Keynes explained the process of income determination in a closed economy and used the theory of multiplier to explain how a small increase in autonomous investment leads to a multiple increase in national income. Now we extend the basic Keynesian model to show how national income is determined in open economy and how the multiplier process works in this extended framework, with exports and imports.

In fact, exports, being autonomous in nature, also have a multiplier effect on national income. We will see that the value of open economy multiplier, called foreign trade (export) multiplier, depends not only on the marginal propensity to save (MPS) but also on the marginal propensity to import (MPI). We start with the import function.

**The Import Function:**

**In an open economy a part of income is spent on imported goods and services. The import function shows the relation of import and the level of national income and is expressed as: **

M = *f*(Y)

where M stands for import and Y for national income. Thus import depends on national income. The import function is represented graphically in Fig. 39.1. We show national income on the horizontal axis and import on the vertical axis.

The import function is M = i + mY, where i is autonomous import having no relation to Y and mY is induced import, which is related to Y. A country can import capital goods or essential items of consumption from its accumulated foreign exchange reserves or by borrowing from foreign countries or even from the IMF or the World Bank.

Here m is the MPI = ∆M/∆Y or the ratio of the change in import to the change in national income which brings it about and the slope of the import function measures this. Suppose i = 50, m = 0.10 and Y = Rs. 5,000. So M will be Rs. 50 + Rs. 500 = Rs. 550.

**The Foreign Trade (Open Economy) Multiplier****:**

In an open economy imports, like savings and taxes, act as a leakage from the circular flow of the income. The reason is that, that part of Y (Rs. 550 in our above example) which is spent on import goes out of the country and does not come back to the circular flow of income.

By comparison, exports, like private investment and government spending (net of transfer) act as injection into the circular flow. This means that exports refer to the expenditure made by foreigners on goods and services produced in the domestic economy (home country).

**Thus national income reaches equilibrium in an open economy when the sum of leakages is equal to the sum of injections: **

S + T + M = I + G + X … (1)

For simplicity we ignore T and G, assuming that the budget of the government is in balance and does not affect the equilibrium value of Y.

**So equation (1) can be rewritten as:**

S + M = I + X … (2)

This does not mean that if S = I, M will automatically be equal to X. The truth is the sum of S + M has to be equal to the sum of I and X. In other words S-l equilibrium does not imply trade balance.

Now if there is a change in any of the four variables, there will be a change in the other three variables as well so that the two sides of the equation (2) are equal once again.

**So we can write: **

∆S + ∆M = ∆I + ∆X …(3)

Here AS = change of saving and can be expressed as s.∆Y, where s is MPS. In the same way AM = m.AY, where m is the MPI.

**So equation (3) can be rewritten as: **

s.∆Y + m.∆Y = ∆I + ∆X

or, ∆Y(s + m) = ∆I + ∆X

or, ∆Y = 1/(s + m) (∆I + ∆X)

= 1/(s + m) (∆A) … (4)

where ∆A = ∆I + ∆X

If ∆I = 0, then

∆A = ∆X and

if ∆X = 0, then

∆A = ∆I

Equation (4) shows that change in either import or export will lead to an increase in ∆Y. But by how much? By a multiple of ∆I, or ∆X. Thus, in an open economy, if investment increases by ∆I, Y will increase 1/(s + m) (∆A = ∆I). Similarly, if exports increase by ∆X, Y will increase by 1/(s + m) (∆A = ∆X). Here 1/(s + m) is the open economy multiplier (m_{0}).

**It may be expressed as: **

m_{0} = 1/(s + m)

The open economy multiplier is the reciprocal of MPS (s) plus MPI (m). Since import is the leakage from the circular flow of income, the open economy multiplier is less than the closed economy multiplier.

If s = 0.3 and of = 0.1 then,

m_{0} = 1/0.3 + 0.1 = 1/0.4 = 2.5.

