Determinants of the size of national income

There are number of factors that determine the level of national income of a given country. Some of these factors are explained as follows:

The stock of natural resources: Natural resources such as minerals, fertile land, water resources, and forest resources are relevant raw materials for the production of goods and services. The country that is rich in natural resources can achieve some level of production from the use of her natural resources. Consequently, the high level of production will increase aggregate output which further translates to the country’s national income. On the other hand, a country which is poor in natural resources will fail to increase production and, therefore, the size of national income will be low.

The size of skilled labour force:Labour force is an input used in the production process. A large stock of skilled labour force will be more efficient/productive in the course of producing goods and services. The raised productivity may lead to high national income. On the other hand, a small stock of unskilled labour is associated with small size of national income.

Size of capital stock: Capital goods help to increase productivity of other factors of production. A country with a large stock of capital is able to raise its production levels leading to high size of national income. On the other hand, the presence of insufficient stock of capital leads to a small size of national income.

Entrepreneurial skills: Experienced and skilled entrepreneurs lead to efficient organisation of other factors of production leading to greater productivity and, hence, raise the size of national income. On the other hand, a country with unexperienced and unskilled entrepreneurs will experience a small size of national income.

The level of technological advancement: High technological progress may lead to high output from the use of fixed resources. The same output can be obtained by the use of a small quantity of resources due to technological advancement. Low level of technology leads to small national income levels.

Determination of national income equilibrium

The equilibrium level of national income is determined by the interaction between aggregate supply (AS) and aggregate demand (AD). In a simplified model this level of national output and income settles at a point where it neither expand nor contracts as shown in Figure 2.2

Aggregate supply of goods and services in a country depends on the productive capacity of the economy. On the other hand, aggregate demand depends on the willingness and ability of the people and firm to spend on consumption of goods (C) and on investment of goods (I). Therefore, aggregate demand (AD) can be expressed as: AD = C + I …………………… .(2.14)

According to Keynes, the national income: Y = C + I = Aggregate Demand as shown in Figure 2.3.

But income has another side, which is spending side. From this point of view, income is spent on consumption and saving. Therefore, income is expressed as:

AS = C + S . . . . . . . . . . . . . . . . . . . . ..(2.15)

According to Keynes, the national income: Y = C + S = Aggregate Supply.

The equilibrium level of national income is determined by bringing together equations (2.14) and (2.15). Thus, the equilibrium level of national income is attained when total injections equal to leakages. In a closed economy in the absence of government sector, the autonomous investment is the only injection and saving is the only leakage. Thus;

Y = Aggregate Demand = C + I

Y = Aggregate Supply = C + S

Given that, Aggregate demand = Aggregate supply, then,

C + I = C + S

C - C + I = S

I = S = equilibrium level of income . . . . . . . . . . . . ..(2.16)

Saving = Investment

Therefore, equilibrium national income determination of leakages-injections approach can be termed as saving-investment approach. At equilibrium, the savings (leakages) must be equal to investment (injections).

In Figure 2.4, the national income is at equilibrium when saving (leakages) is equal to investment (injections) at point E. If savings (leakages) exceed investment (injections), then total expenditure will decline, and the result is to decrease output. On the other hand, if investments exceed savings, then total expenditure will increase, and the result is an increase in output. Only when investments and savings are equal at point E, output will remain the same at Y₁.

In Figure 2.5, the shift in aggregate expenditure curve (AE) leads to changes in equilibrium national income. For example, suppose aggregate demand increases from AE₀ to AE₁ as a result of increase in investment expenditure, equilibrium level of national income increase from Y₁ to

The changes in equilibrium national income can either be a result of an increase or shift in savings or investment curves. For example, a rise in investment expenditure will shift the investment demand curve upward from I₁ to I₂, the result is an increase in equilibrium level of national income from Y₁ to Y₂, as depicted in Figure 2.6.

Consumption function

A consumption function is the expression of relationship between consumption and disposable income. Consumption spending of the people is influenced by the following factors among others: the disposable income of the individual, past saving of the individual, and the rate of interest. The disposable income seems to be the strongest factor among all. Thus, the level of consumption depends on the level of income.

C = f(Y), function of income

The function f(Y) can take variety of forms but we can assume to take a linear form. As a result of this, the generalconsumption function in a linear form is usually expressed as:

C = a + bY . . . . . . . . . . . . . . . . . . ..(2.17)

Where: C represents the consumption level, “a” represents autonomous consumption, “b” represents marginal propensity to consume (MPC) which is the slope of the consumption function and “Y” is the disposable income.

