The Multiplier (Grade 12 NSC Matric Economics): Revision Notes

The Multiplier

What is the multiplier effect?

The multiplier effect describes how a small initial change in spending can create a much larger change in the overall economy's output and income. Think of it like dropping a stone in a pond - the ripples spread outward, creating effects much bigger than the original stone.

When someone spends money in the economy (like government investment or business spending), this creates income for others. Those people then spend part of their new income, which creates income for even more people, and so on. This creates a knock-on effect where the final increase in national income is much larger than the original spending injection.

How to calculate the multiplier

The multiplier can be calculated using these formulas:

$M = \frac{1}{1 - mpc} \text{ OR } M = \frac{1}{mps}$

Where:

• M = the multiplier value
• mpc = marginal propensity to consume (the proportion of extra income that people spend)
• mps = marginal propensity to save (the proportion of extra income that people save)

You can also calculate the multiplier by comparing the total change in income to the original injection:

$M = \frac{\Delta Y}{\Delta I}$

Where:

• $\Delta Y$ = change in total income
• $\Delta I$ = change in investment (the initial injection)

The multiplier in a two sector economy

In a simple two sector economy (households and businesses), the multiplier depends on the marginal propensity to consume (mpc). This tells us what proportion of any extra income gets spent rather than saved.

Here's how it works:

• The larger the mpc, the bigger the multiplier
• The smaller the mpc, the smaller the multiplier
• It's the money that stays in the economy that matters

The multiplier in a four sector economy

In a more realistic four sector model (households, businesses, government, and foreign sector), there are additional leakages that reduce the multiplier effect:

• mps = marginal propensity to save
• mrt = marginal rate of taxation
• mpm = marginal propensity to import

Understanding the multiplier through graphs

The graph above shows how the multiplier works visually. When there's an increase in investment ($\Delta I$), this shifts the aggregate expenditure line upward from AE to AE₁. The economy moves from equilibrium point E to E₁, and the final increase in income (from Y to Y₁) is much larger than the original investment increase.

The 45-degree line represents points where total spending equals total income - these are equilibrium points where the economy settles.

How the multiplier effect works in practice

The Keynesian approach

John Keynes was the famous economist who developed multiplier theory. He believed that economies need spending to grow, and that government could use the multiplier effect to boost economic growth.

The Keynesian approach suggests that government can:

1. Increase government spending (G) and finance it through loans to stimulate economic growth
2. Reduce taxation to put more money in consumers' pockets
3. Reduce company taxes to encourage more business investment

Worked examples and calculations