Multiplier Theory of J. M. Keynes

We know that there are two key concepts Marginal Propensity to consume (MPC), and Marginal Propensity to Save (MPS). What is not consumed is automatically saved, and what is saved, a part or whole of it is automatically invested. The savings in done by the consuming, household sector, and the investment is done by the producing sector.

Change in Income(ΔY) = $100
Change in Consumption(Δ) = $80,
Change in Savings(ΔS) = $20
We also know that ΔY = ΔC + ΔS
Dividing both sides by ΔY,
We get ΔY/ ΔY = ΔC/ΔY + ΔS/ΔY
Or, 1 = ΔC/ΔY + ΔS/ΔY
Or, 1 = 80/100 + 20/100
Or, 4/5 + 1/5 = 1
Or, b + s = 1

We can now use an imaginary table.

Prof. Keynes introduced two major inferences.

1. If income increases, consumption will also increase, but less than proportionately (as part of the change in income is saved.)

2. The Marginal Propensity to Consume (MPC) is less than Average Propensity to Consume (APC). Average Propensity to Consume is Total Consumption divided by Total Income.

The Multiplier

b + s = 1
Or, s = 1 - b
Or, 1/s = 1/(1-b) = the multiplier "m".
"m" is the reciprocal of the marginal Propensity to Save.
m = 1/s = 1/(ΔS/ΔY) = 1/{1-(ΔC/ΔY)}

According to Mr. Keynes, the change in income ΔY = multiplier times change in investment, ΔI.

According to our above example, b = 4/5 and s = 1/5

Therefore, m = 1/s = 1/(1/5) = 5

ΔY = m(ΔI)

If investment changes by $100, then income changes by

ΔY = 5($100) = $500

Thus if investment increases, national income will also increase, not by the same amount, but by a multiple of it. Another point made by Prof. Keynes was that if the consumption expenditure of the community increases, the value of "b" will be larger and larger, and so also the value of the multiplier, and so also the national income.


The multiplier is the reciprocal of Marginal Propensity to Save. Corresponding to each value of "b" there will be a particular value of "s", and corresponding to each value of "s", there will be a particular value of "m".
Change in income ΔY = multiplier (m) times change in investment, ΔI

The Logic of the Multiplier
According to Mr. Keynes, the multiplier means that a small increase in investment will lead to a multiple increase in income. One man's expenditure is another man's income, and vice versa. When a man spends a part of his income, say $X, he creates an income of others of $X. The second person will again save a part of $X, and spend the rest. Again, the second man's expenditure creates an income for the third person. Thus the same money goes on creating incomes for a number of persons. This process leads to the following equations, where "b" is the part of the income spent, or MPC.


Larger the value of "b", greater will be the change in income.
The root cause of unemployment is deficiency in demand. And the only way to stimulate the economy in depression is to increase the demand through public or government expenditure programmes. Fresh expenditure will generate new incomes, and the multiplier process will set in. The multiplier effect will ultimately restore the full-employment situation.

Assumptions: In order to explain the Multiplier theory Mr. Keynes made the following assumptions:

1. Consumption always changes with change in income. In other words, consumption will always depend on income.

2. Marginal Propensity to Consume will remain constant.

3. There is change in Autonomous Investment. Autonomous Investment means when investment takes place even when there is no increase in income.

Limitations: The following factors will set a limit to the working of the multiplier.

1. Leakages: The higher the Marginal Propensity to Consume, the higher will be the value of the multiplier. The income, which is received, should be spent, so that it may again come back as income. If people prefer to keep cash balances idle, for transactions, precautionary or speculative motives, income created will naturally be less.

2. Consumption Goods: With the rise in income, consumption goods should be readily available in sufficient quantities, so that additional income may be spent on them. If there is shortage of goods, additional income received may not be fully spent. The Marginal Propensity to Consume will be low, and therefore the multiplier will be low.

3. Multiplier Period: The time gap between the receipt of income and consumption expenditure is known as the Multiplier Period. The smaller the time span of the multiplier period, the higher will be the value of the multiplier.

4. Investment: Any increase in investment in one sector should not be accompanied by a decrease in investment in another sector. Increments in investments should be repeated at regular intervals.

5. Full Employment Ceiling: If the economy is working at or near full-employment level, fresh investment outlay cannot lead to an increase in the supply of consumption goods. It will not raise aggregate income but will lead to price rise. Full-employment situation is called the economy's inflation threshold.

6. Induced Investment: Just as a change in investment induces consumption, so also induced consumption can influence investment. But the multiplier effect does not take this into consideration.

Conclusion: Though there are some limits in the workings of the multiplier, Mr. Keynes used this concept to advocate public investment during a period of depression.


Must also read: 1. Consumption and savings
2. Consumption Function and Savings Function