If m = 0, then we get the closed economy multiplier which is 3.3.

Now if s = 0.4 and m = 0.1, then

m_{0} = 1/0.4 + 0.1 = 1/0.5 = 2.

The closed economy multiplier is 2.5 in this case.

Thus we see that multiplier for an open economy is less than that of a closed economy since import is a leakage from the circular flow of income.

**Graphical Representation of Open Economy Multiplier without Investment:**

The open economy multiplier is graphically represented in Fig. 39.2. Here we measure national income on the horizontal axis and saving, export and import on the vertical axis. Here we ignore G and I. The initial level of national income is Y_{1}. This is determined by the interaction of upward sloping saving-cum-import schedule S + M, with the initial export schedule X_{1} at point E.

Now there is an increase in autonomous export by ∆X. As a result the export schedule shift upward to X_{2} and X_{2} = X_{1} + ∆X. The new (higher) export schedule intersects the saving- plus-import schedule at point F. As a result national income increases from Y_{1} to Y_{2}. This is greater than (or a multiple) of the initial increase in export due to the operation of the foreign trade multiplier (m_{0}).

Here m0 = ∆Y/∆X = EE’/FE’, since ∆Y = m_{0} (∆X). The value of multiplier is the reciprocal of the slope of the combined S + M schedule since m_{0} = 1/s + m where s = ∆S/∆Y and m = ∆M/∆Y.

**The Working of the Open Economy Multiplier:**

The open economy multiplier works exactly in the same way as does the Keynesian investment multiplier. Suppose due to the change in taste and preference of foreigners for Indian goods (due to improved quality or lower prices), India’s export increases. Initially this additional export may be made from inventories. This will lead to an initial increase in income of India’s exporters.

But it there is further increase in foreign demand for Indian goods, there is a need to increase the production of exported goods. As a result more workers will be employed in export-oriented industries. These people will earn income. They will spend a portion of their income on other home produced goods and a portion on imported goods.

The portion of income which is spent on import will leak out of the circular flow. But the portion which is spent on domestic goods will have an income-creating effect. So production of such goods will increase. Consequently income and employment will also increase in such industries. This is how increases in income will spread throughout the economy following an initial increase in export.

After all, export like investment, is a component of total autonomous expenditure and any increase in autonomous spending has a multiplier effect. In short, the increased expenditure on domestic goods of owing an initial increase in export will go on generating extra income at various rounds through a chain of secondary consumption spending and responding.

**The Open Economy Multiplier with Investment:**

**A. National Income Equilibrium with Trade Balance:**

If we now consider investment along with export as two items of autonomous expenditure, the equilibrium condition of national income is:

S + M = I + X

or, I + X – M = S

or, I + X = S + M

Here the sum of I and X (the two injections) have to be equal to the sum of S and M (the two leakages). The equilibrium condition is shown graphically in Fig. 39.3. The closed economy equilibrium is at point E. We now add import to saving to arrive at the combined S + M schedule.

The difference between S and S + M schedules increases with increase in Y since M increases when Y increases Similarly we add export to investment to arrive at the combined I + X schedule. Here I and I + X schedule are parallel since both I and X are autonomous and thus remain fixed at all levels of Y.

The open economy equilibrium is at point F where S + M = I + X. In this case, since I = S at point E’. X = M. But this is just a coincidence. It is not necessary that at the equilibrium level of national income (Y_{E}), export (X) equals import (M) or that there is a balance in trade account.

**This point is illustrated in Fig. 39.4: **

**B. National Income Equilibrium with Trade Surplus:**

The closed economy equilibrium is at E where S = I, i.e., domestic saving equals domestic investment. The open economy equilibrium is initially at point F, where S + M = I + X, and national income attains its equilibrium value Y* _{f}* . Now suppose export increases from X

_{1}to X

_{2}. As a result the combined I + X schedule shifts upward from I + X

_{1}to I + X

_{2}and intersects the S + M schedule at point H.

