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The foreign trade multiplier, also known as the export multiplier, operates like the investment multiplier of Keynes. It may be defined as the amount by which the national income of a country will be raised by a unit increase in domestic investment on exports. As exports increase, there is an increase in the income of all persons associated with export industries. These, in turn, create demand for goods. But this is dependent upon their marginal propensity to save (MPS) and the marginal propensity to import (MPM). The smaller these two marginal propensities are, the larger will be the value of the multiplier, and vice versa .

#### It’s working

The foreign trade multiplier process can be explained like this. Suppose the exports of the country increase. To begin with, the exporters will sell their products to foreign countries and receive more income. In order to meet the foreign demand, they will engage more factors of production to produce more.

This will raise the income of the owners of factors of production. This process will continue and the national income increases by the value of the multiplier. The value of the multiplier depends on the value of MPS and MPM, there being an inverse relation between the two propensities and the export multiplier.

#### The foreign trade multiplier can be derived algebraically as follows

The national income identity in an open economy is

Y = C + I + X – M

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

The above relationship can be solved as:
Y-C = 1 + X-M

Or, S = I+X-M (S=Y-C)

S + M = I + X

∆I=∆X = ∆S + ∆M

The induced changes in saving and imports when income
changes are given by

∆S = (MPS) (∆Y)

∆M = (MPM) (∆Y)

Substituting these for _S and _M in Equation

For example, starting from equilibrium point E in Figure, if exports rise Autonomously by 200 from X = 300 to X_ = 500,

Therefore, at

CHANGE IN INJECTION = CHANGE IN LEAKAGES

∆l + ∆X = ∆S + ∆M

0+200 = 125 + 75

200 = 200

At the new equilibrium level of national income of,

YE = 1500, exports exceed imports by 125 per period. That is, the automatic change in income induces imports to rise by less than the autonomous increase in exports, so that the adjustment in the balance of payments is incomplete. The foreign trade multiplier k = 2.5 found above is smaller than the corresponding closed economy multiplier,

k = 4 found in Section because in an open economy, domestic income leaks into both saving and imports. This is a fundamental result of open-economy macroeconomics.the unchanged in the top panel of Figure , the new higher (broken-line) I + X function crosses S (Y) + M (Y) function at point E . At YE = 1500, X = 500(EL) and M = 375(EK) so that XM = 125(KL). The same outcome is shown in the bottom panel of Figure 17.3 by point E, where the new and higher (broken-line) XM (Y) function crosses the unchanged S (Y) I function at YE = 1500 and defines the trade surplus of XM = 125.

Note that the smaller MPS + MPM is, the flatter is the S (Y) + M (Y) function in the top panel of Figure 17.3, and the larger would be the foreign trade multiplier and the increase in income for a given autonomous increase in investment and exports. Also to be noted is that Y rises as a result of the autonomous increase in X, and I remains unchanged (i.e.,  I = 0).