in the open economy aggregat

5. Given the following variables in the open economy
aggregate expenditure model, autonomous
consumption (C0) = 200, autonomous investment
(I0) = 200, government spending (G0) = 100,
export spending (X0) = 100, autonomous import
spending (M0) = 100, taxes (TP) = 0, marginal propensity
to consume (c1) = 0.8, marginal propensity
to invest (i1) = 0.1, and marginal propensity
to import (m1) = 0.15,
a. Calculate the equilibrium level of income for the
open economy aggregate expenditure model.
b. If there is an increase in autonomous import
expenditure from 100 to 200 resulting from an
increase in the currency exchange rate, calculate
the new equilibrium level of income and
the value of the multiplier.
c. Compared with the original equilibrium in part
a, if the government decides to impose taxes
(TP) of 100, calculate the new equilibrium level
of income.

Solution

a.) Equilibrium level of income for the open economy aggregate expenditure model:

Y=(C0+c1Y)+(I0+i1Y)+G0+X0-[M0+m1Y]

Y=(200+0.8Y)+(200+0.1Y)+100+100-[100+0.15Y]

Y=500+0.75Y

Y=2000

b.) Multiplier=1/(1-c1-i1+m1)

=1/(1-0.8-0.1+.15) =4

Multiplier= Change in equilbrium income/change in autonomous spending

4= Change in equilbrium income/100

Change in equilbrium income=400

New equilbrium income=2000-400=1600

c.) TP=100

Y=(C0+c1{Y-TP})+(I0+i1Y)+G0+X0-[M0+m1Y]

Y=(200+0.8{Y-100})+(200+0.1Y)+100+100-[100+0.15Y]

Y=420+0.75Y

Y=1680