Answer to Question #268355 in Macroeconomics for Kyla

Question

Prove that the open economy multiplier is the reciprocal of the sum of marginal propensity to save (MPS) and marginal propensity to import (MPM).

Answer 1

In an open economy, there is a multiplier effect because of the flow of money supply in the economy.

Let's prove it with a mathematical equation.

Here, MPS = marginal propensity to save is the ratio of change in save to the change in income.

MPC = marginal propensity to consume is the ratio of change in consumption to the change in income.

MPM = marginal propensity to import is the ratio of change in import to the change in income.

As we know, multiplier, $k = \frac{1}{ 1−MPC}$

As, $MPC + MPS = 1$

Thus $K=\frac{1}{MPS}$

In an open economy,

Multiplier$,k =\frac{ 1}{ 1−(MPC−MPM)}$

because total consumption is the same as consumption less imports because the only consumption is the one which adds to the money flow not the imports as money against imports goes out of the country.

Thus, the actual multiplier as per open economy will be:-

$k = \frac{1}{ 1−MPC +MPM}\\ =\frac{1}{ MPS + MPM}$

Thus, from the calculation, it is very clear that multiplier is inversely related to the sum of the marginal propensity to save and marginal propensity to import.