Question

Given the following variables in the open economy aggregate expenditure model, autonomous consumption (C0) = 800, autonomous investment (I0) = 600, government spending (G0) = 700, export spending (X0) = 400, autonomous import spending (M0) = 700, taxes (TP) = 200, marginal propensity to consume (c1) = 0.75, marginal propensity to invest (i1) = 0.2, and marginal propensity to import (m1) = 0.15.

a. Calculate the equilibrium level of income for the open economy aggregate expenditure model. (Show all your steps carefully.)

b. If there is a decrease in the marginal propensity to consume from 0.75 to 0.65, calculate the new equilibrium level of income and the value of the multiplier. (Again, show all your steps carefully.)

Answer 1

C0 = 800, I0 = 600, G0 = 700, X0 = 400, M0 = 700, T = 200, c1 = 0.75, i1 = 0.2, m1 = 0.15.

a. The equilibrium level of income for the open economy aggregate expenditure model is:

Y = C + I + G + NX = C0 + c1(Y - T) + I0 + i1*Y + G0 + X0 - (M0 + m1*Y),

Y = 800 + 0.75(Y - 200) + 600 + 0.2Y + 700 + 400 - (700 + 0.15Y),

Y = 1650 + 0.8Y,

0.2Y = 1650,

Y = 8250.

b. If there is a decrease in the marginal propensity to consume from 0.75 to 0.65, then the new equilibrium level of income is:

Y = 800 + 0.65(Y - 200) + 600 + 0.2Y + 700 + 400 - (700 + 0.15Y),

Y = 1670 + 0.7Y,

0.3Y = 1670,

Y = 5566.67.

The value of the multiplier is:

m = 1/(1 - c1 + m1) = 1/(1 - 0.65 + 0.15) = 2.