After studying this topic, you should be able to understand
The earlier chapters have focused on income determination in two and three sector models. Thus, the economy that was analysed was a closed economy which is in isolation from the rest of the world. This chapter presents a more realistic picture in that it focuses on a four sector model, or in other words an open economy, which is engaged in trade with the rest of the world. Thus, the aggregate demand will be now determined by the spending of four sectors, namely, households, firms, government and the foreign sector. The foreign sector will include the foreign consumers, the foreign business and the foreign governments.
The chapter also discusses the foreign trade multiplier.
The inclusion of the foreign sector in our analysis influences the level of aggregate demand through the export and import of goods and services. Hence, it is necessary to understand the factors that influence the exports and imports.
Open economy is an economy which is engaged in trade with the rest of the world.
The volume of exports in any economy depends on the following factors:
To simplify our analysis we assume that the exports in any economy are determined by external factors, or in other words forces which are external to the domestic economy. Thus, the level of exports is assumed to be an autonomous variable.
As far as imports are concerned, the volume of imports in any economy depends on the following factors:
The marginal propensity to import is the fraction of any change in income that will be devoted to imports.
To simplify our analysis, we assume that the imports in any economy are determined by the income level in the domestic economy. This brings us to the import function, which in its simplest form can be expressed as a linear function.
M = Ma + mY
Figure 8.1 depicts the import function as an upward sloping line and the exports function as a line parallel to the x-axis (as they are assumed to be determined autonomously).
where, | x-axis = | income or output |
y-axis = | level of exports and imports | |
M = | imports | |
Ma = | autonomous imports (imports at a theoretically zero level of income) | |
m = | ΔM/ΔY = marginal propensity to import (fraction of any change in income that will be devoted to imports) | |
Y = | income level |
In Figure 8.1,
It is important to note that:
Figure 8.1 The Import and Export Functions
Exports, imports and aggregate demand: While exports must be added to the total final expenditures to arrive at the aggregate demand, all the spending on imports do not contribute to the domestic demand, and thus must be deducted from the total final expenditures to arrive at the aggregate demand.
Aggregate demand = Total value of output (or income)
or
where | C = Ca + b Yd = consumption function |
Yd = Y – T = disposable income | |
T = = tax (lump sum income tax) | |
I = I = investment (assumed to be autonomous) | |
G = goverment expenditure (assumed to be autonomous) | |
X = = exports (assumed to be autonomous) | |
M = Ma + mY =imports function |
Substituting for these values in the basic Eq. (1), we get
Y = Ca + bYd + + + – (Ma + mY)
Y = Ca + b(Y – T) + + + – Ma – mY
or
Y – bY + mY = Ca + + + – b – Ma
or
Y (1 – b + m) = Ca + + + – b – Ma
Thus,
AD = AS
or
C + I + G + X = C + S + T + M
(In a four sector model, the injections include investment, government expenditures and exports whereas the leakages include saving, taxes and imports.)
As C is common in both the sides, the equilibrium condition can be written as
where, | I = = investment (assumed to be autonomous) |
G = = government expenditure (assumed to be autonomous) | |
X = = exports (assumed to be autonomous) | |
S = Yd – C = saving function | |
C = Ca + b Yd (consumption function) | |
T = = tax (lump sum income tax) | |
M = Ma + mY (imports function) |
Substituting for these values in the Eq. (3), we get
+ + = S + + Ma + mY
+ + = (Yd – C) + + Ma + mY
+ + = {Y – – [Ca + b Yd} + + Ma + mY
+ + = {Y – – Ca – b(Y – )} + + Ma + mY
Y – bY + mY = Ca + + + – b + Ma
Y (1 – b + m) = Ca + + + – b – Ma
Thus,
(Ca + + + – b – Ma)
The above equation is the same as Eq. (2) above. Hence, both the approaches yield the same equilibrium level of income.
Till now, we have not included transfer payments in our analysis. As already mentioned transfer payments increase the spending capacity of the households, leading to an increase in the equilibrium level of income.