However, there is a certain level of consumption known as autonomous consumption that does not depend on the level of income. It represents part of consumption spending from other sources than disposable income including past savings. It is also the vertical intercept of the consumption function.

Marginal propensity to consume (MPC)

Marginal propensity to consume is a parameter which shows the effect of an additional shilling of disposable income on consumption. Marginal propensity to consume is the proportion by which consumption spending changes resulting from a unit change in income. In other words, marginal propensity to consume is the ratio of change in consumption to change in income. For example, if your income increases by Tshs 40,000, 0.8 of this amount may be devoted for consumption and 0.2 for saving. This fraction of change in consumption over the change in income (which is 0.8 in the example) is what is referred to as the marginal propensity to consume. The MPCis computed using the formula in equation (2.18).

Marginal propensity to consume = Change in consumption
Change in income

MPC = ΔC/ΔY . . . . . . . . . . . . . . . . . . ..(2.18)

Where ΔC = change in consumption
ΔY = change in income

From the equation (2.17) of consumption function, C = a + bY

ΔC/ΔY = Δa/ΔY + bΔY/ΔY

ΔC/ΔY = 0 + b, where we make use of the fact that change in a constant number is equal to zero.

Therefore, MPC = ΔC/ΔY = b . . . . . . . . . . . . . . .(2.19)

Where 0 ≤ b ≤ 1

Average propensity to consume (APC)

Average propensity to consume refers to consumption per income. It shows the percentage of income that is spent on consumption. In other words, average propensity to consume is the ratio of consumption to income. The APC is computed using the formula in equation (2.20).

Average propensity to consume = Consumption/Income

APC = C/Y . . . . . . . . . . . . . . . . . . ..(2.20)

Determinants of the propensity to consume

Marginal propensity to consume is influenced by the following factors:

Income redistribution: Redistribution of income in favour of the poor tends to increase the propensity to consume. This is because the marginal propensity to consume of the low-income groups is high in comparison to that of the rich.

Increased wages: Increase in wage may affect MPC positively. If wages are increased, it will have a direct effect in shifting the consumption function upward.

Social security measures: Social security measures tend to increase the consumption function in the long run. The provision of unemployment relief, medical facilities, and old age pension, remove future uncertainty and the tendency to save is reduced, therefore, leading to an increase in consumption.

Credit facilities: Cheap and easy credit facilities help in shifting the consumption function upward. When loans are easily and cheaply available to the people, more durable consumer goods are purchased resulting to a rise in the propensity to consume.

Development of the means of transport and communication: Well-developed means of transport and communication tend to shift the consumption function upward. The movement of goods become easy, the size of the market expands and prices may fall due to the reduction of transport costs.

Saving function

Saving function expresses a relationship between the level of saving and disposable income. The level of saving depends on the level of disposable income. The saving function can be derived from aggregate supply as follows:

• Recall equation (2.15) which is, AS = Y = C + S

Where; Y is income level, C is consumption level and S is saving level. However, equation (2.17) represents the consumption function which is expressed as;

C = a + bY

Then, substitute equation (2.17) into equation (2.15) to have,

Y = a + bY + S
S = Y − a − bY
S = −a + (1 − b)Y . . . . . . . . . . . . . . . ..(2.21)

Therefore, equation (2.21) represents saving as a function of income.

Marginal propensity to save (MPS)

Marginal propensity to save is a fraction that shows an effect of additional shilling of disposable income on saving. In other words, marginal propensity to save is the ratio of a change in saving and a change in income.

Marginal propensity to save = Change in saving / Change in income

MPS = ΔS/ΔY . . . . . . . . . . . . . . . . . . ..(2.22)

From the saving function: S = −a + (1 − b)Y

Then, a change of S with respect to no change of Ycan be expressed as;

ΔS/ΔY = Δ(−a)/ΔY + (1 − b)ΔY/ΔY

MPS = ΔS/ΔY = 1 − b, where ‘b’ is a marginal propensity to consume.

Where 0 ≤ (1 − b) < 1.

The important point to note here is that, MPC and MPS sum up to one. This can be expressed as:MPC + MPS = 1

This fact is derived from the following:

Y = C + S, since the change in income is associated with the change in consumption plus the change in saving, the following expression is valid;

ΔY = ΔC + ΔS

Divide by the change in income throughout the equation to obtain:

ΔY/ΔY = ΔC/ΔY + ΔS/ΔY

(b = 0), if the entire additional income is saved

(b = 1), if the entire additional income is consumed, indicating that income has no effects on saving.

