We may now present the four-sector model of national income determination by taking into account foreign trade, i.e., exports and imports. Now the^{ }economy has four sectors, viz., the households sector, the business sector, the government sector and the foreign trade (or the rest of the world) sector.

We include the foreign trade in our analysis because exports like I and G, are injections into the circular flow of income and increase Y. By contrast, imports, like S and T, are leakages from the circular flow and reduce Y.

Exports represent that portion of a country’s GDP which is not domestically absorbed by the households, firms and governments. When a country sports a portion of its output foreigners buy such output and spend money on it. So the exporting country earns foreign exchange.

By comparison if a country needs more of certain things (such as crude oil, machinery, or fertilisers) that it cannot produce in adequate amount, then it has to meet this extra demand through imports. The importing country spends money on foreign goods and foreigners’ income goes up (since money goes out of the home country).

In short, national income increases when a country exports certain goods and services and national income falls when it imports certain things. The difference between exports (X) and imports (M) is called net exports (X – M).

So whether a country’s national income will increase or fall due to exports and imports depends on its net exports (or balance of trade). If net exports (NX = X – M) are positive, then aggregate demand (expenditure) of a country will increase. But if net exports are negative, then its aggregate demand expenditure will fall.

**In reality, when a country is able to achieve faster economic growth, its exports rise, provided the following two conditions are satisfied: **

(i) The country is able to generate export surplus (after meeting its consumption needs).

(ii) There is sufficient demand for the products of the country in the world market.

This depends on various factors. But the supply of quality products and maintaining delivery schedules are most important. Thus if external demand conditions are favourable, exports of a country are likely to rise with economic growth and increase in national income. By comparison, imports normally increase with income.

A developing country like India not only imports consumer goods like food but capital goods such as machinery. How much a country will import with an increase in its national income depends on the prospensity (tendency) to import.

However, in the Keynesian model of national income determination, exports and imports are treated as exogenous, i.e., determined by forces outside the model. In other words exports and imports are treated as autonomous, i.e., independent of national income.

**TDE and TFE: **

#### As we know**,** that total domestic expenditure (TDE) has three components, viz., C and I and C Now, in an open economy, we have to introduce a new concept called total final expenditure (TFE) or demand which includes net exports also.

**So we can now write the equation of the equilibrium level of national income as follows: **

Y = C + I + G + (X – M) … (1)

**Since C = a + b (Y – T), we get: **

Y = a + bY – bT + I + G + NX

or Y (1 – b) = a – bT + I + G + NX

or Y = 1/1 – b (a – bT + l + G + NX) … (2)

This means that the equilibrium value of Y is calculated by multiplying the autonomous expenditure multiplier (1/1 – b) by the sum of all fixed autonomous expenditures shown on the right hand side of (2) inside the bracket. In the four sector-economy, aggregate saving (S = Y – C) has to be equal to the sum of private investment, government expenditure and net exports (i.e., S = I + G + NX).

The determination of the equilibrium level of national income is illustrated in Fig. 6A.8.

**Here we proceed in the following five steps: **

1. First we draw the 45° income line F and take this as the guideline.

2. Then we draw the consumption line C.

3. Next we add the fixed (autonomous investment) I to C to derive the combined C + I schedule.

4. Next we add the fixed G to C + I to arrive at the C + I + G schedule.

**5. Finally we add the fixed NX to C + I + G to derive the aggregate demand curve: **

AD = C + I + G + NX.

The AD curve shows total final expenditure in an open economy. It intersects the income line F (or the aggregate supply curve) at point E. We drop a perpendicular from point £ to find out the equilibrium value of F which is 0Y_{E}. And since F = AD, 0Y_{E} = EY_{E}. At the equilibrium level of income Y – C = S = I + G +NX =EF as shown in the diagram.

Here we assume that NX are positive. This is why the AD curve lies above the C + I + G curve But if NX were negative, the AD curve would lie below the C + I + G curve, as is indicated by point E’ and national income would be Y’_{E} which is less than Y_{E}.

**Table 6A.1 illustrates how national income is determined in a four-sector model. **

Here we assume that national income is initially 100. We also assume that MPC = 0 80. So consumption is 80, S is 20. Here I + G + NX = 35 at all levels of Y. Now since AD > AS and I + G + NX > S, Y has to increase. Since AD = 115, there is an unintended fall in inventories of 15.

This means that sales plans of firms are fulfilled, but production plans are not. As soon as the inventories are exhausted, output increases and national income increases to 150. Now AD = 155. So there is an unintended fall in inventories of 5, and, as a result, output increases once again and national income rises to 175.

Now AS = AD, and change in stock is zero. So this is indeed the equilibrium value of Y. Now both the production and sales plans are fulfilled, and therefore no change in output is warranted. Thus three conditions are to be satisfied to ensure national income equilibrium.

