## ⓘ Marginal propensity to consume

In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes. For example, if a household earns one extra dollar of disposable income, and the marginal propensity to consume is 0.65, then of that dollar, the household will spend 65 cents and save 35 cents. Obviously, the household cannot spend more than the extra dollar.

According to John Maynard Keynes, marginal propensity to consume is less than one.

## 1. Background

Mathematically, the M P C {\displaystyle {\mathit {MPC}}} function is expressed as the derivative of the consumption function C {\displaystyle C} with respect to disposable income Y {\displaystyle Y}, i.e., the instantaneous slope of the C {\displaystyle C} - Y {\displaystyle Y} curve.

M P C = d C d Y {\displaystyle {\mathit {MPC}}={\frac {dC}{dY}}}or, approximately,

M P C = Δ C Δ Y {\displaystyle {\mathit {MPC}}={\frac {\Delta C}{\Delta Y}}}, where Δ C {\displaystyle \Delta C} is the change in consumption, and Δ Y {\displaystyle \Delta Y} is the change in disposable income that produced the consumption.Marginal propensity to consume can be found by dividing change in consumption by a change in income, or M P C = Δ C / Δ Y {\displaystyle {\mathit {MPC}}=\Delta C/\Delta Y}. The MPC can be explained with the simple example:

Here Δ C = 50 {\displaystyle \Delta C=50} ; Δ Y = 60 {\displaystyle \Delta Y=60} Therefore, M P C = Δ C / Δ Y = 50 / 60 = 0.83 {\displaystyle {\mathit {MPC}}=\Delta C/\Delta Y=50/60=0.83} or 83%. For example, suppose you receive a bonus with your paycheck, and its $500 on top of your normal annual earnings. You suddenly have $500 more in income than you did before. If you decide to spend $400 of this marginal increase in income on a new business suit, your marginal propensity to consume will be 0.8 $ 400 / $ 500 {\displaystyle \$400/\$500}.

The marginal propensity to consume is measured as the ratio of the change in consumption to the change in income, thus giving us a figure between 0 and 1. The MPC can be more than one if the subject borrowed money or dissaved to finance expenditures higher than their income. The MPC can also be less than zero if an increase in income leads to a reduction in consumption. One minus the MPC equals the marginal propensity to save in a two sector closed economy, which is crucial to Keynesian economics and a key variable in determining the value of the multiplier. In symbols, we have: Δ C Δ Y + Δ S Δ Y = 1 {\displaystyle {\frac {\Delta C}{\Delta Y}}+{\frac {\Delta S}{\Delta Y}}=1}.

In a standard Keynesian model, the MPC is less than the average propensity to consume APC because in the short-run some autonomous consumption does not change with income. Falls increases in income do not lead to reductions increases in consumption because people reduce add to savings to stabilize consumption. Over the long-run, as wealth and income rise, consumption also rises; the marginal propensity to consume out of long-run income is closer to the average propensity to consume.

The MPC is not strongly influenced by interest rates; consumption tends to be stable relative to income. In theory one might think that higher interest rates would induce more saving the substitution effect but higher interest rates also mean than people do not have to save as much for the future.

Economists often distinguish between the marginal propensity to consume out of permanent income, and the marginal propensity to consume out of temporary income, because if consumers expect a change in income to be permanent, then they have a greater incentive to increase their consumption. This implies that the Keynesian multiplier should be larger in response to permanent changes in income than it is in response to temporary changes in income though the earliest Keynesian analyses ignored these subtleties. However, the distinction between permanent and temporary changes in income is often subtle in practice, and it is often quite difficult to designate a particular change in income as being permanent or temporary. What is more, the marginal propensity to consume should also be affected by factors such as the prevailing interest rate and the general level of consumer surplus that can be derived from purchasing.

## 2. MPC and the multiplier

MPCs importance depends on the multiplier theory. MPC determines the value of the multiplier. The higher the MPC, the higher the multiplier and vice versa. The relationship between the multiplier and the propensity to consume is as follows:

Y = C + I {\displaystyle Y=C+I} Δ Y = Δ C + Δ I {\displaystyle \Delta Y=\Delta C+\Delta I} Δ Y = c Δ Y + Δ I {\displaystyle \Delta Y=c\Delta Y+\Delta I} where c {\displaystyle c} is M P C {\displaystyle {\mathit {MPC}}} Δ Y − c Δ Y = Δ I {\displaystyle \Delta Y-c\Delta Y=\Delta I} Δ Y 1 − c = Δ I {\displaystyle \Delta Y1-c=\Delta I} Δ Y = Δ I 1 − c {\displaystyle \Delta Y={\frac {\Delta I}{1-c}}} Δ Y Δ I = 1 − c {\displaystyle {\frac {\Delta Y}{\Delta I}}={\frac {1}{1-c}}} K = 1 − c {\displaystyle K={\frac {1}{1-c}}} where, K {\displaystyle K} is multiplier and K = Δ Y Δ I {\displaystyle K={\frac {\Delta Y}{\Delta I}})}Since c {\displaystyle c} is the MPC, the multiplier K {\displaystyle K} is, by definition, equal to 1 / 1 − M P C {\displaystyle 1/1-MPC}. The multiplier can also be derived from MPS marginal propensity to save and it is the reciprocal of MPS, K = 1 / M P S {\displaystyle K=1/{\mathit {MPS}}}

The above table shows that the size of the multiplier varies directly with the MPC and inversely with the MPS. Since the MPC is always greater than zero and less than one (i.e. 0 < M P C < 1 {\displaystyle 0