What is the multiplier?
The multiplier is a macroeconomic concept that explains how an initial change in spending in an economy can lead to a larger final change in national income, national output, or Gross Domestic Product (GDP).
A rise in investment, government spending, or exports, for example, would cause the income of other individuals or firms to increase. Further spending creates further income. The sequence continues until the impact subsides. As they spend part of their income, additional income is generated for others. Repeated spending increases the effect in the economy until the effect finally dies out. The spending of one economic unit becomes an income to another economic unit.
How the multiplier works
A major influence on the size of the multiplier is the Marginal Propensity to Consume (MPC), which is the proportion of extra income that households spend rather than save. Additional income can only be generated if money is spent. If a greater proportion of income received is saved, the multiplier effect will be small as little income is being spent.
Assuming a firm spends $1,000 on machinery, it becomes an income for the machinery manufacturer. The manufacturer’s income in Round 1 is $1,000. The manufacturer pays its workers and suppliers the sum of $800 ($1,000 x 0.8), since the MPC is 0.8; in Round 2, the workers and suppliers earn an income of $800. The workers and suppliers spend part of their income on goods and services ($800 x 0.8 = $640), generating income of $640 for other firms (Round 3). These other firms also pay their workers $512 (Round 4), and the process continues. In the end, the national income will rise by more than the initial spending due to the extra incomes created along the way.
It is not all the income that is spent by the recipient. Some of it gets withdrawn from the circular flow of income through leakages like savings, taxation, and imports. These leakages or withdrawals reduce the size of each successive round of spending, eventually bringing the multiplier process to an end.
Table 1: The multiplier process
| Spending (MPC = 0.8) | Extra income created | |
| Round 1 | $1000 | |
| Round 2 | $1,000 x 0.8 = $800 | $800 |
| Round 3 | $800 x 0.8 = $640 | $640 |
| Round 4 | $640 x 0.8 = $512 | $512 |
| Round 5 | $512 x 0.8 = $409.60 | $409.60 |
| … | … | …. |
How to calculate the multiplier
If we know the change in national income and the amount of additional spending or injection, the multiplier is obtained by dividing the change in national income by the additional injection. For example, if an additional investment of $50 million increases the national income or GDP by $150 million, the multiplier is 3 ($150 million/$50 million).
The multiplier can, however, be calculated by using a formula if the change in national income is not given. The formula for calculating the multiplier is determined by the type of economy. But the general formula is: one divided by the marginal propensity to withdraw. The withdrawal in a two-sector economy is savings; the withdrawals in a three-sector economy are savings and taxes; the withdrawals in a four-sector economy are savings, taxes, and imports.
The multiplier for a two-sector economy:
or
The multiplier for a three-sector economy:
The multiplier for a four-sector economy:
Example
Suppose MPS = 0.1, MPT = 0.4 and MPM = 0.3, Calculate:
(i) the multiplier ; (ii) the change in GDP if investment rises by $200 million.
Solution
(i) Multiplier = 1
———————
0.1 + 0.4 + 0.3
= 1.25
(ii) Change in GDP = $200 million x 1.25
= $250 million
Factors affecting the size of the multiplier
Marginal propensity to consume and marginal propensity to save
The greater the MPC, the greater the income created for others and the larger the multiplier effect. Marginal Propensity to Save (MPS) is the proportion of extra income that is saved. If households save a greater proportion of every extra income, the multiplier size will be small. The bigger the MPS, the lower the size of the multiplier. Low consumer confidence, for instance, encourages consumers to save rather than consume.
The marginal propensity to tax
Taxes are withdrawals from the circular flow of income. If the proportion of extra income paid as tax (MPT) rises, less of the extra income is available for spending; less spending reduces the amount of additional income created, and the size of the multiplier. A low MPT will boost spending and lead to a larger multiplier effect.
Marginal propensity to import
A high marginal propensity to import (MPM) indicates that a significant portion of additional income is spent on imports. Therefore, the size of the multiplier is large if MPM is low and vice versa. This is because imports generate income abroad, not in the domestic economy.
Limitations of the multiplier
The economy must operate below maximum capacity
There must be spare capacity for the GDP to expand following an increase in demand. If the economy is operating at full capacity, all resources are fully employed, and there are no idle resources that can be deployed to raise output. Consequently, there will be a multiplier effect resulting from the injection.
Continous investment
A country’s productive capacity keeps declining year in, year out due to the depreciation of capital goods. Machines, for example, are subject to wear and tear and obsolescence. Therefore, continuous investment is required to keep pace with rising demand. The size of the multiplier will be small if investment is not undertaken continuously,
No time lag between income receipt and spending
There is a time lag between the receipt of income and spending. And the full effects of increased spending may take months or years to materialise. The multiplier process is delayed if the income earned is not spent immediately. The multiplier depends on the marginal propensity to consume. Therefore, delayed consumption leads to a delay in the multiplier effect in the economy.
Consumer goods must be available
For the multiplier to be effective, goods must be available for consumers to buy. As consumers spend on goods, additional incomes are generated for others. This increases the size of the multiplier.
No shortage of resources
If there is a shortage of resources, more goods cannot be produced, thereby reducing the multiplier effect.
The economy must be closed
Spending on goods from other countries rather than domestic products reduces the size of the multiplier. Therefore, the multiplier effect is great if there are no income outflows from the country due to imports.
No inflationary pressure
It is assumed that there is no inflation. Rising consumption raises demand, causing a rise in the general price level. Inflation reduces purchasing power and the amount of goods bought. Consequently, the size of the multiplier is reduced.