We have our basic Eq. (1)
Y = C + I + G + X – M | |
where, | C = Ca + bYd = consumption function |
Yd = Y – T + R = disposable income | |
T = = tax (lump sum income tax) | |
I = = investment (assumed to be autonomous) | |
G = = government expenditure (assumed to be autonomous) | |
X = = exports | |
M = Ma + mY = imports | |
R = = transfer payments (assumed to be autonomous) |
Substituting for these values in the basic equation, we get
Y = Ca + b (Y – + ) + + + – Ma – mY
or
Y – bY + mY = Ca + + + – b + bR + Ma
or
Y (1– b + m) = Ca + + + – b + bR + Ma
Thus,
Equilibrium: The determination of the equilibrium income by the aggregate demand–aggregate supply approach in a four sector economy has been depicted in the Figure 8. 2(a).
Figure 8.2 Determination of Equilibrium Income or Output in a Four Sector Economy
At point E, curves AD1 and AD2 intersect to determine the equilibrium income at Y. At this level of income, exports equal imports or X = M.
To the left of point E, curve AD2 is above AD1 indicating that exports exceed imports or X > M.
To the right of point E, curve AD2 is below AD1 indicating that imports exceed exports or X < M.
Equilibrium: The determination of the equilibrium income by the leakages and injections approach in a four sector economy has been depicted in the Figure 8.2(b).
The leakages now include saving, taxation and imports whereas the injections are investment, government expenditure and imports.
where, | x-axis | = disposable income |
y-axis | = planned saving, planned investment, taxes and government expenditure, exports and imports | |
S | = planned saving | |
I | = = investment function | |
X | = = exports | |
M | = imports function | |
S + + M | = planned saving plus taxes plus imports | |
+ + | = planned investment plus government expenditure plus exports | |
Point E1 | = the three sector equilibrium where the planned saving and taxes curve, S + and investment plus government expenditure curve, + intersect to determine the equilibrium income at Y1 | |
Point E2 | = the four sector equilibrium where the planned saving, taxes and imports curve, S + + M and investment plus government expenditure plus exports curve, + + intersect to determine the equilibrium income at Y2 |
We find that in a four sector economy the two approaches to the determination of the equilibrium income, the aggregate demand-aggregate supply approach and the leakages equal injections approach, both yield the same result.
The introduction of foreign trade has the affect of reducing the equilibrium level of income from Y1 to Y2.
To have an understanding of the multiplier in the foreign sector, we assume that due to an increase in the income level in the other countries there occurs an increase in the exports of the domestic country. To meet this increased demand for exports, there is an increase in the domestic production which leads to an increase in the income and hence in the consumption expenditure (depending on the marginal propensity to consume). A part of this increase in the consumption expenditure will be directed towards imports, depending on the marginal propensity to import. This will further lead to a second stage of expansion; though due to the leakage from the economy in the form of imports, there will occur only a restricted increase in the income. Further increases in the income will become smaller and smaller. The size of the multiplier will be lower when the marginal propensity to import is positive.
In a four sector economy, the equilibrium level of income is
Assume that there is an increase in exports by ΔX. Hence,
Subtracting Eq. (2) from Eq. (5), we get
where, | ΔX = | change in exports |
b = | marginal propensity to consume | |
ΔY = | change in income | |
= foreign trade multiplier |
The value of the multiplier in an open economy is less than that in a closed economy. This is because in the open economy, there is an additional leakage in the form of imports. Thus as long as the marginal propensity to import is positive, the size of the multiplier gets reduced. A zero marginal propensity to import implies a multiplier, which is the same as the ordinary multiplier, 1/1 – b.
Another way of analysing the effect of the marginal propensity to import on the multiplier is by expressing the multiplier as 1/1 –(b – m).
Here, we can write
b = | marginal propensity to purchase both domestically and foreign produced goods |
m = | marginal propensity to purchase foreign produced goods |
b – m = | marginal propensity to purchase domestically produced goods |
It is to be observed that
With
What is the difference between the two equations? Comment.
Numerical Problem 1
The fundamental equations in an economy are given as:
Consumption function C = | 100 + 0.80 Y |
Investment function = | 150 |
Tax T = | 60 |
Government expenditure G = | 100 |
Exports X = | 50 |
Imports M = | 0.05 Y. |
Find the following:
Numerical Problem 2
For the credentials of the Numerical Problem 1, find
Numerical Problem 3
In an economy, the following information is given:
Find the equilibrium level of the national income.
