Consumption, Saving, Investment and Multiplier
Senior 5 · Economics
Consumption, Saving, Investment and Multiplier
Lesson 4 of 4
50 min
Suppose the government pays a contractor Frw 10 billion to build a district road. The contractor pays wages, buys cement and hires lorries. The workers spend much of their wages on food, transport and clothes; the traders and farmers who sell to them spend much of what they receive; and so on. Each round is smaller than the last, because at every step some income is saved, taxed or spent on imports. When the rounds die away, national income has risen by more than the Frw 10 billion first spent. How much more is the question of the multiplier. Investment itself also responds to rising sales, through the accelerator.
Definition
Multiplier (): the number by which a change in an injection (investment, government spending or exports) is multiplied to give the resulting change in national income:
With an MPC of 0.75, an injection of 100 creates 100 of income in round 1; 75 of that is spent in round 2; 0.75 × 75 = 56.25 in round 3; and so on:
In a closed economy without government, the only withdrawal is saving, so
The bigger the MPC, the less leaks out in each round, and the bigger the multiplier.
| Multiplier | Formula | Meaning |
|---|---|---|
| Investment multiplier | Effect on income of a change in investment | |
| Government expenditure multiplier | Same size: G is an injection like I | |
| Tax multiplier | A tax cut raises disposable income, but only the MPC share of it is spent in the first round, so it is smaller, and negative for a tax rise | |
| Balanced-budget multiplier | Raising G and T by the same amount raises income by that amount | |
| Open-economy (full) multiplier | With leakages to saving, taxes (marginal propensity to tax, MPT) and imports (MPM); the denominator is the marginal rate of withdrawal (MRW) | |
| Export multiplier | Effect of a rise in exports, an injection |
The employment multiplier, the ratio of total new jobs to the jobs first created, is studied with unemployment in Unit 7.
Worked example 1: closed-economy multipliers
MPC = 0.8 (illustrative).
(a) Investment rises by Frw 200 billion: , so billion.
(b) Taxes rise by Frw 100 billion: tax multiplier , so billion.
(c) Government spending and taxes both rise by Frw 100 billion: billion. The balanced-budget multiplier is 1.
Worked example 2: why Rwanda's multiplier is small
In 2025 Rwanda's imports were Frw 8,213 billion and GDP Frw 23,387 billion (NISR), so on average
Suppose, for illustration, that out of each extra franc of income 0.15 is saved, 0.15 is taxed and 0.30 is spent on imports.
A Frw 300 billion rise in government spending would raise income by about billion. In a closed economy with only the 0.15 saving leakage, the multiplier would have been . Imports are the biggest leak.
Definition
Accelerator principle: net investment depends on the rate of change of output or sales, not on their level:
where is the accelerator coefficient, the capital–output ratio: the value of capital needed to produce one unit of output a year.
Worked example 3: a small change in sales, a big change in investment
A firm needs Frw 2 of machinery for each Frw 1 of annual sales () and replaces machinery worth 20 each year (illustrative units).
| Year | Sales | Capital needed (2 × sales) | Net investment | Replacement | Gross investment |
|---|---|---|---|---|---|
| 1 | 100 | 200 | 0 | 20 | 20 |
| 2 | 100 | 200 | 0 | 20 | 20 |
| 3 | 110 | 220 | 20 | 20 | 40 |
| 4 | 125 | 250 | 30 | 20 | 50 |
| 5 | 130 | 260 | 10 | 20 | 30 |
| 6 | 130 | 260 | 0 | 20 | 20 |
| 7 | 125 | 250 | -10 | 20 | 10 |
From year 2 to year 3, sales rise by 10% but gross investment doubles, from 20 to 40. In year 5 sales are still rising, but more slowly, and investment falls, from 50 to 30. In year 6 sales stay at their peak, and net investment drops to zero. When sales dip in year 7, the firm does not even replace all its worn-out machines.
Multiplier and accelerator together. A rise in investment raises income through the multiplier; the rise in income raises investment through the accelerator; and so on. When growth slows, the accelerator cuts investment, and the multiplier cuts income. Paul Samuelson (1939) showed that this interaction can produce the waves of the business cycle.
Warning
Two common slips. (1) Using the closed-economy formula when the question gives taxes and imports: use . (2) Applying the accelerator to the level of output: investment depends on the change in output, so constant sales, however high, give zero net investment.
Important
Discuss. The government plans to spend Frw 100 billion more on rural feeder roads, built mainly with local labour and local materials, or on imported buses for Kigali. Which is likely to have the larger multiplier effect on Rwanda's national income, and why? What other factors should decide between them?
EconplusDal, "Multiplier Effect and Accelerator" (about 10 minutes). Note how he calculates the multiplier from the marginal propensities to withdraw, then compare his accelerator example with the table above.
Practice
Further reading
Sources and credits
Written by Ganzaa: the text, the three diagrams, the tables, the worked examples and the practice items. The marginal propensities and the accelerator figures are illustrative.