1. Y = C + I + G +NX (assuming NX > 0)

2. S = I + G + NX (the only leakage = the sum of three injections, assuming away taxes)

3. No undesired change (accumulation or exhaustion) in stocks.

However, if producers overreact to the excess demand pressure and the consequent exhaustion of stocks and produce an output of 200, they will be left with an-unsold stock of 5 (since aggregate demand of 195 will now be less than aggregate supply of 200).

In such a situation a cutback on production is inevitable. As production falls, national income will fall. The process will continue until and unless Y returns to 200’at which all the above three conditions of national income equilibrium are satisfied.

**Induced Imports and Income Determination****: **

Now we modify our analysis slightly and assume that only exports are autonomous, i.e., independent of national income. So take exports as fixed (X = X). But imports have both autonomous and induced components so the import function now becomes:

M =M + mY

where M denotes autonomous imports and mY stands for induced imports which depends on two factors—(i) the marginal propensity to import (m) and (ii) the level of national income (F). Here m is the ratio of the increase in imports to the income in national income (Y) (which brings it about) and is expressed as AM/AY.

Note that an increase (decrease) in Y leads to an increase (decrease) in imports and not vice-versa. Since m is assumed to remain constant, whether Y is high or low, as Y increases, mY will increase, depending on the fixed value of m.

**The Equilibrium Condition of**** Y: **

**Now the equilibrium condition of Y is written as: **

Y = C + I + G + (X – M) … (1)

where C = a + b (Y – T) and

M = M+ mY.

**By substituting the consumption function and import function in equation (1), we get: **

Y = a + b(Y – T) + I + G + [X – (M + mY)]

or, Y = a + bY – bT + l + G + X – M – mY.

or, Y – bY + mY = a – bT + I + G + x – M

or, Y(1 – b + m) = a – bT + l + G + X – M

Y = 1/1 – b + m (a – bT + I + G + X – M)

where the first term on the r.h.s of this equation 1/1 – b + m = 1/s + m is called the foreign trade multiplier or open economy multiplier. Since the value of this multiplier depends on both MPC and MPI, the open economy multiplier is less than the closed economy multiplier. Suppose b = 2/3. So the closed economy multiplier will be 3. Now suppose 10% of Y leaks out in the form of imports. This implies that m = 1/10. So the value of the open economy multiplier will be = 1/1/3 + 1/10 = 2.3.

It may be noted that a change in any of the components of autonomous spending such as C, I, G, X, or M will lead- to a multiple increase in Y through the foreign trade (open economy) multiplier

1/1 – b + m = 2.3 in our above example. Thus if exports increase by AX (= Rs. 20 cr.) national income will increase by ΔY = 1/1 – b + m (ΔX) = 2.3 (Rs. 20 cr.) = Rs. 46 cr.

**Effect of Proportional Income Tax****: **

We may now extend the four-sector model further by incorporating the effect of proportional income tax. A proportional tax will change the value of the foreign trade multiplier by affecting MPC. Suppose the tax function is T = T + tY, where T is a constant lumpsum tax and t is proportional tax rate (which is a fixed percentage of national income).

**Now the foreign trade multiplier becomes: **

Now if exports increase by ΔX, national income will increase of ΔY through the foreign trade or open economy multiplier.

**Example:**

**Problem 1:**

**Suppose an economy is described by the following equations:**

(a) Find out the equilibrium value of income

(b) Calculate net exports.

(c) What is the value of the open economy multiplier?

**Solution:**

So an increase in exports by Rs. 10 crores will lead to an increase in Y by Rs. 20 crores.

**Problem 2: **

**Suppose an economy is described by the following structural equations: **

C= 10 + b(Y – 40 – tY)

I = 50

X = 20

M = 5 + 0.1Y.

Here we assume that (a) MPC = 0.75, (b) the budget of the government is in balance, (c) the proportional tax rate t = 0.20.

**Now answer the following questions: **

(a) Find out the equilibrium level of national income.

(b) What is the value of the foreign trade multiplier?

(c) What is the value of imports at equilibrium income?

(d) If equilibrium national income is less than the full-employment level of income by Rs. 100 crores, what should be the increase in government spending or in exports to attain the full-employment level of income?

(e) What will be the required increase in exports to attain the same target?

**Solution: **

The reduced form equation of the equilibrium level of income is

**Since the budget of the government is in balance we have G = T = 40. Now putting the values of the parameters and variables we have: **

(c) The equilibrium value of imports can be found out by putting the equilibrium value of national income 170 in the import function.

**Thus: **

M = 5 + 0.1 × 170

= 22.

**(d) The required increase in government expenditure to attain Rs 100 increase in income can be found out by multiplying the government expenditure multiplier by the increase in government expenditure: **

ΔY = m_{G }× ΔG

or, 100 = 2 × ΔG

or, ΔG = 100/2 = 50.

**(e) Now since the value of the foreign trade multiplier is 2, the required increase in exports to achieve the same target will be: **

So exports are to be increased by the same amount as government expenditure. This is an interesting coincidence.