# The Keynesian multiplier

The followers of Keynes believed that fiscal policy can be a powerful lever to move the economy because the effect of an increase in spending or a cut in taxes would be multiplied by stimulating additional demand for consumption goods by households.

Imagine that in the midst of a recession the government spends \$100 million for new highway bridge construction. Idle workers and machines will be put to work on bridge construction, resulting in an increase in GDP of \$100 million over the period of construction. In addition, construction workers and firm owners will find that their incomes have risen by \$100 million. These people will spend at least part of that \$100 million on additional consumer goods and services, but they will also save some of the additional income. This sets off a chain reaction in which additional spending boosts the income of sellers of goods and services who, in turn, spend more on other goods and services.

Let's build a simple model to see how the marginal propensity to consume determines the impact of a change in government spending on GDP. We begin with a hypothetical \$100 increase in government purchases of goods and services in an economy which consists of households having identical marginal propensity to consume which we will abbreviate mpc. To simplify the model, households in our model provide goods or services directly to the government, so we can imagine that the government pays the \$100 to one household, say household #1.

Now household #1 will spend the fraction equal to its mpc of that additional income to purchase consumption goods, and for simplicity we suppose that the purchase is made directly from household #2. Seeing its disposable income rise by \$1 times mpc, household #2 will purchase additional consumer goods worth mpc times that amount, say from household #3. We see that the additional consumption spending at each step of this chain reaction is mpc times the amount at the prior step.

This table depicts a chain reaction of spending which continues on indefinitely as it produces ever smaller increments to GDP.

 Round 1 Initial Spending by Govt 100 m Round 2 80% of 100 m spend 80 Round 3 80% of 80m spend 64 Round 4 80% of 64m spend 51.2 Round5 80% of 51.20 m spend 40.96 Round 6 80% of 40.96m spend 32.768 Round 7-19 Goes on till all money is spent Round 20 60% of 0.01 0.01 Total spending, including the initial spending by government 249.99

## Components of Multiplier

• Marginal propensity to consume (MPC):Proportion of income which is spent by the household
• Marginal propensity to withdraw (MPW): Proportion of income which does not re-enter the cycle. It is the total of MPS+MRT+MPM.
• Marginal propensity to save (MPS): Proportion of income which is saved.
• Marginal rate of taxation (MRT): Proportion of income which goes out as taxes to government
• Marginal propensity to import (MPM): Proportion of income which goes out as import expenditure.

## Formula

1/(1-mpc)

Or 1/mpw

Or 1/mps+mrt+mpm

The government spending and tax cut multipliers depend on the marginal propensity to consume, the fraction of each additional dollar of disposable income that households will spend on consumption. If the mpc is large then the multipliers are large, but if the mpc is zero, then government spending will have no multiplier effect on the economy and a tax cut will have no effect at all. The key parameter is the mpc and the key question is: how large is the mpc?

## Example

Calculate the multiplier for any economy where the MPC=.75

Investment = \$50,000

The result will be….

1/1-.75 = 1/.25 = 4

i.e. 4X50,000=\$200,000

Thus any injection of \$50,000 into the economy will lead to 4 times increase in National income i.e. \$200,000

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