So national income increases from Y_{E} to Y_{F}. Now at this level of income S > I by the distance GJ. Here import is HG and is less than export which is HJ. So the excess of saving over investment (GJ) measures export surplus. Thus we see that the equilibrium level of national income can be reached even if export is greater than import.

So it is not necessary to have a balance in the trade account in order to attain the equilibrium level of national income. Now the export surplus can be used to lend funds to foreigners or to invest in foreign countries. This point may be explained further. We know that:

S + M = I + X

or, S – I = X – M

Thus we see that if S > I, X has to be greater than M. In other words, the excess of saving over investment has to be matched by an excess of export over import. Thus to achieve the equilibrium level of Y, it is enough to ensure that S + M = I + X. A simple example will make this point clear. Suppose S = 120, M = 160, X = 180 and I = 100. Then S – I = 20 and X – M = 20.

Thus any surplus in the trade account is to be offset by a deficit in the capital account so as to ensure that the balance of payments always balances.

**C. National Income Equilibrium with Trade Deficit:**

In Fig. 39.5 we show an exactly opposite type of situation. The closed economy equilibrium is at point E, where S-1. The initial open economy equilibrium is at point F, where S + M = I + X) and the national income attains its equilibrium value Y_{e}. Now suppose there is a fall in autonomous export from X_{1} to X_{0} (Here X_{0} = X_{1} – ∆X). As a result the I + X schedule shifts downward to I + X_{0} and intersects the S + M schedule at point G.

So equilibrium national income falls to Y_{D}. At this level of income, domestic investment exceeds domestic saving by HJ and import (GJ) exceeds export (GH). Thus the excess of domestic investment over domestic saving (HJ) is balanced by excess of import over export.

In this case since the country suffers from trade deficit, it has to borrow funds from abroad or to encourage foreigners to invest in the home country so as to be able to cover the excess of I over S. Thus any deficit in trade account has to be matched by a surplus in the capital account so as to ensure that the balance of payments always balances, at least in the accounting sense (if not in the economic sense).

**An Increase in Imports and the Reverse Multiplier Process:**

Since import is a leakage from the multiplier process an increase in import will lead to a multiple contraction of income. In Fig. 39.6 we show the working of the process in absence of saving and investment. In this case national income attains its initial equilibrium value Y_{E} at point E where the import schedule M_{1} intersects the export schedule.

Now suppose due to a change in taste and preference of domestic consumers for foreign goods there is an increase in import and the import schedule shifts upward from M_{0} to M_{1}. In this case import increases by ∆M (= EF) even at the same level of income (Y_{E}) . Now the new higher import schedule (which is parallel to M_{1}) intersects the export schedule at point G. As a result national income falls from Y_{E} to Y_{D}.

This happens because a rise in import leads to a fall in expenditure of consumers on domestic goods. Thus domestic expenditure is not reduced but is switched from home-made goods to foreign-made goods. The fall in expenditure leads to a fall in production, employment and income in several domestic industries. In facts there is multiple contraction of income due to a fall in expenditure on domestic goods in several rounds, following an initial decline in the demand for home-produced goods.

**Import Paradox:**

Now we see that an increased desire to import leads to a fall in actual imports. The initial desire to import Y_{e}F amount of goods leads to a fall in national income. As a result actual import (Y_{D}G) is less than desired import (Y_{E}F). This is known as the import paradox, which is comparable to the paradox of thrift.

**Final Comment: the Value of the Keynesian Multiplier:**

We have noted that the value of the Keynesian investment multiplier is greater than 1. However, R.G. Lipsey has pointed out that if each component of autonomous spending, i.e., C, I, G, and X has an import content, then the value of the autonomous expenditure multiplier may even be less than one. This means that the multiplier effect is not only lost but is reversed as well. In this case rise in any component of autonomous spending will lead to a multiplier fall in national income.