# Marginal propensity to consume

In economics, the marginal propensity to consume (MPC) is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income (income after taxes and transfers). 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 (without borrowing).

According to John Maynard Keynes, marginal propensity to consume is less than one.[1]

## Background

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:

Income Consumption
120 120
180 170

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 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.[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 and the multiplier

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 ). 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.

## Significance of MPC

When income increases, the MPC falls but 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 ${\displaystyle {\mathit {MPC}}<{\mathit {APC}}}$ . 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.

### MPC and nature of country

The MPC is higher in the case of poorer people than in rich[3]. When a person earns a higher income, the cost of their basic human needs amount to a smaller fraction of this income, and correspondingly their average propensity to save is higher than that of a person with a lower income. The marginal propensity to save of the richer classes is greater than that of the poorer classes. If, at any time, it is desired to increase aggregate consumption, then the purchasing power should be transferred from the richer classes (with low propensity to consume) to the poorer classes (with a higher propensity to consume). Likewise, if it is desired to reduce community consumption, the purchasing power must be taken away from the poorer classes by taxing consumption. The marginal propensity to consume is higher in a poor country and lower in the case of rich country. The reason is same as stated above. In the case of rich country, most common of the basic needs of the people have already been satisfied, and all the additional increments of income are saved, resulting in a higher marginal propensity to save but in a lower marginal propensity to consume. In a poor country, on the other hand, most of the basic needs of the people remain unsatisfied so that additional increments of income go to increase consumption, resulting in a higher marginal propensity to consume and a lower marginal propensity to save. This is the reason MPC is higher in the underdeveloped countries of Asia and Africa, and lower in developed countries such as the United States, the United Kingdom, Singapore and Germany.

### The MPC of individuals

Much of the current discussion seems to rely on the MPC being unique to a country, and homogeneous across such an economic entity; and the theory and the mathematical formulae apply to this use of the term. However, individuals have an MPC, and furthermore MPC is not homogeneous across society. Even if it was, the nature of the consumption is not homogeneous. Some consumption may be seen as more benevolent (to the economy) than others. Therefore, spending could be targeted where it would do most benefit, and thus generate the highest (closest to 1) MPC. This has traditionally been regarded as construction or other major projects (which also bring a direct benefit in the form of the finished product). Clearly, some sectors of society are likely to have a much higher MPC than others. Someone with above average wealth or income or both may have a very low (short-term, at least) MPC of nearly zero—saving most of any extra income. But a pensioner, for example, will have an MPC of 1 or even greater than 1. This is because a pensioner is quite likely to spend every penny of any extra income. Further, if the extra income is seen as regular extra income, and guaranteed into the future, the pensioner may actually spend MORE than the extra £1. This would occur where the extra income stream gives confidence that the individual does not need to put aside as much in the form of savings; or perhaps can even dip into existing savings. More importantly, this consumption is much more likely to occur in local small business—local shops, pubs and other leisure activities for example. These types of businesses are themselves likely to have a high MPC, and again the nature of their consumption is likely to be in the same, or next tier of businesses, and also of a benevolent nature. Other individuals with a high, and benevolent, MPC would include almost anyone on a low income—students, parents with young children, and the unemployed.

## References

1. ^ Keynes, John M. (1936). The General Theory of Employment, Interest and Money. New York: Harcourt Brace Jovanovich. p. 96. The fundamental psychological law ... is that men [and women] are disposed, as a rule and on average, to increase their consumption as their income increases, but not as much as the increase in their income.
2. ^ Barro, Robert; Grilli, Vittorio (1994). European Macroeconomics. Macmillan. pp. 417–8. ISBN 0333577647.
3. ^ http://equitablegrowth.org/equitablog/wealth-inequality-marginal-propensity-consume/