Consider an open economy in which the real exchange rate is fixed and equal to o

Question

Consider an open economy in which the real exchange rate is fixed and equal to one. Consumption, Investmentnt, and Government spending are given by:

C=10+0.8 (Y-T), I=10, G=10, and T=10, IM=0.3Y and X=0.3Y* where Y* denotes foreign output.

A) Solve for equilibrium output in the domestic economy

B) Given Y* what is the multiplier in this economy? If we were to close the economy-so exports and imports were identically equal to zero-what would the multiplier be? Why would the multiplier be different in a closed economy?

Explanation / Answer

A.

Equilibrium Output = Y = C+I+G + X – IM

Y = 10+0.8 (Y-T) + 10+ 10 + 0.3Y* - 0.3Y

Y = 10 + .8Y - .8*10 + 20 + .3Y* - .3Y

Y+.3Y - .8Y = 22 + .3Y*

.5Y = 22+.3Y*

Y=1/.5*(22+.3Y*)

Y = 2*(22+.3Y*)

B.

As per the above equilibrium output condition,

Multiplier = 2

If, Export = Import

Y = C+I+G + X – IM

X = IM

Y = C+I+G

Y = 10+0.8 (Y-T) + 10+ G

Y = 10+.8(Y – 10) + 10+ G

Y - .8Y = 12+G

.2Y = 12+G

Y = 5*(12+G)

Here, the multiplier is 5.

Difference in multiplier is due to change in economic conditions. In open economy, export and import were varying in nature. Thus, multiplier effect was 2. But, in closed conditions, imports are equal to export. Thus, multiplier effect is big.

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