Welcome to the Multiplier!
Ever wondered how a single decision by the government to build a new bridge can end up boosting the whole economy by much more than the cost of the bridge itself? That is the magic of the multiplier. In this chapter, we are going to look at the "ripple effect" of spending in the economy. Don't worry if it sounds like magic now; by the end of these notes, you'll see it's just a simple cycle of spending and earning!
What is the Multiplier?
The multiplier effect occurs when an initial injection (like government spending, investment, or exports) into the circular flow of income leads to a larger final increase in real National Income (GDP).
The Multiplier Process: A Step-by-Step Story
Imagine the government decides to spend £100 million building a new hospital. This is the initial injection. Here is what happens next:
1. Income for Workers: The construction company and its workers receive that £100 million as income.
2. Respending: Those workers don't just put all that money under a mattress! They spend some of it at local supermarkets, cafes, and cinemas.
3. New Income for Others: The supermarket owners and cafe staff now have extra income. They, in turn, spend some of that money on other goods and services.
4. The Result: This cycle continues. The final increase in total national income is much bigger than the original £100 million spent by the government.
Quick Review: The multiplier is simply the ratio of the final change in income to the initial change in injection.
The "Leaky Bucket" Analogy
If the multiplier is so great, why doesn't the economy grow forever? Think of the economy as a bucket being filled with water (spending). Every time money is passed from person to person, some of it "leaks" out of the bucket.
These leakages (also called withdrawals) are:
1. Savings (S): Putting money in a bank instead of spending it.
2. Taxes (T): The government taking a slice of your paycheck.
3. Imports (M): Spending money on goods from other countries (the money leaves our economy).
Key Takeaway: The more "leaks" there are, the smaller the multiplier will be, because there is less money left in the cycle to be spent in the next round.
The Math: Marginal Propensities
To calculate the multiplier, we need to know how much people usually spend or save when they get extra income. We call this the "Marginal Propensity."
1. Marginal Propensity to Consume (MPC)
The MPC is the portion of any extra income that a consumer spends. For example, if you get £10 extra and spend £8 of it, your MPC is 0.8.
2. The Withdrawals (MPW)
The Marginal Propensity to Withdraw (MPW) is the sum of all the "leaks":
\( MPW = MPS + MPT + MPM \)
Where:
- MPS: Marginal Propensity to Save
- MPT: Marginal Propensity to Tax
- MPM: Marginal Propensity to Import
Note: Because you either spend your extra income or you don't, \( MPC + MPW = 1 \). This means \( 1 - MPC \) is the same thing as \( MPW \).
How to Calculate the Multiplier Ratio
There are two main formulas you need to know. Both will give you the same answer!
Formula 1:
\( Multiplier = \frac{1}{(1 - MPC)} \)
Formula 2:
\( Multiplier = \frac{1}{MPW} \)
Let's try an example!
If consumers in the UK spend 80% of any new income they receive, what is the multiplier?
1. Identify the MPC: It is 0.8.
2. Use Formula 1: \( \frac{1}{(1 - 0.8)} = \frac{1}{0.2} = 5 \).
The Multiplier is 5. This means if the government spends £1bn, total national income will eventually rise by £5bn!
Common Mistake to Avoid: When calculating \( 1 / 0.2 \), students sometimes think the answer is 0.5. Remember, you are seeing how many times 0.2 goes into 1. The answer is 5!
Significance of the Multiplier for Aggregate Demand (AD)
The multiplier is very important for the AD/AS model. When there is an injection (like an increase in Investment), the AD curve shifts to the right.
However, because of the multiplier, the AD curve doesn't just shift once—it shifts even further. A small shift in investment can lead to a massive shift in total Aggregate Demand.
Why does the size of the multiplier matter to the government?
If the government wants to close a "recessionary gap" (when the economy is underperforming), they need to know the size of the multiplier. If the multiplier is large, they only need a small amount of spending to fix the economy. If the multiplier is small, they will have to spend a lot more money to get the same result.
Did you know? During the 2008 financial crisis, many governments used "stimulus packages" (spending money) hoping the multiplier would help their economies recover faster.
Factors Affecting the Size of the Multiplier
The multiplier is not the same in every country. It will be smaller if:
- Taxes are high: People have less disposable income to spend.
- People are afraid: If people are worried about the future, they save more (High MPS).
- We buy lots of imports: If we spend our extra money on German cars or American software, the money leaks out of the UK economy (High MPM).
Memory Aid: Think of the "TIMS" factors that reduce the multiplier: Taxes, Imports, and Money Saved.
Summary Key Takeaways
- The multiplier shows how an initial injection leads to a bigger final increase in National Income.
- MPC is how much we spend; MPW (MPS + MPT + MPM) is how much "leaks" out.
- Formula: \( Multiplier = 1 / MPW \) or \( 1 / (1 - MPC) \).
- A larger MPC means a larger multiplier.
- Governments use the multiplier to decide how much to intervene in the economy.
Don't worry if this seems tricky at first! Just remember the bridge example: one bridge leads to many paychecks, and many paychecks lead to lots of shopping!