# Spending Multiplier

Spending multiplier (also known as fiscal multiplier or simply the multiplier) represents the multiple by which GDP increases or decreases in response to an increase and decrease in government expenditures and investment. It is the reciprocal of the marginal propensity to save (MPS). Higher the MPS, lower the multiplier, and lower the MPS, higher the multiplier.

The spending multiplier is closely related to the multiplier effect. Assume that households consume 80% of any increase in their income and that the government increases its expenditure by $20 billion. Any government expenditure is actually income of households in the form of wages, interest, rent and profit. Since MPC is 0.8, households will consume$16 billion of the increased income (= 0.8 × $20billion). The$16 billion increase in consumption will trigger second round of increase in incomes (for people associated with production of the consumed products and services) which in turn will trigger second round of consumption amounting to $12.8 billion (= 0.8 × 0.8 ×$20 billion), and so on. The resulting effect is that the GDP increases by a multiple of initial increase in government expenditures. This multiple is the spending multiplier. A decrease in government expenditures decreases GDP by a multiple in the same fashion.

## Formula

 Spending Multiplier = 1 = 1 MPS 1 − MPC

Where,
MPS stands for marginal propensity to save which is the percentage of any addition in income which households are going to save; and
MPC stands for marginal propensity to consume and it is the percentage of any addition in income which households are expected to consume.

By definition, MPS + MPC = 1 and MPS = 1 − MPC.

## Examples

Example 1: Lucre Island is a pirate country in which people rarely plan. They are known to spend whatever they can grab.

Since the country have a marginal propensity to consume of almost 100%, marginal propensity to save is 0 (= 1 − 100%), which gives us an infinite spending multiplier (1 ÷ 0 = ∞)

Example 2: Khembalung is a country home to Buddhist monks. They live an extremely simplistic life, and though the country is replete with precious stones, the monks are rarely interested in any luxuries and they have almost zero marginal propensity to consume.

The country has a marginal propensity to consume of almost 0, which gives us a marginal propensity to save of 1 and a spending multiplier of 1. This means that there is no multiplier effect.

Example 3: Average per capita income in Anvilania rose from $42,300 dollars to$50,000 while corresponding figures for per capita consumption rose from $35,400 to$42,500. Find the spending multiplier.

Solution

 MPC = Increase in Consumption = 42,500 − 35,400 = 92.2% Increase in Income 50,000 − 42,300

MPS = 1 − MPC = 1 − 92.2% = 7.8%

 Spending Multiplier = 1 = 1 = 12.82 MPS 7.8%

Written by Obaidullah Jan