Theory of Multiplier – SS2 Economics Lesson Note (Third Term)

The multiplier is the number by which a change in investment or consumption spending is multiplied to give the change in national income. It equals 1 / (1 – MPC), or 1 / MPS. The higher the MPC, the larger the multiplier. For example, an MPC of 0.8 gives a multiplier of 5.

Behavioural objectives

By the end of the lesson, students should be able to:

• state the theory of the multiplier;
• distinguish between the consumption multiplier and the investment multiplier;
• calculate the multiplier from the marginal propensity to consume or to save;
• calculate the change in income or in spending using the multiplier;
• explain the equilibrium level of income and the conditions needed to maintain it.

What is the theory of the multiplier?

The theory of the multiplier states that an increase in consumer or business investment spending in a country produces a multiplier effect by raising the level of national income.

The multiplier effect can result from changes in consumption expenditure, which is known as the consumption multiplier, or from changes in investment, which is known as the investment multiplier.

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

What determines the size of the multiplier?

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

Worked example: an increase in investment

Consider a ₦100 million increase in investment. Suppose 4/5 of the investment was consumed and 1/5 was saved.

Increase 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, the multiplier is 5.

How is the multiplier calculated?

The multiplier, denoted by K, is usually calculated with these formulae:

• K = 1 / (1 – MPC) = 1 / MPS
• K = ∆Y / ∆C

Where:

• K = multiplier
• MPC = marginal propensity to consume
• MPS = marginal propensity to save
• ∆Y = change in national income
• ∆C = change in consumption expenditure
• I = investment

Example

If the marginal propensity to consume is 0.8, calculate the multiplier. By how much must consumption expenditure be increased to increase income by ₦10,000?

Solution

(a) K = 1 / (1 – MPC) = 1 / (1 – 0.8) = 1 / 0.2 = 5

The multiplier K has a value of 5.

(b) K = ∆Y / ∆C

5 = ₦10,000 / ∆C

Cross multiply: 5 x ∆C = 10,000 x 1

∆C = 10,000 / 5 = ₦2,000

What is the equilibrium level of income?

The equilibrium level of income is a situation where the total amount people wish to save equals the total investment of business units. It is the point at which aggregate saving equals aggregate investment.

At the equilibrium level of income, there is a balance between, or equality of, saving and investment, as illustrated in the diagram below.

At the equilibrium level of income, there is also a balance between aggregate demand and aggregate supply, and there is no tendency to increase or decrease output. The business sector is satisfied that the right volume of output has been achieved and will not alter it.

Conditions for maintaining equilibrium income

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

How does S = I arise?

Income earners (households) can spend their income on consumption of goods and services or save it, hence Y = C + S. Firms can spend their income on running overhead expenses or invest it, hence Y = C + I. Putting the two equations together gives S = I, where aggregate saving equals aggregate investment. This indicates the general equilibrium level of income.

Note: For Y to be constant, the level of savings (S) must equal investment (I). By implication, the amount of consumption goods and services produced by firms will equal the aggregate demand of the people (households).

Evaluation

1. State the theory of the multiplier.
2. Write the formula for the multiplier in terms of MPC and in terms of MPS.
3. If the marginal propensity to consume is 0.9, calculate the multiplier.
4. Why does a high MPC give a high multiplier?
5. State the condition for equilibrium level of income in terms of saving and investment.

Assignment

1. If a firm earns an annual income of ₦80m and spends ₦50m on procurement of working materials, calculate the APS of the firm. (a) 0.38 (b) 0.72 (c) 0.91 (d) 0.11
2. If the marginal propensity to save is 0.45, calculate the multiplier. (a) 0.75 (b) 2.2 (c) 0.14 (d) 0.95
3. In question 2 above, calculate the level of investment which is required to raise income by ₦12,000. (a) ₦1,456 (b) ₦5,454.55 (c) ₦4.646 (d) ₦4,890.1
4. If the MPS is 0.3, what is the MPC? (a) 0.1 (b) 0.5 (c) 0.7 (d) 0.15
5. At the equilibrium level of income of an economy, the total expenditure equals ……. (a) total assets (b) total output (c) total investment (d) total capital
6. If the monthly income of an individual increases from ₦8,000 to ₦12,000 and his level of consumption increases by ₦60.00, calculate the marginal propensities to save and consume.
7. Briefly explain the three different ways by which the equilibrium level of income of an economy can be determined.