## What Is the Consumption Function?

The consumption function, or Keynesian consumption function, is an economic formula that represents the functional relationship between total consumption and gross national income. It was introduced by British economist John Maynard Keynes, who argued the function could be used to track and predict total aggregate consumption expenditures.

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## Understanding the Consumption Function

The classic consumption function suggests consumer spending is wholly determined by income and the changes in income. If true, aggregate savings should increase proportionally as gross domestic product (GDP) grows over time. The idea is to create a mathematical relationship between disposable income and consumer spending, but only on aggregate levels.

The stability of the consumption function, based in part on Keynes' Psychological Law of Consumption, especially when contrasted with the volatility of investment, is a cornerstone of Keynesian macroeconomic theory. Most post-Keynesians admit the consumption function is not stable in the long run since consumption patterns change as income rises.

## Calculating the Consumption Function

The consumption function is represented as:

﻿\begin{aligned}&C\ =\ A\ +\ MD\\&\textbf{where:}\\&C=\text{consumer spending}\\&A=\text{autonomous consumption}\\&M=\text{marginal propensity to consume}\\&D=\text{real disposable income}\end{aligned}﻿

## Assumptions and Implications

Much of the Keynesian doctrine centers around the frequency with which a given population spends or saves new income. The multiplier, the consumption function, and the marginal propensity to consume are each crucial to Keynes’ focus on spending and aggregate demand.

The consumption function is assumed stable and static; all expenditures are passively determined by the level of national income. The same is not true of savings, which Keynes called “investment,” not to be confused with government spending, another concept Keynes often defined as investment.

For the model to be valid, the consumption function and independent investment must remain constant long enough for national income to reach equilibrium. At equilibrium, business expectations and consumer expectations match up. One potential problem is that the consumption function cannot handle changes in the distribution of income and wealth. When these change, so too might autonomous consumption and the marginal propensity to consume.

## Other Versions

Over time, other economists have made adjustments to the Keynesian consumption function. Variables such as employment uncertainty, borrowing limits, or even life expectancy can be incorporated to modify the older, cruder function.

For example, many standard models stem from the so-called “life cycle” theory of consumer behavior as pioneered by Franco Modigliani. His model made adjustments based on how income and liquid cash balances affect an individual's marginal propensity to consume. This hypothesis stipulated that poorer individuals likely spend new income at a higher rate than wealthy individuals.

Milton Friedman offered his own simple version of the consumption function, which he called the “permanent income hypothesis.” Notably, the Friedman model distinguished between permanent and temporary income. It also extended Modigliani’s use of life expectancy to infinity.

More sophisticated functions may even substitute disposable income, which takes into account taxes, transfers, and other sources of income. Still, most empirical tests fail to match up with the consumption function’s predictions. Statistics show frequent and sometimes dramatic adjustments in the consumption function.