Numerical Problem 4
Suppose the basic functions in an economy are as follows:
C = 130 + 0.80Yd | |
= 160 | |
T = 150 | |
G = 150 | |
X = 150 – 0.05Y |
Numerical Problem 5
The equations in an economy are given as:
Consumption function C = 200 + bYd
Investment function = 70
Tax T = 60
Government expenditure G = 70
Exports X = 20
Imports M = 10 + 0.1 Y
Marginal propensity to consume, b = 0.8.
Find
Consumption function C = | 50 + 0.50 Yd |
Investment function = | 350 |
Tax T = | 60 |
Government expenditure G = | 200 |
Exports X = | 90 |
Imports M = | 0.05Y |
Find
Consumption function C = | 100 + 0.60 Yd |
Investment function = | 400 |
Tax T = | 200 |
Government expenditure G = | 300 |
Exports X = | 300 |
Imports M = | 200. |
Find
Find the equilibrium level of the national income.
C = 50 + 0.60 Yd
= 60
T = 30
G = 28
X = 20 + 0.05Y
Consumption function C = | 50 + bYd |
Investment function = | 40 |
Tax T = | 20 |
Government expenditure G = | 40 |
Exports X = | 20 |
Imports M = | 20 + 0.1 Y |
Marginal propensity to consume, b | = 0.75. |
Find the following:
Solution 1
C = 100 + 0.8Yd
C = 100 + 0.8 (Y – T)
C = 100 + 0.8 (Y – 60)
The equilibrium condition is given as Y = C + I + G + X – M
Thus,
Y = 100 + 0.8 (Y – 60) + 150 + 100 + (50 – 0.05Y)
Y = 100 + 0.8 Y – 48 + 300 – 0.05Y
Y – 0.8Y + 0.05Y = 352
0.25Y = 352
Y = 1408
The equilibrium level of income is 1408.
Checking the answer
In equilibrium in a four sector model, leakages equal injections or C + I + G + X = C + S + T + M.
The consumption function is
C = 100 + 0.8 Yd
C = 100 + 0.8 (1408 – 60)
C = 100 + 0.8 (1348)
C = 1178.4
The saving function is
S = Yd – C
S = (Y – 60) – 1178.4
S = (1408 – 60) – 1178.4 = 169.6
S = 169.6
Thus,
I + G + X = S + T + M
150 + 100 + 50 = 169.6 + 60 + 0.05Y
300 = 229.6 + 0.05 (1408)
300 = 300
Net Exports: X – M = 50 – 70.4 = – 20.4
X – M = – 20.4
There is a deficit in the balance of trade.
Solution 2
The equilibrium condition is given as Y = C + I + G + X – M
Thus,
Y = 100 + 0.8 (Y – 70) + 150 + 110 + (50 – 0.05Y)
Y = 100 + 0.8 Y – 56+ 310 – 0.05Y
Y – 0.8Y + 0.05Y = 354
0.25Y = 354
Y = 1416
The equilibrium level of income is 1416. Hence, there is an increase in the income level by 8.
The equilibrium condition is given as Y = C + I + G + X – M.
Thus,
Y = 100 + 0.8 (Y – 60) + 150 + 100 + (80 – 0.05Y)
Y = 100 + 0.8 Y – 48 + 330 – 0.05Y
Y – 0.8Y + 0.05Y = 382
0.25Y = 382
Y = 1528
The equilibrium level of income is 1528.
Imports M = 0.05 Y = 0.05 (1528) = 76.4
Net Exports: X – M = 80 – 76.4 = 3.6
X – M = 3.6
There is a surplus in the balance of trade.
Where, | ΔG =change in government expenditure |
b = marginal propensity to consume | |
ΔY = change in income | |
GM = government expenditure multiplier | |
m = marginal propensity to import |
In the present example,
b = 0.80
ΔY = 1600 – 1408 = 192
Thus,
ΔG = 192 (0.25) = 48
ΔG = 48
The level of government expenditures required to achieve the full employment output is 48.