Therefore, (MPC + MPS = 1) . . . . . . . . . . . . . . . ..(2.23)

Table 2.5 further elaborates on the computations of income, consumption, saving, average propensity to consume, average propensity to save, marginal propensity to consume, and marginal propensity to save.

Table 2.5: Income, consumption, saving and their propensities

Average propensity to save (APS)

Average propensity to save is saving per income. It is the percentage of income that is saved. In other words, average propensity to save is the ratio of saving to disposable income.

• Average propensity to save = Saving / Income

 . . . . . . (2.24)

The important point to note here is that, (APC) and (APS) sum up to one, expressed as:

(APC + APS = 1)

This fact is derived from the following; (Y = C + S)

Divide by income (Y) throughout the equation to obtain:

Therefore, (APC+APS=1) . . . . . . . . . . . . . . . ..(2.25)

Determinants of saving

Saving is determined by three major factors. These factors include the following:

Willingness to save: A portion of income can be saved only if a person has a desire to save. Willingness to save depends on the family affection, precaution, standard of living and social status. Thus, the higher the willingness to save the higher the savings.

Ability to save: Ability to save means the capacity to save. One cannot save without having the ability to save. The ability to save depends on factors like size of national income, natural resources, trade, industrial development, agricultural development, efficiency of labour, distribution of wealth and income.

Facilities and conducive saving environment: Saving depends also on the facilities and conducive saving environment such as peace and security, taxation policy, value of money, banking facilities, investment opportunities, and economic policy of the government.

Investment multiplier

Investment multiplier is a measure of the relationship between change in the equilibrium level of national income and the change in autonomous investment. Investment multiplier is the number of times by which change in investment has to be multiplied to get the resulting change in equilibrium national income. Investment multiplier is given by the following formula:

Where, (K) is investment multiplier, (Y) is income, and (I) is investment. The multiplier effect is the situation where initial change in the level of investment spending brings about more than a proportionate change in equilibrium national income. Figure 2.7 shows the investment multiplier in a saving and investment framework. The original equilibrium was at point E in which (Y_0) is an equilibrium national income. The increase in investment spending from (I_0) to (I_1), has the multiplier effect, since it increases the equilibrium national income from (Y_0) to (Y_1).

Figure 2.8 shows the multiplier effect using aggregate demand and aggregate supply framework. The initial equilibrium was at point (E_1), with equilibrium national income being at (Y_1), the increase in investment spending by (Delta I) has the multiplier effect because it increases the aggregate demand (AD) from (AD = C + I) to (AD = C + I + Delta I). The effect is increase in equilibrium national income from (Y_1) to (Y_2).

Derivation of investment multiplier

In a closed economy and where there is no government sector, the aggregate demand is equal to consumption (C) plus investment (I); that is, (AD = Y = C + I), and the consumption function is given as (C = a + bY). From these equations, the investment multiplier can be derived as follows:

Given that,

Equation (2.14) is (Y = C + I) and equation (2.17) is (C = a + bY)

Substituting equation (2.17) into (2.14) to obtain equation (2.27):

(Y = a + bY + I) . . . . . . . . . . . . . . . . . . . .. (2.27)

Then, find the first derivative or change of (Y) with respect to change of (I) by differentiating equation (2.27) to obtain equation (2.28).

 . . . . . .(2.8)

The derivative of any constant number equals to zero, plugging this expression in equation (2.28) and collecting the like terms we obtain the following:

 . . . . . . . . (2.29)

Since “b” is marginal propensity to consume (MPC), we can write

But, 1-MPC =MPS

Therefore, The investment multiplier (K) is

Alternatively,

Given that;

C=a+bY . . . . . . . . . . . . . . . . . . . .. (2.30)

Y₀=C+I₀ . . . . . . . . . . . . . . . . . . . .. (2.31)

Substitute equation (2.30) into (2.31).

