Marginal propensity to consume

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

${\displaystyle {\mathit {MPC}}={\frac {dC}{dY}}}$

or, approximately,

${\displaystyle {\mathit {MPC}}={\frac {\Delta C}{\Delta Y}}}$, where ${\displaystyle \Delta C}$ is the change in consumption, and ${\displaystyle \Delta Y}$ 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 ${\displaystyle {\mathit {MPC}}=\Delta C/\Delta Y}$. The MPC can be explained with the simple example:

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

The above figure illustrates the consumption function. The slope of the consumption function tells us how much consumption increases when disposable income increases by one currency unit. That is, the slope of the consumption function is the MPC.

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 (which might occur if, for example, the increase in income makes it worthwhile to save up for a particular purchase). 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:${\displaystyle {\frac {\Delta C}{\Delta Y}}+{\frac {\Delta S}{\Delta Y}}=1}$.

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 average 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.[2] 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.

MPC's 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:

${\displaystyle Y=C+I}$

${\displaystyle \Delta Y=\Delta C+\Delta I}$

${\displaystyle \Delta Y=c\Delta Y+\Delta I}$ (where ${\displaystyle c}$ is ${\displaystyle {\mathit {MPC}}}$)

${\displaystyle \Delta Y-c\Delta Y=\Delta I}$

${\displaystyle \Delta Y(1-c)=\Delta I}$

${\displaystyle \Delta Y={\frac {\Delta I}{(1-c)}}}$

${\displaystyle {\frac {\Delta Y}{\Delta I}}={\frac {1}{(1-c)}}}$

${\displaystyle K={\frac {1}{(1-c)}}}$ (where ,${\displaystyle K}$ is multiplier and ${\displaystyle K={\frac {\Delta Y}{\Delta I}})}$

Since ${\displaystyle c}$ is the MPC, the multiplier ${\displaystyle K}$ is, by definition, equal to ${\displaystyle 1/(1-MPC)}$. The multiplier can also be derived from MPS (marginal propensity to save) and it is the reciprocal of MPS, ${\displaystyle K=1/{\mathit {MPS}}}$

${\displaystyle \Delta C/\Delta Y}$ (MPC)	${\displaystyle \Delta S/\Delta Y}$ (MPS) [${\displaystyle 1-{\mathit {MPC}}}$]	${\displaystyle K}$ (multiplier coefficient)
0	1	1
1/2	1/2	2
2/3	1/3	3
3/4	1/4	4
4/5	1/5	5
8/9	1/9	9
9/10	1/10	10
1	0	${\displaystyle \infty }$

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. ${\displaystyle 0<{\mathit {MPC}}<1}$), the multiplier is always between one and infinity (${\displaystyle 1<K<\infty }$). If the multiplier is one, it means that the whole increment of income is saved and nothing is spent because the MPC is zero. On the other hand, an infinite multiplier implies that MPC is equal one and the entire increment of income is spent on consumption. It will soon lead to full employment in the economy and then create a limitless inflationary spiral. But these are rare phenomenon. Therefore, the multiplier coefficient varies between one and infinity.

When income increases, the MPC falls more than the APC. Conversely, when income falls, the MPC rises and the APC also rises but at a slower rate than the former. Such changes are only possible during cyclical fluctuations whereas in the short-run there is no change in the MPC and ${\displaystyle {\mathit {MPC}}<{\mathit {APC}}}$. John maynard Keynes is concerned primarily with the MPC, for his analysis pertains to the short-run while the APC is useful in the long-run analysis. The post-Keynesian economists have come to the conclusion that over the long-run APC and MPC are equal and approximate 0.9. In the Keynesian analysis the MPC is given more prominence. Its value is assumed to be positive and less than unity which means that when income increases the whole of it is not spent on consumption. On the contrary, when income falls, consumption expenditure does not decline in the same proportion and never becomes zero. The Keynesian hypothesis is that the marginal propensity to consume is positive but less than unity (${\displaystyle 0\leq \Delta C/\Delta Y<1}$) is of great analytical and practical significance. Besides telling us that consumption is an increasing function of income and it increases by less than the increment of income, this hypothesis helps in explaining 1) The theoretical possibility of general overproduction or "underemployment equilibrium" and also 2) The relative stability of a highly developed industrial economy. For it implies that the gap between income and consumption at all high levels of income is too wide to be easily filled by investment with the possible consequences that the economy may fluctuate around underemployment equilibrium. Thus the economic significance of the MPC lies in filling the gap between income and consumption through planned investment to maintain the desired level of income.

• Average propensity to save
• Average propensity to consume
• Consumer theory
• Keynesian economics
• Marginal propensity to save

• Hall, Robert E.; Taylor, John B. (1986). "Consumption and Income". Macroeconomics: Theory, Performance, and Policy. New York: W. W. Norton. pp. 63–67. ISBN 0-393-95398-X.
• Lindauer, John (1976). "Consumption Functions". Macroeconomics (Third ed.). New York: Wiley. pp. 40–43. ISBN 0-471-53572-9.
• Wonnacott, Paul (1984). "The Consumption Function". Macroeconomics (Third ed.). Homewood: Irwin. pp. 58–62. ISBN 0-256-02497-9.