The Consumption Function — Keynes's Psychological Law and APC/MPC

The consumption function expresses the relationship between total consumption expenditure (C) and the level of national income (Y) in an economy — written generally as $C=f(Y)$, and commonly modelled in its simplest linear form as:

where $a>0$ is autonomous consumption (the consumption that occurs even at zero income, financed by past savings or borrowing — households must eat and pay for basic needs even with no current income) and $b$ is the Marginal Propensity to Consume (MPC), the fraction of each ADDITIONAL rupee of income that is spent on consumption.

J. M. Keynes based this relationship on what he called the Fundamental Psychological Law of Consumption, which has three related propositions:

1. When income increases, consumption also increases, but by a SMALLER amount than the increase in income (i.e., $0<MPC<1$) — people do not spend every extra rupee they earn.
2. The increased income is divided between consumption and saving in some proportion.
3. As income increases, BOTH consumption and saving tend to increase, but MPC itself typically falls (people save a progressively larger share) as income rises further, though for a simple linear consumption function MPC is treated as a constant.

Two related ratios describe consumption behaviour precisely:

Average Propensity to Consume (APC) $=\dfrac{C}{Y}$ — the FRACTION of total income spent on total consumption.

Marginal Propensity to Consume (MPC) $=\dfrac{\Delta C}{\Delta Y}$ — the fraction of an ADDITIONAL rupee of income spent on additional consumption; for the linear function $C=a+bY$, MPC is simply the constant slope $b$.

Because of the autonomous term $a$, APC is always HIGHER than MPC for a linear consumption function with $a>0$ — a larger SHARE of a low income must go toward basic (autonomous) consumption, so APC falls steadily as income rises, even while MPC (the slope) stays constant.