Y₀(1-b) = a + I₀

 . . . . . . . . . . . .(2.32)

Where;

Y₀ = Original income and

I₀ = Original investment

Suppose income increases to (Y₁) as a new national income level, then we write

Y₁ = a + bY₁ + I₁

Collect like terms together

Y₁ - bY₁ =a + I₁

Y₁(1 - b) ==a + I₁

Divide both sides by 1-b

 . . . . . . .(2.33)

The change in income is obtained by taking the equation (2.33) minus equation (2.32). That is,

Assume no change in autonomous consumption

But, Y₁ - Y₀ =ΔY

I_{1 -} I₀ = ΔI

Therefore, 

Divide both sides by ΔI

But also 1- MPC=MPS, therefore K= ¹/_MPS

Example 2.1

The marginal propensity to consume (MPC) of a certain economy is 0.75. The following procedures are followed to compute the investment multiplier.

Given the marginal propensity to consume is 0.75, we know that MPS = 1 – MPC. Therefore, the marginal propensity to save, MPS = 1 – 0.75 = 0.25.

Investment Multiplier (K) =

The multiplier of 4 means that the initial change in investment will be multiplied 4 times to obtain the final change in equilibrium national income.

Example 2.2

You are given the following consumption function and investment function; (C=200+0.80Y) and (I=50), respectively; where, (C) is consumption, (I) is investment and (Y) is disposable income.

Compute:

(a) The equilibrium level of income;

(b) The level of consumption at equilibrium; and

(c) The final change in national income given that change in investment is Tshs500.

Solution:

(a) The equilibrium level of income

Given that, (Y=C+I), where

C = 200 + 0.80Y and I = 50.

Since (Y = C + I), insert the consumption and investment equations into the income equation as follows:

(Y = 200 + 0.80Y + 50)

Collect the like terms on one side and solve for (Y).

(Y = 250 + 0.80Y) solving for (Y), therefore, (Y - 0.80Y = 250)

0.2Y = 250, divide both sides by 0.2

Therefore, Y=1,250

The equilibrium income is TShs 1,250

(b)

The level of consumption

Given that, C = 200 + 0.80Y and
Y = 1,250, substitute (Y) into consumption function.

C = 200 + 0.80 imes 1,250

= 200 + 1,000 = 1,200

Consumption is TShs 1,200.

(c)

Final change in national income

Given ΔI= Tshs 500 and C=200+0.8Y, then b=MPC=0.8

Investment Multiplier (K)=

Assumptions of the investment multiplier

The following are assumptions of the simple investment multiplier:

First, the investment multiplier assumes that the marginal propensity to consume is constant implying that, each round of new income generate a predictable constant fraction of new spending.

Second, investment multiplier assumes the economy operate below full employment level. Only with idle resources and increase in demand lead to a pure increase in investment, hence no inflation.

Third, the investment multiplier assumes that investment is autonomous meaning it is exogenous and not influenced by current income. It is independent shock that set multiplier process.

Fourth, the investment multiplier assumes that consumption is affected by current income; and the new level of investment is maintained steadily for the completion of the multiplier process.

Relationship between investment multiplier and marginal propensity to consume

The marginal propensity to consume (MPC) and the investment multiplier are directly related. That is, the larger the value of MPC, the larger the value of investment multiplier; and the lower the MPC, the smaller the investment multiplier. The value of MPC vary from 0 to 1 inclusive. Suppose the MPC is given by 0.99 which is very large, the investment multiplier will be On the other hand, if the MPC is 0.10, which is small, the investment multiplier will be small1.1 times.

Relationship between investment multiplier and marginal propensity to save

The marginal propensity to save (MPS) and the investment multiplier are inversely related. That is, the larger the MPS the smaller the investment multiplier; and the smaller the MPS the larger the investment multiplier. Similar to MPC, the value of MPS vary from 0 to 1 inclusive. Suppose the MPS is given by 0.99, which is very large, the investment multiplier will be small . Onthe other hand, if the MPS is given by 0.01 which is small, the size of investment multiplier will be times.

Leakages or withdrawals of multiplier

Leakages are the potential diversions of the income stream that tend to weaken the multiplier effect of new investment. Saving is a major leakage of the multiplier process. The disposable income of the individual can be saved or consumed. The higher the marginal propensity to save, the smaller the size of the multiplier; hence, the greater the amount of leakage.

Importance of multiplier

The importance of multiplier in modern economics lies in the following:

Highlights the importance of change in planned savings and autonomous consumption on income and employment: Fluctuations in income and employment are due to fluctuations in the rate of investment. A change in investment leads to a cumulative change in income and employment by the multiplier process.

Important tool in the formulation of economic policies geared to investment: If investment is small, the government can design policies to promote investment because a rise in investment has a large multiplier effects on income.

