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# Theory of Multiplier

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In today’s class, we will be talking about the theory of multiplier. Enjoy the class!

### Theory of Multiplier

CONTENT

• Meaning of Multiplier
• Equilibrium Level of Income

#### DEFINITION OF MULTIPLIER

The theory of the multiplier– states that an increase in consumer or business investment spending in a country would produce a multiplier effect by raising the level of national income.  The multiplier effect can be as a result of changes in consumption expenditure, which is known as consumption multiplier or investment changes, which is known as investment multiplier.

The concept of multiplier shows that a small change in investment can have a magnified effect on income. Multiplier = 1 / (1-MPC) where MPC equals marginal propensity to consume.

The total increase in income depends on the marginal propensity to consume. If MPC is high, the Multiplier will be high and rise in income will be high when people spend on consumption, the level of national income rises.

Example:

Considering #100 million increase in investment, suppose 4/5 of the investment was consumed 1/5 would have been saved.

Increases in Income = Investment / 1- MPC

= 100m/ (1- 4/5) = 100m / (1/5)

= 100m x 5/1

= 500 million

The total increase in income is five times the initial increase in investment. Therefore, Multiplier is 5.

The multiplier denoted by K is usually calculated with the aid of formula

1. K =          1          = 1

1 – mpc         mps

K = ∆Y

∆C

Where K = multiplier

Mpc = marginal propensity to consume

Mps  =  marginal propensity to save.

Y = change in national income

C = Consumption expenditure

I  =  Investment

Example 1

• If the marginal propensity to consume is 0.8, calculate the multiplier.
• By how much must consumption expenditure be increased to increase income by N10,000.

Solution

(a).                 K =          1       =         1      =    1          =    5

1 – mpc         1 – 0.8 0.2

The multiplier K has a value of 5

(b)                K = ∆Y

∆C

5   = N10,000

C

Cross multiply

5 x C = 10,000  x  1

C =10,000   =   N2,000

5

EVALUATION

1. What is meant by the multiplier?
2. Calculate the total national income if the total national savings is N250m and the APS is 0.4
3. If the mps is 0.4 what is the mpc.

#### EQUILIBRIUM LEVEL OF INCOME

Equilibrium Level of Income– is a situation where the total amount people wish to save equals total investment of business units. It refers to a point at which the aggregate saving equals aggregate investments. At the equilibrium level of income, there is a balance between or equality of saving and investment as illustrated in the diagram below:

Again, at the equilibrium level of income, there is a balance between the aggregate demand and aggregate supply, and there will be no tendency to increase or decrease output. The business sector is satisfied that the right volume of output has been achieved and there will be no tendency to alter it.

For equilibrium national income to be maintained, the volume of total withdrawals from the circular flow of income must be equal to the volume of total injections. That is, the total amount of saving must be equal to the total value of the investment, and aggregate expenditure must be equal to total output.

Income earners (household) can spend their income on consumption of goods and services or save it, hence, Y = C + S. On the other hand, the firms can spend its income on the running overhead expenses or invest it, hence, Y = C + I. Probing this equation further, we will arrive at a situation of, S = I, where the aggregate saving equals aggregate investment that indicates the general equilibrium level of income.

NOTE: For Y to be constant, the level of savings (S) must be equal to investment (I). By implication, the number of consumer goods and services produced by firms will be equal to the aggregate demand of the people (household).

EVALUATION

1. Explain what is meant by the equilibrium level of income in an economy.
2. How is the equilibrium level of income in an economy attained?

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