Government purchases are commonly assumed to be totally autonomous in the introductory analysis of Keynesian economics. That is, any induced government purchases that realistically exist are ignored. Doing so not only simplifies the analysis, but also places the focus on how and why autonomous government purchases changes, and how such changes affect the macroeconomy. More sophisticated, and realistic, analysis then includes induced government purchases.

Government purchases are induced because governments, especially state and local governments, are prone to use tax revenues generated by a growing, expending economy to finance government purchases. If the economy is growing and expanding, then income is greater and so too is tax revenue. Because most state and local governments face legal constraints that restrict spending to tax revenue, more revenue means more spending and less revenue means less spending. As such, government purchases are induced by the increase in aggregate income and production. While induced government purchases are not nearly as big or important as induced consumption, they do play a key role in Keynesian economics. They affect the determination of equilibrium and the magnitude of the multiplier',500,400)">multiplier process.

Induced government purchases are reflected by the slope of the government purchases line and the marginal propensity for government purchases (MPG). The MPG is important to the slope of the aggregate expenditures line',500,400)">aggregate expenditures line which also affects the value of the expenditures multiplier.

Induced: An Equation

G

=

g

+

hY

As with any linear equation, the two key parameters that characterize this government purchases equation are slope and intercept. Induced government purchases are indicated by the slope of the government purchases equation. Autonomous government purchases are indicated by the intercept.

• An Induced Slope: The slope of the government purchases equation (h) measures the change in government purchases resulting from a change in income. If income changes by $1, then government purchases changes by $h. This slope is generally assumed and empirically documented to be greater than zero, but less than one (0 < h < 1). It is conceptually identified as induced government purchases and is measured as the marginal propensity for government purchases (MPG).


• An Autonomous Intercept: The intercept of the government purchases equation (g) measures the amount of government purchases undertaken if income is zero. If income is zero, then government purchases are $g. The intercept is generally assumed and empirically documented to be positive (0 < g). It is conceptually identified as autonomous government purchases.

Induced: A Line

Government Purchases Line

However, government purchases are realistically induced by the level of income and production in the economy. An induced government purchases line has a positive slope. And because government purchases are only modestly induced by income and production, an induced government purchases line has a slight slope. A click of the [Induced A Little] button illustrates induced government purchases (with a comparison to the autonomous government purchases line).

The new red line, labeled G' in the exhibit, is the positively-sloped government purchases line for the equation: G = 2 + 0.05Y. This line indicates that greater levels of income generate greater government purchases by the government sector.

The two primary characteristics of this government purchases line--slope and intercept--indicate the difference between autonomous government purchases and induced government purchases.

• An Induced Slope: The slope of this new government purchases line is positive, but less than one. In this case the slope is equal to 0.05, a $1 change in aggregate production induces a $0.05 change in government purchases. This positive slope indicates induced government purchases. Moreover, the slope of the line is also the marginal propensity for government purchases (MPG).


• An Autonomous Intercept: This new government purchases line, like the original line, intersects the vertical axis at a positive value of $2 trillion. And once again this indicates autonomous government purchases.

Other Induced Expenditures

• Consumption is unquestionably the most important induced expenditure. It is not only the largest of the four aggregate expenditures, but it is also the most induced of the four. It captures the fundamental psychological law and triggers the largest change in expenditures resulting from a change in income or production.


• Investment is induced by income because an expanding economy generally boosts business profit, which is then used for investment expenditures on capital goods.


• Net exports, the difference between exports and imports, are induced through imports, which are induced in the same fashion as government purchases. An increase in income is not just used to purchase domestic goods, but also imported goods.