The Multiplier and the Consumption Function

Module 16

Spending

In 2009, the US Congress passed the American Recovery and Reinvestment Act – a $787 billion program to spark job growth and combat the recession.

Why did economists think a stimulus package would help the economy?

Spending

Each $1 spent by the government would produce some multiple of dollars earned and spent by consumers

The Government Spends Money that ends up in someone’s pocket

That person spends some of that money and it ends up in someone else’s pocket

And so on…

And so on…

Figure 10.1 The Circular-Flow DiagramRay and Anderson: Krugman’s Macroeconomics for AP, First EditionCopyright © 2011 by Worth Publishers

Spending

But spending can also come from other sources – including investment…

Spending

Suppose the housing construction industry spent an additional $100 billion on new construction of homes:

1) That’s an additional $100 billion to GDP2) That $100 billion goes to others who will spend some of it3) Let’s say the people who get the $100 billion save $20 billion

and spend the rest4) That’s $80 billion in more activity that goes into pockets as

profits or wages5) Those people in turn save $16 billion and spend $64 billion6) And so on…

The Multiplier

The initial $100 billion investment is called the autonomous change in spending.

How much total increase to GDP should result from this $100 billion autonomous change in spending?

We could add up all the rounds of spending…

Change in GDP = ($100 billion + $80 billion + 64 billion + …)

But this is an infinite series, and who has the time?

The Multiplier

Instead, we can calculate the multiplier (M) – a value by which we can multiply the autonomous change in spending to obtain the change in output:

ΔY = M x ΔAAS

Δ = change inY = output (GDP)AAS = autonomous spending

The Multiplier

To determine the value of this multiplier, we need to know what proportion of the money people receive they will end up spending

We call this the marginal propensity to consume (MPC)

MPC = Δ Consumer spendingΔ Disposable income

The Multiplier

Total spending would equal:AAS + MPC (AAS) + MPC2(AAS) + MPC3(AAS)…

OrAAS (1 + MPC + MPC2 + MPC3…)

And(1 + MPC + MPC2 + MPC3…) = 1 = M

(1-MPC)

The Multiplier

In our example, people spent $80 billion of the $100 billion, so:

MPC = 80/100 = .8

We can then use the formula for the multiplier:M = 1/(1-MPC)M = 1/(1-.8) = 1/.2 = 5

Total increase in GDP = ΔY = M x ΔAAS = 5 x $100 Billion = $500 Billion

Spending and Saving

Notice in our example that whatever money was not spent, was saved.

We can also calculate a marginal propensity to save (MPS)

MPS = Δ Consumer savingsΔ Disposable income

Spending and Saving

Since these represent the only two options for disposing of income, we can say that:

MPC + MPS = 1

Which also means: MPS = 1-MPC

So the multiplier = 1/(1-MPC) OR 1/MPS

Example

1. Data show that when consumers received an additional $20 million in income, they put $5 million in the bank

a. Calculate the marginal propensity to consume

b. How much would output increase with an autonomous aggregate spending increase of $30 million

Example

2. Suppose a $1 million business investment generates a $2.5 million increase in GDP

a. Calculate the marginal propensity to consume

Household Consumption

How does household consumer spending relate to household income?

There will be some spending, no matter what income level – we call this autonomous consumer spending

And then spending of additional income will be governed by the MPC

Figure 16.1 Current Disposable Income and Consumer Spending for American Households in 2008Ray and Anderson: Krugman’s Macroeconomics for AP, First EditionCopyright © 2011 by Worth Publishers

The Consumption Function

An equation showing how an individual household’s consumer spending varies with the

household’s disposable income

c = a + MPC × yd

Where:c = consumer spendinga = autonomous consumer spendingyd = disposable income

Figure 16.2 The Consumption FunctionRay and Anderson: Krugman’s Macroeconomics for AP, First EditionCopyright © 2011 by Worth Publishers

Aggregate Consumption Function

An equation showing how aggregate consumer spending varies with aggregate disposable income

C = A + MPC × YD

Where:C = aggregate consumer spendingA = autonomous aggregate consumer

spendingYD = aggregate disposable income

Income Effect

• If you expect that your income will continue to rise, you will spend more now than your current income would otherwise indicate

• Permanent Income Hypothesis– Milton Friedman– Consumer spending is more dependent on

expectations of future income than of current income

Figure 16.4 Shifts of the Aggregate Consumption FunctionRay and Anderson: Krugman’s Macroeconomics for AP, First EditionCopyright © 2011 by Worth Publishers

Effect of Expected Income

Incomes expected to rise:Increase in autonomous

spending

Incomes expected to fall:Decrease in autonomous

spending

Wealth Effect

• Wealth– accumulated savings and assets over time– Affects consumer spending– Increased aggregate wealth increases aggregate

spending

• Life-Cycle Hypothesis– People plan their spending across their lifetimes– Save more earlier, spend out of savings later

Investment Spending

• Investment spending also drives GDP and the business cycle, though to a lesser extent than consumer spending

• Recessions often start with declines in investment spending– Planned v. actual spending– What affects investment spending?

Interest Rates

• The cost of borrowing money

• Particularly affects construction industry as interest rates will be faced by both producers and consumers

• Inverse relationship – as interest rates rise, investment spending falls

Expected Growth in GDP

• If businesses expect sales to grow more in the future, they will increase investment spending in the present– New production capacity

• If business expect slow growth, investment spending declines– maintain or replace obsolete production capacity

Inventories

• Businesses will often satisfy demand out of inventories

• Higher than planned inventories can result from lower than expected sales– Unplanned inventory investment– Increasing inventories could mean economy is slowing

Actual Investment Spending=Planned investment spending + Unplanned inventory investment

ProblemsFor each event, explain whether the initial effect is a change in planned investment spending or a change in unplanned inventory investment, and indicate the direction of the change

1. An unexpected increase in consumer spending

2. A sharp rise in the cost of borrowing

3. A sharp increase in the economy’s growth rate of real GDP

4. An unanticipated fall in sales