Helps the government to decide upon the amount of investment to be injected into the economy. This will eventually reduce unemployment and achieve full employment level.

Helps in bringing equality between saving and investment: When there is a disequilibrium between saving and investment, an increase in investment will lead to the increase in income more than the increase in initial investment. As a result of the increase in income, saving also increases and equals investment.

Highlights the importance of deficit financing: During depression the government will adopt an expansionary fiscal policy by increasing government expenditure or by creating deficit budget. The creation of a deficit budget is financed through deficit financing which helps to increase income and employment by multiplier times the increased investment.

Exercise 2.3

1. If the MPC is 0.6, what is the value of MPS?

2. Show why the sum of MPC and MPS is equal to one.

3. Suppose as consumption function is given by C =100+0.4Y and investment function by I = 50, where C is consumption expenditure, I is investment expenditure and Y is the disposable income. Compute:

1. The equilibrium level of income;
2. The consumption level at equilibrium; and
3. Final change in equilibrium income if change in investment is TShs 10,000.

Chapter summary

1. National income is the monetary value of all final goods and services produced in the economy by factors of production in a certain period of time, usually one year.

2. The total income in the economy must be equal to the total expenditure because in every transaction the firm receives revenue that is the same amount as spent by the households.

3. The Gross Domestic Product (GDP) measures the total expenditure on all final goods and services produced in a given period and total income earned by all factors of production participated in producing these goods and services. In simple terms, GDP is the market value of all final goods and services produced within a country in a year.

4. The GDP identity comprises of four components namely; consumption spending, investment spending, government spending, and net exports. Consumption spending includes goods and services consumed by the households. Investment spending is the purchase of intermediate goods used in the production of goods and services, and inventories by the firms. Government spending is the spending on purchasing of goods and services by government ministries, departments and agencies. Net exports include the values of goods and services produced in the domestic economy and sold outside the country (exports), minus the value of goods and services produced outside the nation's borders and sold within the economy (imports).

5. The Gross National Product (GNP) is the market value of all final goods and services produced by the citizens of a particular country in a given period of time regardless of their location. It is a GDP plus the net factor income from abroad.

6. Economists prefer to use real GDP to measure economic prosperity of a nation since the higher the real GDP, the better the well-being of the people. The nation can afford to provide good education system, affordable health services, and good transport and communication system. But GDP does not include leisure which adds to the standard of living, government spending on non-welfare improving activities, and does not show how income is distributed. Therefore, GDP is an imperfect measure of the economic welfare of a country.

7. In the national income computations, economists usually use three methods namely; the output method, the income method and the expenditure method. In the output method, the value added at each stage of production is aggregated for all goods and services produced in an economy to arrive to GDP. In the income method, the incomes earned by all factors of production are aggregated to come up with one figure. In the expenditure method, the GDP is computed by aggregating the expenditures of households on final goods and services, the expenditure of firms on intermediate goods, government purchases of goods and services and net exports. In theory, all the three methods result to the same figure of GDP. But practically, because the data are not perfect, sometimes the figures may be different.

8. The process of computing national income is not straight forward. There are some challenges which are worthwhile to mention. Some of these problems are double counting, inadequate statistical data, and non-marketable goods and services.

9. The level of national income is determined by the Aggregate Demand (AD) and the Aggregate Supply (AS). The equilibrium level of national income is determined by AD, since AS remains more or less constant in the short run. Therefore, the national output is assumed to be as much as the effective demand.

10. The effective demand is divided into two components: The demand for consumption goods by people and government in the economy and demand for intermediate goods by firms.

11. The equilibrium level of national income is determined by leakages-injections approach, whereby in the closed economy with no government sector saving is the only leakage and investment is the only injection. Thus, at equilibrium leakages must be equal to injections. That is, savings must be equal to investment. That is why the leakages-injections approach is sometimes known as the savings-investment approach.

12. The shift in aggregate expenditure leads to the changes in the equilibrium national income. For instance, if the aggregate expenditure increases (shifting upward), the equilibrium national income also increases and the vice versa is true in case of decrease in aggregate expenditure. Therefore, in the leakages-injections approach a shift in savings or investment curves leads to the changes in the equilibrium national income.

13. The relationship between change in the equilibrium national income and investment is expressed by the investment multiplier. The investment multiplier is an average number of times in which initial change in the investment multiplies several times to give the final change in the equilibrium national income.