Grade 11

Advanced

10 min

Lesson 5 of 12

The Spending Multiplier and Crowding Out

Not Started

Calculating the ripple effects of government spending and the potential downsides of deficit spending.

If the government spends $1 billion on a new highway, does the economy grow by exactly$ 1 billion, or is there a hidden 'echo' that makes it worth much more—or potentially much less?

Learning Objectives

1.Calculate the spending multiplier using the Marginal Propensity to Consume (MPC).
2.Explain how the 'crowding out' effect can diminish the effectiveness of fiscal policy.
3.Compare the total economic impact of a $1 billion spending increase versus a$ 1 billion tax cut.

The Magic of the Multiplier

When the government spends money, that money doesn't just sit there; it becomes income for workers and business owners. These people then spend a portion of that income, which becomes income for someone else. This cycle is the Spending Multiplier. To calculate it, we look at the Marginal Propensity to Consume (MPC)—the fraction of every extra dollar earned that a person spends. The portion they don't spend is the Marginal Propensity to Save (MPS). Since every dollar is either spent or saved,

MPC + MPS = 1

. The formula for the Spending Multiplier (

k

) is:

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

or simply

k = \frac{1}{MPS}

Suppose the government spends $100 million on a bridge and the MPC in the economy is$ 0.8 $. 1. First, find the MPS:$ 1 - 0.8 = 0.2 $. 2. Calculate the multiplier:$ k = \frac{1}{0.2} = 5 $. 3. Calculate the total impact:$ \ $100\text{ million} \times 5 = \$ 500\text{ million} $. The initial$ 100 million injection resulted in a $500 million increase in Total Output (GDP).

Quick Check

If the MPC is 0.75, what is the spending multiplier?

First find the MPS (

1 - 0.75

), then divide 1 by that number.

Answer

Spending vs. Tax Cuts

Not all fiscal policy is created equal. A tax cut is generally less 'powerful' than a direct increase in government spending. Why? Because when the government spends

1, that full dollar enters the economy immediately. When the government cuts taxes by

1, people save a portion of that dollar (the MPS) before spending the rest. Therefore, the Tax Multiplier (

k_t

) is always smaller than the spending multiplier and is calculated as:

k_t = \frac{-MPC}{MPS}

This means a

1 billion tax cut will always result in less GDP growth than

1 billion in new spending.

An economy has an MPC of $0.9$ . The government wants to increase GDP by $100 billion. 1. Spending Multiplier:$ k = \frac{1}{0.1} = 10 $. Required spending:$ \ $100 / 10 = \$ 10\text{ billion} $. 2. Tax Multiplier:$ k_t = \frac{-0.9}{0.1} = -9 $. Required tax cut:$ \ $100 / 9 \approx \$ 11.11\text{ billion}$. Notice that you need a larger tax cut to achieve the same result as direct spending.

Quick Check

Why is the tax multiplier smaller than the spending multiplier?

Think about what happens to the very first dollar of a tax cut versus a government purchase.

Answer

Because households save a portion of a tax cut (the MPS) instead of spending the entire amount immediately.

The Crowding Out Effect

While the multiplier suggests that government spending is a 'free lunch,' the Crowding Out Effect provides a reality check. To fund deficit spending, the government must borrow money by selling bonds. This increases the demand for loanable funds, which pushes up interest rates. When interest rates rise, private businesses find it more expensive to borrow for new factories or equipment. Consequently, **Private Investment ( $I$ )** decreases. This 'crowds out' the private sector, potentially cancelling out the gains from the initial government spending.

Imagine the government spends $50 billion to stimulate the economy ($ MPC = 0.8 $). 1. Theoretical gain:$ 50 \times 5 = \ $250\text{ billion}$ increase in GDP. 2. However, the borrowing causes interest rates to rise from $3\%$ to $5\%$ . 3. Due to higher rates, private firms cancel $\$ 30\text{ billion} $in planned projects. 4. The 'lost' investment also has a multiplier:$ 30 \times 5 = \ $150\text{ billion}$ decrease in GDP. 5. Net Effect: $\$ 250 - \ $150 = \$ 100\text{ billion} $. The policy was only$ 40\%$ as effective as predicted.

Key Takeaways

1The Spending Multiplier ( $1/MPS$ ) quantifies how an initial change in spending ripples through the economy to create a larger total change in GDP.
2The Tax Multiplier is always smaller than the Spending Multiplier because consumers save a portion of their tax tax savings.
3Crowding Out occurs when government borrowing raises interest rates, which reduces private investment and weakens the impact of fiscal policy.

Quick Check

Multiple Choice

If the MPC is $0.9$ , what is the total change in GDP resulting from a $\$ 10$ billion increase in government spending?

Multiple Choice

Which of the following best describes the 'Crowding Out' effect?

True/False

A $500 tax cut will have a larger impact on GDP than$ 500 in new government spending.

What's Next?

Review Tomorrow

In 24 hours, try to write down the formulas for the Spending Multiplier and the Tax Multiplier from memory and explain why one is larger.

Practice Activity

Look up a recent news article about a government infrastructure project. Try to estimate the 'multiplier effect' it might have on that local city's economy.

Browse

Browse

The Spending Multiplier and Crowding Out

Learning Objectives

The Magic of the Multiplier

Spending vs. Tax Cuts

The Crowding Out Effect

Key Takeaways

Quick Check

What's Next?

The Spending Multiplier and Crowding Out

Learning Objectives

The Magic of the Multiplier

Spending vs. Tax Cuts

The Crowding Out Effect

Key Takeaways

Quick Check

What's Next?