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# The Concept of the Multiplier

The multiplier concept measures the effect of a change in the national income and employment brought about as a result of a change in investment. It is a numerical figure which shows the number of times the income of the country to community has increased or decreased over the original increases or decreases in investment, or consumption expenditure. It is a ratio of change in income to change in consumption as given below: Where

M = the multiplier
MPC = Marginal Propensity to Consume
MPS = Marginal Propensity to Save
ΔY = Change in Income
ΔC = Change in Consumption

The value of the multiplier is dependent on the marginal propensity to consume. The higher the MPC, the higher the multiplier and vice versa. The lower the MPS, the higher the multiplier will be and vice versa. A high MPC usually results in a high national income.

Example:

(i) If the MPC is 80% or 0.8 what will be the value of the multiplier?
(ii) if an increase in income of 444,000 is to be achieved, by how much must the consumption expenditure be increased?

Solution

(i) MPC = 0.8 Putting the value of MPC into equation (1) (ii) ΔY = ₦4,000
M = 4
Putting the values of ΔY and M into equation (2) ΔC = ₦4,000 C = ₦1,000

The consumption expenditure must be increased by ₦1,000.

The Multiplier and Investment

Investment is an expenditure on capital goods, therefore an increase in investment spending also have a multiplying effect that will lead to an increase in the national income and vice versa. The relationship is shown as: Example:
Given the marginal propensity to save as 0.4, calculate:

(i) The multiplier
(ii) The actual investment level that will increase income by ₦20,000

Solution

Given MPS = 0.4
(i) M = 2.5
ΔI = Change in investment
ΔY = Change in Income = ₦20.000
Substituting the values of M and Y into equation 1 2.5 = ₦20,000
2.51= ₦20,000

The required level of investment is ₦8,000.

The Multiplier and Government Spending
Government spending has a multiplier effect on the national income similar to that of the individual and business firms spending. When government spending is raised, this also raises the national income level. M = Multiplier
ΔG = Change in government spending

Example:
Calculate the extent to which the national income of a country will increase if government spending increases by ₦5,000,000 given an MPC of 0.75.

The national income will increase by ₦12.5 million.

Equilibrium Level of Income
The equilibrium level of income refers to that level of national income where total savings are equal to total investment, i.e. withdrawals are equal to injections into the flow. This is the point, once attained, at which there is no tendency for change. Individuals have the freedom to spend their income on consumer goods, or save it Y = C+ S. The business units can choose to manufacture either consumer goods or capital goods i.e. Y = C+1. Hence, if the equilibrium level of Y is to be sustained, then the savings must be equal to investment. Alternatively the quantities of goods and services produced must be equal to that demanded by the households. Equilibrium level of income

From the above figure, equilibrium level of income is at Ye where the aggregate demand is equal to the amount produced. At Y2, aggregate demand is less than aggregate output. The excesses remain unsold. The market forces of demand and supply will come into play in order to restore equilibrium in the market. Producers will cut down production until equilibrium is restored. If the expenditure is less than income, this means aggregate demand is higher than the output of the firms. There is excess demand, ED at this point. Firms will be encouraged to produce until the equilibrium position of ye is once again attained.