﻿ Marginal propensities and the multiplier | Learn Economics

# Marginal propensities

Marginal propensities are an important concept in economics and refer to the likelihood (propensity) that a change in an injection in the circular flow of income will affect other components of the circular flow.

## Average and marginal propensities

Average propensity is the general tendency to allocate income towards a particular use - such as towards spending or saving. The average propensity to consume is the proportion of income that is spent, as shown below:

 AVERAGE PROPENSITY TO CONSUME (APC)  = CONSUMPTION C INCOME Y

Consider the following hypothetical example of an individual's spending and saving intentions at different income levels.

 INCOME SPENDING SAVING 40000 30000 10000 50000 35000 15000 60000 40000 20000 70000 45000 25000 80000 50000 30000

If we assume this individual has an income of 70,000, average propensity to consume (APC) is:

 AVERAGE PROPENSITY TO CONSUME (APC)  = 45000 = 0.643 70000

Marginal propensity is the specific tendency to allocate additional income towards a particular use - such as allocating and extra amount of income towards spending or saving. The marginal propensity to consume (MPC) is expressed as:

 MARGINAL PROPENSITY TO CONSUME (MPC)  = CHANGE IN CONSUMPTION ΔC CHANGE IN INCOME ΔY

In the above example, the marginal propensity to consume when income increases from 70,000 to 80,000 is:

 MARGINAL PROPENSITY TO CONSUME (MPC)  = ΔC = 5000 = 0.5 ΔY = 10000

### Average propensities

As well as the average propensity to consume we can also look at the average propensity to save (APS), the average propensity to pay tax (APT), and the average propensity to import (APM), which are calculated as:

 AVERAGE PROPENSITY TO SAVE (APS)  = SAVINGS S INCOME Y

 AVERAGE PROPENSITY TO TAX (APT)  = TAX PAID T INCOME Y

 AVERAGE PROPENSITY TO IMPORT (APM)  = IMPORT SPENDING M INCOME Y

### Marginal propensities

As well as the marginal propensity to consume, other marginal propensities include:

 MARGINAL PROPENSITY TO SAVE (MPS)  = CHANGE IN SAVING ΔS CHANGE IN INCOME ΔY
 MARGINAL PROPENSITY TO TAX (MPT)  = CHANGE IN TAXATION ΔT CHANGE IN INCOME ΔY
 MARGINAL PROPENSITY TO IMPORT (MPM)  = CHANGE IN IMPORTS ΔM CHANGE IN INCOME ΔY

## Marginal propensity to withdraw (MPW)

The marginal propensities, MPS, MPT, and MPM all relate to withdrawals out of the circular flow of income. These marginal withdrawals can be combined to create a single marginal propensity to withdraw (MPW), as shown below; We can now add some figures to illustrate the marginal propensity principles. If new income of 100 is added to the circular flow, and 20 is allocated to savings, 22 to taxation and 18 to imports, total withdrawals total 60, with 40 continuing to circulate in the economy. It must be true, therefore, that MPC + MPW = 1. New income can either be spent (giving us the MPC), or not spent, and withdrawn (giving us the MPW). ## Marginal propensities and the multiplier

A central feature of Keynesian analysis of national income equilibrium is the role of the multiplier process in helping understand how an new injection of spending adds to national income.

Given that income circulates between households and firms, any new injection of income will continue to add to income as it circulates. The extent to which a new injection adds to final income depends on the ratio of spending to withdrawing new income.

If individuals decide to spend a greater proportion of their new income on goods and services from domestic firms, then the multiplier process will continue for an extended period.

### Additional income and the multiplier process

In the following example, the additional income is 100, and the mpc = 0.4. This means that 40% of the new income is spent. This expenditure becomes incomes for others in the economy, and the recipients of this income spend 40%, and so on, until the new income generated approaches zero. The final change in income depends upon the marginal propensity to consume (MPC). In the above example, the final income will be 100+40+16+6.4+2.6..and so on.

If the mpc is much higher, say at 0.8, then 80% of new income is spent. The impact will approach zero at a much higher level of final income: 100+80+64+51.2+40.9 ...and so on. This illustrates the multiplier process - an initial injection of new spending leads to an increase in final income by a multiple factor.

### The multiplier ratio

We can calculate the value of the expenditure multiplier with a simple formula, which is:

 THE MULTIPLIER  = 1 or 1 1 - mpc mrw

In the above examples, where the mpc = 0.4, the multiplier would be:

 THE MULTIPLIER  = 1 or 1 = 1.67 1 - 0.4 0.6

This means the initial injection of 100 would lead to a final increase in income of 167.

In the example, where the mpc is much higher, at 0.8, the multiplier would be:

 THE MULTIPLIER  = 1 or 1 = 5.0 1 - 0.8 0.2

This means the initial injection of 100 would lead to a final increase in income of 500.

### Implications

The size of the expenditure multiplier is significant for policy makers in that the final value of any injection of government spending will depend on the size of the multiplier.

For example, in the case shown in the diagram below, an economy is faced with an output gap of 400bn. The current situation of the economy is that equilibrium national income is at 600bn, and full employment equilibrium is estimated to be at 1000bn, shown at Yf. The expenditure multiplier for this economy is estimated to be 2.0.

Because of the multiplier effect, the injection of new government spending (G) only needs to be 200bn to close the output gap.

## The size of the multiplier

Certain factors will reduce the size of the multiplier:

### Size of multiplier depends on:

1. Whether the economy is more 'open' or more 'closed'- which determines the size of the marginal propensity to import. An open economy has a relatively large trade sector as a proportion of GDP.
2. The marginal propensity to tax - a high marginal tax rate reduces the size of the multiplier.
3. Household's preference to save - a greater preference to save reduces the size of the multiplier.
4. Whether an injection of government spending - which, in theory, will have a multiplier effect - causes an opposite effect, called 'crowding out' where private sector investment falls as public sector spending increases.
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