2.4.4 The Multiplier
Edexcel A-Level Economics (9EC0) | Theme 2.4.4
What Is the Multiplier?
Definition: The multiplier is the process by which an initial injection, such as an increase in government spending, investment, or exports, leads to a larger final increase in national income and real GDP.
Multiplier Ratio:
\[ k = \frac{\text{Final Change in Real GDP}}{\text{Initial Injection}} \]
For example, if a £2 billion increase in government spending leads to a £6 billion rise in GDP, the multiplier is 3.
The Multiplier Process: How It Works
Initial Injection: There is a rise in spending, for example if the government builds a new hospital.
Income: That spending becomes income for builders, architects, and other workers involved.
Spending: These recipients spend a proportion of their new income according to their marginal propensity to consume (MPC).
Further Rounds: This spending becomes income for other people, who then also spend a proportion, creating repeated rounds of expenditure.
Total Effect: The total increase in national income is therefore a multiple of the original injection.
The Role of Marginal Propensities
These show what happens to each extra pound of income and are crucial for determining the size of the multiplier.
| Term | What It Means | Formula |
|---|---|---|
| MPC | The proportion of extra income spent on domestic goods and services. | \( \Delta C / \Delta Y \) |
| MPS | The proportion of extra income saved. | \( \Delta S / \Delta Y \) |
| MPT | The proportion of extra income paid in tax. | \( \Delta T / \Delta Y \) |
| MPM | The proportion of extra income spent on imports. | \( \Delta M / \Delta Y \) |
Key Relationship: MPC + MPS + MPT + MPM = 1, because all extra income is either consumed, saved, taxed, or spent on imports.
Calculating the Multiplier
The size of the multiplier depends on leakages. Larger leakages mean a smaller multiplier.
Formula using MPC:
\[ k = \frac{1}{1 - MPC} \]
Formula using Withdrawals:
\[ k = \frac{1}{MPS + MPT + MPM} \]
\[ k = \frac{1}{MPW} \]
If MPC is 0.8, then total leakages are 0.2, so:
\[ k = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5 \]
This means an initial £1 billion injection would create a final increase in GDP of £5 billion.
The Multiplier Effect on Aggregate Demand
Factors Affecting the Size of the Multiplier
- High MPC and low leakages: Create a larger multiplier.
- High tax rates (MPT): Make the multiplier smaller because more income leaks out through taxation.
- High propensity to import (MPM): Reduces the multiplier because spending leaks abroad.
- High interest rates: Encourage saving, so the multiplier becomes smaller.
- Negative multiplier effect: A fall in injections causes a multiplied contraction in national income.
Significance for Government Policy
- Fiscal Policy: Governments use the multiplier to estimate how changes in G or T will affect economic growth.
- Time Lags: The multiplier does not work instantly and takes time to pass through the economy.
- Spare Capacity: The multiplier has a bigger effect on output when the economy has spare capacity. At full capacity it is more likely to raise prices.
Exam Preparation
- Define the multiplier clearly and explain the process through the circular flow of income.
- Be able to calculate the multiplier using both formula approaches.
- Draw the multiplier effect on an AD/AS diagram.
- Analyse how factors such as tax rates, exchange rates, and confidence affect the size of the multiplier.
- Evaluate the importance of the multiplier for government fiscal policy.