Answer to Question #201376 in Macroeconomics for priscilla

Question

Prove the foreign investment multiplier is equal to 1 all over mpm + mps (1/mpm+mps)

Answer 1

We derive the foreign investment multiplier as follows:

The national income identity in an open economy is given by $Y=C+I+C-M$

Y is the national income, C national consumption,I total investment, X exports and M thee imports.

This relationship can also be arranged as

$Y-C=I+C-M \\ or\\S=I+C-M(S=Y-C)\\S+M=I+X$

S denotes savings

At equilibrium level of income $S+M=I+X$

In open economy

$I=S\\ I_d+I_f=S....(1)$

I_d denotes domestic investment while I_f denotes foreign investment.

$I_f=X-M....(2)$

Substitute (2) into( 1)

$I_d+X-M-S \\ or\\ I_d+X=S+M$

Which is the equilibrium condition of national income in open economy.

The foreign trade investment multiplier coefficient (K_f)is equal to:

$K_f=\frac{∆Y}{∆X}\\ and\\∆X=∆S+∆M$

Divide both sides by ∆Y

$\frac{∆X}{∆Y}=\frac{∆S+∆M}{∆Y}$

$\frac{∆Y}{∆X}=\frac{∆Y}{∆S+∆M}$

$K_f=\frac{∆Y}{∆S+∆M}$

$K_f=\frac{1}{\frac{∆S}{∆Y}+\frac{∆M}{∆S}}$

$K_f=\frac{1}{MPS+MPM}$