Average propensity to consume and save

Spending and saving play key roles in an economy. Spending keeps money circulating, while saving removes it from the flow. The average propensity formulas show the share of total national income that goes towards consumption or saving.

Average propensity to consume (APC)

$\text{APC}=\frac{\text{consumption}}{\text{total income}}$

Where:

• Consumption = Amount spent on goods and services
• Total income = Overall national income

Average propensity to save (APS)

$\text{APS}=\frac{\text{amount saved}}{\text{total income}}$

Where:

• Amount saved = Portion of income not spent
• Total income = Overall national income

Marginal propensity to consume and save

Marginal propensities focus on how changes in income affect spending and saving. These concepts are central to understanding economic multipliers, as they show how additional income circulates or leaves the economy.

Marginal propensity to consume (MPC)

$\text{MPC}=\frac{\text{change in consumption}}{\text{change in income}}$

Where:

• Change in consumption = Increase in spending due to extra income
• Change in income = Additional income received

Marginal propensity to save (MPS)

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

Where:

• Change in saving = Increase in saving due to extra income
• Change in income = Additional income received

Significance of MPC and MPS

• Link to multiplier - MPC and MPS influence the multiplier's size. A higher MPC means more spending, leading to a larger multiplier effect as money circulates further.
• Impact of saving - High MPS reduces the multiplier, as saved money does not generate further income for others.
• Variations by income and development - Lower-income individuals and less developed economies typically have higher MPCs, resulting in larger multipliers.

Calculating the multiplier effect using MPC

The multiplier effect shows how an initial injection of money leads to a greater rise in national income, depending on how much of that income is spent.

The multiplier using MPC

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

Where:

• MPC = Marginal propensity to consume

A higher MPC results in a larger multiplier, as more income is respent in the economy.

Worked example - Calculating the multiplier using MPC

An economy receives an injection of £100 million. If every extra £1 of income results in 80p being spent on goods and services within the country, calculate the MPC, the multiplier, and the total increase in national income.

Step 1: Identify the values

• Change in consumption per £1 = £0.80
• Injection = £100 million

Step 2: Determine the MPC

$\text{MPC}=\frac{\text{change in consumption}}{\text{change in income}}$

$\text{MPC}=\frac{0.80}{1}=0.80$

Step 3: Calculate the multiplier

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

$\text{Multiplier}=\frac{1}{1-0.80}$

$\text{Multiplier}=\frac{1}{0.20}=5$

Step 4: Calculate total increase in national income

Total increase = injection × multiplier
Total increase = £100 million × 5 = £500 million

Marginal propensity to withdraw and the multiplier

Extra income can be withdrawn from the economy rather than spent, reducing circulation. This approach provides another way to calculate the multiplier.

Marginal propensity to withdraw (MPW)

$\text{MPW}=\text{MPS}+\text{MPT}+\text{MPM}$

Where:

• MPS = Marginal propensity to save (proportion saved)
• MPT = Marginal propensity to tax (proportion paid in taxes, also known as marginal tax rate)
• MPM = Marginal propensity to import (proportion spent on imports)

Relationship between MPC and MPW

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

Since income is either spent or withdrawn, a lower MPW means a higher MPC and greater circulation.

The multiplier using MPW

$\text{Multiplier}=\frac{1}{\text{MPW}}$

Where:

• MPW = Marginal propensity to withdraw

A smaller MPW leads to a larger multiplier, as less income leaves the economy.

Worked example - Calculating the multiplier using MPW

In an economy, the marginal propensity to save is 0.2, the marginal propensity to tax is 0.25, and the marginal propensity to import is 0.15. Calculate the MPW and the multiplier.

Step 1: Identify the components of MPW

• MPS = 0.2
• MPT = 0.25
• MPM = 0.15

Step 2: Calculate MPW

MPW = MPS + MPT + MPM
MPW = 0.2 + 0.25 + 0.15 = 0.6

Step 3: Calculate the multiplier

$\text{Multiplier}=\frac{1}{\text{MPW}}$

$\text{Multiplier}=\frac{1}{0.6}=1.67\text{ (to 3 s.f.)}$

Factors influencing the size of the multiplier

The multiplier's magnitude depends on how income is handled in the economy, affecting overall growth from injections.

Key factors affecting multiplier size

• MPC level - Higher MPC increases the multiplier, as more income is spent and recirculated.
• MPW level - Lower MPW enlarges the multiplier, with fewer withdrawals through saving, taxes, or imports keeping money in the economy.
• Tax rates - Low marginal tax rates reduce MPT and thus MPW, leading to a larger multiplier.
• Income and development levels - Lower incomes and less developed economies often show higher MPCs, resulting in bigger multipliers.