AP MACRO UNIT 3 FORMULAS

Marginal Propensity to Consume (MPC)

The proportion of an aggregate raise in pay that a consumer spends on the consumption of goods and services as opposed to saving it. (D.I. is disposable income)

$$\text{MPC}=\frac{\Delta Consumption}{\Delta D.I.}$$

Marginal Propensity to Save (MPS)

The proportion of an increase in income that is saved rather than spent on consumable goods and services.

$$\text{MPS}=\frac{\Delta Spending}{\Delta D.I.}or1-MPC$$

Tax Multiplier

A measure of the change in aggregate output (GDP) caused by a change in government taxes. (D.I. is disposable income)

$$\text{Tax Multiplier}=\frac{-\text{MPC}}{1 - \text{MPC}}=-\frac{MPC}{MPS}$$

Relationship between MPC and MPS

The sum of the Marginal Propensity to Consume (MPC) and the Marginal Propensity to Save (MPS) must equal 1, representing that any change in disposable income is either consumed or saved.

$$\text{MPC} + \text{MPS} = 1$$

GDP using the Expenditure Approach

The sum of all expenditures made on final goods and services in an economy over a period of time.

$\text{GDP or AD }=C+I+G+(X-M)$
Where:

• $C$ = Consumption

• $I$ = Investment

• $G$ = Government Spending

• $X$ = Exports

• $M$ = Imports

Spending Multiplier

The ratio of the change in real GDP caused by an autonomous change in aggregate spending.

$\text{Spending Multiplier} = \frac{1}{1 - \text{MPC}}$ or $\frac{1}{\text{MPS}}$

impact of a change in spending on Real GDP

The change in real GDP resulting from an autonomous change in aggregate spending.

$$\Delta \text{Real GDP} = \text{Spending Multiplier} \times \Delta \text{Autonomous Spending}$$

impact of a change in taxes on Real GDP

The change in real GDP resulting from a change in government taxes.

$$\Delta \text{Real GDP} = \text{Tax Multiplier} \times \Delta \text{Taxes}$$

Required change in spending to close an output gap

The amount by which autonomous spending needs to change to close a specified output gap.

$$\text{Required Spending} = \frac{\text{Output Gap}}{\text{Spending Multiplier}}$$

Required change in taxes to close an output gap

The amount by which taxes need to change to close a specified output gap.

$$\text{Required Taxes} = \frac{\text{Output Gap}}{\text{Tax Multiplier}}$$