Here, we have the consumptisubon function as
C = 50 + 0.5 Yd
C = 50 + 0.5 (Y – T)
C = 50 + 0.5 (Y – 120)
The equilibrium condition is given as Y = C + I + G + X – M
Thus,
Y = 50 + 0.5 (Y – 120) + 200 + 150 + (70 – 50)
Y = 50 + 0.5 Y – 60 + 350 + 20
Y – 0.5Y = 360
0.5Y = 360
Y = 720
The equilibrium level of income is 720.
Checking the answer
In equilibrium in a four sector model, leakages equal injections
or
C + I + G + X = C + S + T + M
The consumption function is C = 50 + 0.5 Yd
C = 50 + 0.5 (720 – 120)
C = 50 + 0.5 (600)
C = 350
The saving function is S = Yd – C
S = (Y – T) – C
S = (720 – 120) – 350 = 250
S = 250
Thus,
I + G + X = C + S + T + M
200 + 150 + 70 = 250 + 120 + 50
420 = 420
Solution 4
C = 130 + 0.8Yd
C = 130 + 0.8 (Y – T)
C = 130 + 0.8 (Y – 150)
The equilibrium condition is given as Y = C + I + G + X – M.
Thus,
Y = 130 + 0.8 (Y – 150) + 160 + 150 + (150 – 0.05Y)
Y = 130 + 0.8 Y – 120 + 460 – 0.05Y
Y – 0.8Y + 0.05Y = 470
0.25Y = 470
Y = 1880
The equilibrium level of income is 1880.
Net Exports: X – M = 150 – 0.05 (1880) – 0
X – M = 56
There is a surplus in the balance of trade.
Y = 130 + 0.8 Y – 120 + 470 – 0.05Y
Y – 0.8 Y + 0.05Y = 480
0.25Y = 480
Y = 1920
The equilibrium level of income is 1920 which is an increase by 40.
Imports M = 0
Net Exports: X – M = 150 – 0.05 (1920)– 0
X – M = 54
Y = 130 + 0.8 (Y – 150) + 160 + 150 + (140 – 0.05Y)
Y = 130 + 0.8 Y – 120 + 450 – 0.05Y
Y – 0.8Y + 0.05Y = 460
0.25Y = 460
Y = 1840
The equilibrium level of income is 1840, which is a decrease by 40.
Imports M = 0
Net Exports: X – M = 140 – 0.05 (1840)– 0
X – M = 48
There is a surplus in the balance of trade.
Solution 5
C = 200 + 0.8Yd
C = 200 + 0.8 (Y – T)
C = 200 + 0.8 (Y – 60)
The equilibrium condition is given as Y = C + I + G + X – M
Thus,
Y = 200 + 0.8 (Y – 60) + 70 + 70 + 20 – 10 – 0.1Y
Y = 200 + 0.8Y – 48 + 150 – 0.1Y
Y – 0.6Y – 0.1Y = 302
0.3Y = 302
Y = 1006.67
The equilibrium level of income is 1006.67.
M = 110.67
The equilibrium level of imports is 110.67.
The equilibrium level of income is 1200.
(b) X – M = 30
There is a surplus in the balance of trade.
The equilibrium level of income is 1400.
(b) Y = 1240
The equilibrium level of income is 1240.
X – M = 50
There is a surplus in the balance of trade.
(c) ΔG = 165
The level of government expenditures required to achieve the full employment output is 165.
The equilibrium level of income is 1950.
(b) X – M = 100
There is a surplus in the balance of trade.
The equilibrium level of income is 1950.
The equilibrium level of income is 400.
(b) X – M = 40
There is a surplus in the balance of trade.
(c) Y = 500
The equilibrium level of income is 500, which is an increase by 100.
X – M = 45
There is a surplus in the balance of trade.
(d) Y = 360
The equilibrium level of income is 360.
X – M = 24
There is a surplus in the balance of trade.
The equilibrium level of income is 328.57.
(b) Foreign trade multiplier = 2.86
(c) M = 52.86
The equilibrium level of imports is 52.86.