The multiplier and the accelerator

Introduction: The Ripple Effect of the Economy

Welcome to one of the most exciting parts of Macroeconomics! Have you ever wondered why a single government decision to build a new bridge or a sudden increase in business investment seems to boost the whole economy far more than the original cost of the project? Or why a small slowdown in growth can suddenly make businesses stop buying new equipment altogether?

In this chapter, we will explore the Multiplier and the Accelerator. These two concepts explain how small changes in spending can lead to much bigger changes in national income. Think of it as the "ripple effect" in a pond—one small pebble creates circles that spread far and wide.

Don't worry if this seems tricky at first! We will break it down step-by-step with simple formulas and real-world stories.

1. The National Income Multiplier

The multiplier effect occurs when an initial injection (like Investment, Government spending, or Exports) into the circular flow of income leads to a larger final increase in National Income (GDP).

How it Works: The Story of the New Hospital

Imagine the government spends £100 million to build a new hospital.
1. Builders and architects earn that £100 million as income.
2. They don't save all of it; they spend some at local shops and on holidays.
3. The shopkeepers and travel agents now have new income, and they spend a portion of it too.
4. This cycle continues, and the total increase in national income ends up being much more than the original £100 million.

Key Terms You Need to Know

To calculate the multiplier, we need to understand how much people spend or save when they get extra income. We use the term "Marginal Propensity" (which just means "tendency to spend/save the next pound earned").

• MPC (Marginal Propensity to Consume): The fraction of extra income that is spent on domestic goods.
• MPS (Marginal Propensity to Save): The fraction of extra income that is saved.
• MPT (Marginal Propensity to Tax): The fraction of extra income taken in taxes.
• MPM (Marginal Propensity to Import): The fraction of extra income spent on goods from abroad.
• MPW (Marginal Propensity to Withdraw): The sum of all leakages from the circular flow. \( MPW = MPS + MPT + MPM \).

Calculating the Multiplier

The symbol for the multiplier is k. You can calculate it using these two simple formulas:

\( k = \frac{1}{1 - MPC} \)

OR, even simpler:

\( k = \frac{1}{MPW} \)

Example: If people spend 80% of any extra income they receive (MPC = 0.8), the multiplier is:
\( k = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5 \).
This means every £1 injected into the economy creates £5 of total growth!

Quick Review: Average vs. Marginal

The syllabus also asks you to know Average propensities.
Average Propensity to Consume (APC) = \( \frac{Total\ Consumption}{Total\ Income} \).
Marginal Propensity to Consume (MPC) = \( \frac{Change\ in\ Consumption}{Change\ in\ Income} \).
Always remember: Marginal is about the extra or the change.

Key Takeaway: The size of the multiplier depends on leakages. If people save a lot, pay high taxes, or buy lots of imports (high MPW), the multiplier will be small because the money "leaks" out of the cycle quickly.

2. The Accelerator Effect

While the multiplier is about Spending creating Income, the Accelerator is about Growth creating Investment.

The Accelerator Effect suggests that the level of planned investment by firms depends on the rate of change of national income. If the economy starts growing faster, firms need more machines and factories to keep up with the demand. This leads to a massive surge in investment spending.

An Everyday Analogy: The Pizza Shop

Imagine a pizza shop that has one oven and can serve 100 people a day.
- If they get 100 customers every day, they just maintain the oven they have.
- If demand speeds up to 150 customers, they suddenly have to buy a whole new oven.
- A small increase in customers led to a 100% increase in their investment (from 0 new ovens to 1 new oven). That is the accelerator!

The Multiplier-Accelerator Interaction

These two often work together to create the Economic Cycle (Booms and Recessions):
1. An injection (e.g., more Exports) triggers the Multiplier, increasing National Income.
2. As Income grows, firms see rising demand and trigger the Accelerator by investing in new capital.
3. This Investment is itself a new injection, which triggers another Multiplier effect!
4. This "knock-on" effect helps explain why economies often experience rapid "Booms."

Did you know? The accelerator also works in reverse! If the rate of growth slows down (even if the economy is still growing, just more slowly), firms may stop investing entirely, which can lead to a recession.

3. Output Gaps and the AD/AS Model

To understand the impact of the multiplier and accelerator, we look at Output Gaps. This is the difference between where the economy is and where it could be if it were using all its resources perfectly.

Types of Output Gaps

• Negative Output Gap (Recessionary Gap): Actual GDP is less than Potential GDP. There is spare capacity, high unemployment, and "slump" conditions.
• Positive Output Gap (Inflationary Gap): Actual GDP is greater than the sustainable Potential GDP. The economy is "overheating," usually causing high inflation as resources are overstretched.

Showing Gaps on Diagrams

You need to be able to show these in two ways:

1. The AD/AS Model

On an Aggregate Demand / Aggregate Supply diagram:
- A Negative Output Gap is the distance between the current equilibrium and the Long-Run Aggregate Supply (LRAS) curve.
- The Multiplier effect is shown by a shift in the AD curve to the right being larger than the initial injection.

2. The Production Possibility Curve (PPC)

- If the economy is operating inside the PPC curve, there is a Negative Output Gap (unemployed resources).
- Moving towards the curve represents using the multiplier to close that gap.
- The PPC curve itself represents the Potential GDP (the LRAS).

Common Mistake to Avoid: Don't confuse a "decrease in growth" with a "decrease in GDP." An economy can still be growing (GDP is rising), but if it's growing slower than its potential, the Negative Output Gap might actually be getting wider!

4. Summary and Evaluation

To get the top marks, you need to evaluate these concepts. Here is a quick summary of factors to consider in your exam answers:

Why the Multiplier might be small in reality:

• Time Lags: It takes time for money to be spent and re-spent.
• Crowding Out: If the government borrows to spend, interest rates might rise, reducing private investment.
• High Propensity to Import: In countries like the UK, a lot of extra income is spent on foreign goods (leakage).

Causes and Consequences of Output Gaps:

• Negative Gap: Caused by a fall in AD (e.g., lower consumer confidence). Consequence: Unemployment and low inflation.
• Positive Gap: Caused by a surge in AD. Consequence: Rapid inflation and "overheating."

Key Takeaway: The Multiplier and Accelerator are powerful tools that explain why small changes in the components of AD can lead to large swings in the economic cycle. Understanding the propensities (MPC, MPW) is the "secret key" to calculating exactly how big those swings will be.