Marginal Utility

Marginal Utility and Diminishing Marginal Utility

Marginal utility follows the concept of diminishing marginal utility. The more of a certain good we consume, the smaller the satisfaction we get from consuming additional units of that good. This describes the concept of diminishing marginal utility.

Let's try to understand it better with the following example.

The above example demonstrates that marginal utility will rise rapidly in the beginning, then it will begin to rise in smaller increments until no satisfaction is gained from consuming an extra unit of the good. In other words, it starts big, then reduces with each addition. Let's have a look at Figure 1.

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The marginal utility graph shown in Figure 1 offers a visual illustration of the concept of diminishing marginal utility. With the marginal utility on the vertical axis and the quantity of the good consumed on the horizontal axis, the marginal utility curve slopes downward as marginal utility decreases with each additional unit consumed.

The total utility curve also demonstrates diminishing marginal utility.

Let's explain how using Figure 2.

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Figure 2 above shows a total utility curve. As more units of a good are consumed, total utility increases until reaching its peak, where it doesn't increase anymore. Taking it further could even show the total utility curve sloping downwards after the tipping point and getting back to zero! Think of it as over-consuming a particular good and deriving a negative utility or dis-utility from it.

Marginal Utility Formula

The marginal utility formula is expressed as the change in total utility divided by the change in units consumed.

Mathematically, this is written as:

$MU=\frac{\mathrm{\Delta }TU}{\mathrm{\Delta }Q}$

Where MU is marginal utility, TU is total utility, and Q is the units consumed.

We can further derive some important equations for marginal utility. To accomplish this, let's say you are choosing between buying some Fritos and some Coke.

Define the following:

F=Fritos

C=Coke

MU_i = Marginal Utility for Good i

D_i = Change in Consumption of Good i

P_i = Price of Good i

Then we have:

$0=M{U}_F(D_F)+M{U}_C(D_C)$

This equation says that the marginal utility multiplied by the change in consumption of Fritos must be offset by the marginal utility multiplied by the change in consumption of Coke. This is because points on the same indifference curve provide the same utility.

Rearranging the equation, we have:

$-(\frac{D_C}{D_F})=\frac{M{U}_F}{M{U}_C}$

the expression, $-(\frac{D_C}{D_F})$ is the Marginal Rate of Substitution (MRS) between Fritos and Coke.

$MRS=\frac{M{U}_F}{M{U}_C}$

When utility is maximized, the marginal rate of substitution of Fritos for Coke equals the ratio of the prices of the two goods in question.

Therefore, when utility is maximized:

$MRS=\frac{P_F}{P_C}$

Since:

$MRS=\frac{M{U}_F}{M{U}_C}$

We have:

$\frac{M{U}_F}{M{U}_C}=\frac{P_F}{P_C}$

We can rearrange the expression once again to get:

$\frac{M{U}_F}{P_F}=\frac{M{U}_C}{P_C}$

This equation represents the equal marginal principle.

• The equal marginal principle is met when the marginal utility per dollar spent is equal for all goods consumed.

Marginal Utility Example

Trying an example of marginal utility will help strengthen your understanding of the concept!

Consider the example below.

The table below shows the utility of a consumer eating bags of potato chips.

Bags consumed (units)	Total Utility	Marginal utility
1	8	8
2	14	6
3	18	?
4	20	2
5	20	0

Table 1 - Consumer utility from potato chips example

What is the marginal utility when the consumer eats the third bag of potato chips?

Draw the marginal utility curve of the consumer.

Solution:

Using this formula:

$MU=\frac{\mathrm{\Delta }TU}{\mathrm{\Delta }Q}$

We can compute the marginal utility of the third bag of chips as:

$MU=\frac{18-14}{3-2}$

$MU=4$

We can then draw the marginal utility curve as presented in Figure 3 below.

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Fig. 3 - Marginal utility curve example

Marginal Utility Importance

The importance of marginal utility is that it helps to explain one of the most fundamental concepts in all of economics; the reason the demand curve slopes downward. If an increase in consumption of a certain good brings less and less utility the more that is consumed, known as diminishing marginal utility, at a certain point the consumer will cease consumption of that good, at least at the current price. However, if the price of that good comes down, the consumer just may want to consume another unit, or two, or more, of the good.

Put another way, there is only so much of a certain good a consumer is willing to purchase at a given price. Thus, at price P₁ a consumer may buy X units of the good, but if the price falls to P₂ they may buy one more or several more units, and if the price falls further to P₃, still more units will be purchased.

There will come a point, however, where even if the price falls to near zero, the consumer will discontinue consumption of the good. This will usually be due to a budget constraint, or the amount available to spend on that good. However, it could also be due to saturation, that is, so much of the good has been consumed already that even at a price of zero, the consumer will not want any more.

In sum, at a certain high price, the consumer will purchase none of the good. But, as the price falls, the consumer will purchase more and more of the good until they either reach their budget constraint or saturation. This is how diminishing marginal utility explains the downward-sloping demand curve, which is fundamental to the study of economics.