The marginal propensity for government purchases is important to the study of Keynesian economics. First, the MPG reflects induced government purchases. Second, the MPG is the slope of the government purchases line, which makes it important to the slope of the aggregate expenditures line, as well. Third, the MPG affects the multiplier process and affects the magnitude of the expenditures and tax multipliers.

The MPG Formula

MPG

=

change in government purchases change in income

• First, it quantifies induced government purchases, that is, how much government purchases are induced by extra dollar. If income or production changes by $1, then government purchases change by the value of the MPG. Income induces the change in government purchases at a rate measured by the MPG.


• Second, the MPG is actually a measure of the slope of the government purchases line that plots the relation between government purchases and income. The measurement of slope is generally given as the "rise" over the "run." For the government purchases line, the rise is the change in government purchases and the run is the change in income.

The Slope Of The Line

Government Purchases Line

This government purchases line reflects a plot of the following government purchases equation:

G

=

2

+

0.05Y

In particular, as specified in this government purchases equation, the slope of this government purchases line is equal to 0.05. This slope value indicates that each $1 change in income induces a $0.05 change in government purchases. In general, slope is calculated as the "rise" over the "run," that is, the change in the variable on the vertical axis (government purchases) divided by the change in the variable on the horizontal axis (production or income).

The change in government purchases divided by the change in income or production is the specification of the marginal propensity for government purchases. That is, the slope of the government purchases line is the marginal propensity for government purchases. To highlight this point, click the [Slope] button in this exhibit.

Moreover, because the government purchases line is a straight line, the slope is constant over the entire range of income. This means that the marginal propensity for government purchases is also constant.

Multiplier

The basic multiplier process results because a change in production (such as what occurs when autonomous investment expenditures purchase capital goods) generates income, which then induces consumption. However, the resulting consumption is also an expenditure on production, which generates more income, which induces more consumption. This next round of consumption also triggers a change in production, which generates even more income, and which induces even more consumption.

And on it goes, round after round. The end result is a magnified, multiplied change in aggregate production initially triggered by the change autonomous investment, but amplified by the change in induced consumption.

The multiplier process with induced consumption is augmented by induced government purchases. The change in production and income generated by the autonomous change in government purchases induces changes in both consumption AND GOVERNMENT PURCHASES. Because both are expenditures on production, both generate more income, which induces more consumption AND GOVERNMENT PURCHASES, which generates more income, and which induces even more consumption AND GOVERNMENT PURCHASES.

The MPG enters into the process along with the marginal propensity to consume (MPC) because it determines how much government purchases are induced along with the induced change in consumption with each change in production and income. If the MPG is greater, then the multiplier process is also greater as more government purchases are induced with each round of activity.

This connection between the multiplier process, the marginal propensity to consume, and the marginal propensity for government purchases is illustrated in the standard formula for an expenditures multiplier:

expenditures multiplier

=

1 (1 - (MPC + MPG))

For example, given a marginal propensity to consume of 0.75, a marginal propensity for government purchases of 0.05 results in a multiplier of 4. In contrast, a larger marginal propensity for government purchases of 0.15 results in a larger multiplier of 10.

Other Marginals

Here a few of the more important marginals:

• Marginal Propensity to Consume: The most important marginal in the study of Keynesian economics is the marginal propensity to consume (MPC). This embodies the fundamental psychological law indicating that an increase in income induces changes in consumption. The MPC is the slope of the consumption line and thus forms the foundation of the slope of the aggregate expenditures line. This marginal is also key to the magnitude of the multiplier process.


• Marginal Propensity to Save: The flip side of consumption is saving. The fundamental psychological law indicates that an increase in income induces changes in both consumption and saving. The marginal propensity to save (MPS) quantifies the saving part of this relation. It indicates the change in saving resulting from a change in income. In fact, if the MPC and MPS are calculated based on after-tax disposable income, then the two marginals sum to one: MPG + MPS = 1.


• Marginal Propensity to Invest: Consumption is not the only one of the aggregate expenditures induced by income and with a corresponding marginal. The marginal propensity to invest (MPI) is the change in investment induced by a change in income. The induced change in investment is not nearly as big as consumption, but it does affect the slope of the aggregate expenditures line and the size of the multiplier.


• Marginal Propensity to Import: The last of the four aggregate expenditures, net exports (exports minus imports), also has a corresponding marginal. However, the marginal is not for net exports proper, but for the imports part. The marginal propensity to import (MPM) is the change in imports induced by a change in income. The induced change in imports is closely connected to the marginal propensity for government purchases. That is, a portion of government purchases is actually used to purchase imports, which is reflected the marginal propensity to import.