Marginal propensity to consume and save

In macroeconomics, understanding how people use additional income is key to analyzing economic changes. When disposable income (the income available after taxes) increases, individuals decide how much to spend and how much to save. These decisions are captured by two important concepts: the marginal propensity to consume and the marginal propensity to save.

Marginal propensity to consume (MPC)

The marginal propensity to consume (MPC) measures the proportion of an additional dollar of disposable income that is spent on consumption, such as buying goods and services. This occurs because extra income often leads to more spending, which stimulates the economy.

Formula for MPC:

$\text{MPC}=\frac{\text{change in consumer spending}}{\text{change in disposable income}}$

Where:

• Change in consumer spending = Increase in spending on goods and services ($)
• Change in disposable income = Increase in income after taxes ($)

Marginal propensity to save (MPS)

The marginal propensity to save (MPS) measures the proportion of an additional dollar of disposable income that is saved rather than spent. This represents money set aside, which temporarily removes it from the spending cycle in the economy.

Formula for MPS:

$\text{MPS}=\frac{\text{change in saving}}{\text{change in disposable income}}$

Where:

• Change in saving = Increase in saved income ($)
• Change in disposable income = Increase in income after taxes ($)

Relationship between MPC and MPS

Any additional disposable income is either spent or saved, so the sum of MPC and MPS always equals 1. This relationship is crucial because a higher MPC means more spending, which can amplify economic growth, while a higher MPS means more saving, which can slow it down.

Formula for the relationship between MPC and MPS:

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

The expenditure multiplier and its role in aggregate demand

The expenditure multiplier explains how an initial change in spending can lead to a larger overall change in economic output. This happens because one person's spending becomes another person's income, creating a chain reaction of further spending. The multiplier is tied to the MPC, as it shows how much aggregate demand (total spending in the economy) expands from changes in components like investment or government spending.

How the expenditure multiplier works

A $1 increase in autonomous expenditures (spending not dependent on income levels, such as new investments) triggers additional rounds of spending. For example, if a business invests in new equipment, the workers paid for that equipment spend part of their earnings, and so on. The size of this ripple effect depends on the MPC.

Formula for the expenditure multiplier:

$\text{Expenditure multiplier}=\frac{1}{1-\text{MPC}}$

Where:

• MPC = Marginal propensity to consume

This formula demonstrates that a higher MPC results in a larger multiplier, as more of each dollar is respent in the economy.

The tax multiplier and its impact on aggregate demand

The tax multiplier shows how changes in taxes affect aggregate demand and overall economic output. Unlike direct spending changes, tax adjustments influence disposable income, which then affects consumption based on the MPC. A tax cut increases disposable income and boosts spending, while a tax increase does the opposite.

How the tax multiplier works

When taxes change, they indirectly alter spending through disposable income. The tax multiplier is typically smaller in magnitude than the expenditure multiplier because it first affects income before spending. It is negative for tax increases, indicating a reduction in aggregate demand.

Formula for the tax multiplier:

$\text{Tax multiplier}=-\frac{\text{MPC}}{1-\text{MPC}}$

Where:

• MPC = Marginal propensity to consume

The negative sign reflects that higher taxes reduce spending, while lower taxes increase it.

How changes in spending and taxes affect real GDP

Real GDP (gross domestic product adjusted for inflation) measures the total output of goods and services in an economy. Changes in spending or taxes can shift aggregate demand, leading to adjustments in real GDP. These changes create multiplier effects that amplify the initial impact.

Effects of spending changes on real GDP

An increase in autonomous spending, such as government purchases, raises aggregate demand. This leads to higher production, employment, and income, with the expenditure multiplier magnifying the effect. As a result, real GDP increases by more than the initial spending change, assuming the economy has unused resources.

Effects of tax changes on real GDP

A tax cut boosts disposable income, encouraging more consumption and increasing aggregate demand. The tax multiplier shows the total rise in real GDP. Conversely, a tax increase reduces disposable income and spending, lowering aggregate demand and real GDP.

These dynamics illustrate how fiscal policy (government decisions on spending and taxes) can stabilize or stimulate the economy, especially during recessions or booms.

Calculating changes in real GDP using multipliers

To determine the impact on real GDP, multiply the initial change in spending or taxes by the appropriate multiplier. This calculation assumes a closed economy without other complicating factors.

Formula for change in real GDP from spending changes:

$\text{Change in real GDP}=\text{initial change in spending}\times \text{expenditure multiplier}$

Formula for change in real GDP from tax changes:

$\text{Change in real GDP}=-\text{initial change in taxes}\times \text{tax multiplier}$

Note that the negative sign in the tax formula accounts for the inverse relationship: tax cuts (negative change) increase GDP, while tax increases (positive change) decrease it.

Worked example - Calculating change in real GDP from a spending increase

Suppose the government increases autonomous spending by $50 billion in an economy where the MPC is 0.8. Calculate the expenditure multiplier and the total change in real GDP.

Step 1: Identify the values

• Initial change in spending = $50 billion
• MPC = 0.8

Step 2: Calculate the expenditure multiplier

$\text{Expenditure multiplier}=\frac{1}{1-0.8}=\frac{1}{0.2}=5$

Step 3: Calculate the change in real GDP

$\text{Change in real GDP}=\$50\text{ billion}\times 5=\$250\text{ billion}$

Step 4: Interpretation

The initial $50 billion spending increase leads to a $250 billion rise in real GDP due to the multiplier effect.

Worked example - Calculating change in real GDP from a tax cut

In an economy with an MPC of 0.75, the government cuts taxes by $20 billion. Calculate the tax multiplier and the total change in real GDP.

Step 1: Identify the values

• Initial change in taxes = -$20 billion (negative for a cut)
• MPC = 0.75

Step 2: Calculate the tax multiplier

$\text{Tax multiplier}=-\frac{0.75}{1-0.75}=-\frac{0.75}{0.25}=-3$

Step 3: Calculate the change in real GDP

$\text{Change in real GDP}=-(\$20\text{ billion})\times (-3)=\$60\text{ billion}$

Step 4: Interpretation

The $20 billion tax cut results in a $60 billion increase in real GDP, showing how tax reductions can stimulate economic output.