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## Multiplier Macroeconomics

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In Macroeconomics, it is important to understand the following relationships:

Disposable income and consumption

Disposable income and saving

The interest rate and investment

Changes in spending and changes in real GDP

The Relationship Between Income and Consumption

Disposable (after-tax) income equals

savings (S) plus consumption (C).

Economists define personal saving as “not spending” or “that part of disposable income not consumed.”

The Consumption Schedule or “Consumption Function”

In the aggregate, households increase their spending as their disposable income rises and spend a larger proportion of a small disposable income than of a large disposable income.

Many factors determine the nation’s levels of consumption and saving, but the most significant is disposable income.

“Saving Function”

There is a direct relationship between saving and disposable income but saving is a smaller proportion of a small DI than of a large DI. Households consume a smaller and smaller proportion of DI as DI increases; therefore, they must be saving a larger and larger proportion.

Dissaving (consuming in excess of after-tax income) will occur at relatively low DIs.

Households can consume more than their incomes by liquidating (selling for cash) accumulated wealth or by borrowing.

Non income Determinants of Consumption and Saving(Other than disposable income, what else effects consumption and saving?)

Wealth

Expectations

Real Interest Rates

Household Debt

Taxation

Changes in wealth, expectations, interest rates, and household debt will shift consumption in one direction and saving in the opposite direction.

In contrast, a change in taxes will result in consumption and saving moving in the same direction. A tax increase shifts both downward, and a tax decrease shifts them upward.

Income minus taxes = Disposable Income

Marginal Propensity to Consume (MPC)

The proportion, or fraction, of any change in income consumed is called the marginal propensity to consume (MPC). The MPC is the ratio of a change in consumption to a change in the income that caused the consumption change.

MPC = change in consumption

change in income

Marginal Propensity to Save (MPS)

The fraction of any change in income saved is the marginal propensity to save (MPS). The MPS is the ratio of a change in saving to the change in income that brought it about:

MPS = change in saving

change in income

Marginal Propensities

- How much of every additional dollar in income is consumed? MPC
- How much of every additional dollar iin income is saved? MPS
- MPC + MPS = $1 of additional income
- .: MPC = 1 – MPS
- .: MPS = 1 – MPC
- Remember, people do two things with their disposable income, consume it or save it!

THE SPENDING MULTIPLIER (Sometimes called the expenditures multiplier)

When C or Ig or G or Xn increases, real GDP also increases.

But the total increase in real GDP is larger than the initial increase in spending.

The multiplier is the amount by which a change in any component of spending is magnified or multiplied to determine the change that it generates in real GDP.

The Ripple Effect

- INTERACTIVE GRAPHIC: A look at how one business closing changed the spending habits of just one person - OrlandoSentinel.com

A change in spending ultimately changes output and income by more than the initial change in investment spending. This is called the multiplier effect.

Calculating the Spending Multiplier

- The Spending Multiplier can be calculated from the MPC or the MPS.
- Multiplier = 1/1-MPC or 1/MPS
- Multipliers are (+) when there is an increase in spending and (–) when there is a decrease in spending
- You multiply the multiplier times the initial increase in spending to determine total effect on real GDP.

MPS, MPC, & Multipliers

- Ex. Assume U.S. citizens spend 90¢ for every extra $1 they earn. Further assume that the real interest rate (r%) decreases, causing a $50 billion increase in gross private investment. Calculate the effect of a $50 billion increase in IG on U.S. Aggregate Demand (AD).
- Step 1: Calculate the MPC and MPS
- MPC = ΔC/ΔDI = .9/1 = .9
- MPS = 1 – MPC = .10
- Step 2: Determine which multiplier to use, and whether it’s + or -
- The problem mentions an increase in Δ IG .: use a (+) spending multiplier
- Step 3: Calculate the Spending and/or Tax Multiplier
- 1/MPS = 1/.10 = 10
- Step 4: Calculate the Change in AD
- (Δ C, IG, G, or XN) * Spending Multiplier
- ($50 billion Δ IG) * (10) = $500 billion ΔAD

Calculating the Tax Multiplier

- When the government increases or decreases taxes, the multiplier is determined using a different formula because tax increases or tax decreases will change disposable income.
- Tax Multiplier (note: it’s negative if it is a tax increase)
- = -MPC/1-MPC or -MPC/MPS
- If there is a tax-CUT, then the multiplier is +, because there is now more money in the circular flow

MPS, MPC, & Multipliers

- Ex. Assume Germany raises taxes on its citizens by €200 billion . Furthermore, assume that Germans save 25% of the change in their disposable income. Calculate the effect the €200 billion change in taxes on the German economy.
- Step 1: Calculate the MPC and MPS
- MPS = 25%(given in the problem) = .25
- MPC = 1 – MPS = 1 - .25 = .75
- Step 2: Determine which multiplier to use, and whether it’s + or -
- The problem mentions an increase in T.: use (-) tax multiplier
- Step 3: Calculate the Spending and/or Tax Multiplier
- -MPC/MPS = -.75/.25 = -3
- Step 4: Calculate the Change in AD
- (Δ Tax) * Tax Multiplier
- (€200 billion Δ T) * (-3) = -€600 billion Δ in AD

The Balanced Budget Multiplier

- When Government spending increases are matched with an equal increase in taxes (to balance the budget), the resulting change in real GDP ends up being = to the change in Government spending
- Why?
- 1/MPS + -MPC/MPS = 1- MPC/MPS = MPS/MPS = 1
- The balanced budget multiplier always = 1
- 1 times the increase in Government spending = Total impact on real GDP

MPS, MPC, & Multipliers

- Ex. Assume the Japanese spend 4/5 of their disposable income. Furthermore, assume that the Japanese government increases its spending by ¥50 trillion and in order to maintain a balanced budget simultaneously increases taxes by ¥50 trillion. Calculate the effect the ¥50 trillion change in government spending and ¥50 trillion change in taxes on Japanese Aggregate Demand.
- Step 1: Calculate the MPC and MPS
- MPC = 4/5 (given in the problem) = .80
- MPS = 1 – MPC = 1 - .80 = .20
- Step 2: Determine which multiplier to use, and whether it’s + or -
- The problem mentions an increase in G and an increase in T.: combine a (+) spending with a (–) tax multiplier
- Step 3: Calculate the Spending and Tax Multipliers
- Spending Multiplier = 1/MPS = 1/.20 = 5
- Tax Multiplier = -MPC/MPS = -.80/.20 = -4
- Step 4: Calculate the Change in AD
- [ Δ G * Spending Multiplier] + [ Δ T * Tax Multiplier]
- [(¥50 trillion Δ G) * 5] + [(¥50 trillion Δ T) * -4]
- [ ¥250 trillion ] + [ - ¥200 trillion ] = ¥50 trillion Δ AD

How Large is the Actual Multiplier Effect?

The Council of Economic Advisers, which advises the U.S. President on economic matters, has estimated that the actual multiplier effect for the United States is about 2.

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