# Marginal Utility

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## Marginal Utility Definition

Marginal utility is defined as the additional satisfaction you get from consuming an extra unit of a given good. This is the quick definition of marginal utility, but let's explain the concept in more detail. Marginal utility is a derivative of utility, and utility is simply the satisfaction we get from consuming a given good. When we consume a certain quantity of a given good, the total satisfaction or happiness we gain from that consumption is the total utility. It is important to draw the distinction between marginal utility and total utility.

Utility is defined as the level of satisfaction, or happiness, a consumer attains from consuming a certain good or bundle of goods. It has no value other than to compare goods and bundles of goods.

Total utility is defined as the total amount of satisfaction, or happiness, a consumer attains from consuming a certain amount of a good or bundle of goods.

Marginal utility is the additional utility, or satisfaction, obtained from the consumption of one additional unit of a certain good.

The example below will help make things clearer.

Let's assume that the utility of Josh is quantified in "utils". Josh consumed a total of 4 cookies. After the first cookie, his utility was 6 utils, the second cookie consumed added 5 utils, the third added 3 utils, and the last cookie added 1 util.

Combining Josh's utility with each added cookie gives us 15 utils, and this is his total utility. But, since marginal utility is the additional satisfaction from consuming an extra unit of the good, his marginal utility from consuming the second cookie, for instance, is 5 utils.

Marginal utility influences consumer choice.

To learn about consumer choice, take a look at our article:

- Consumer Choice.

## 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.

Diminishing marginal utility is a concept that says the more of a good a consumer has, the less of that good the consumer wants, hence the less marginal utility they will obtain as consumption of that good increases.

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

Amy enjoys potato chips and goes through 3 packs easily. In the beginning, Amy gets a high amount of satisfaction from eating a bag of chips. This is especially true for the first bag of chips eaten. However, as Amy eats more packs of chips, the amount of satisfaction she gets from each new pack is less than the satisfaction she gets from eating the previous pack.

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.

Fig. 1 - Marginal utility curve

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.

Fig. 2 - Total utility curve

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:

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

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

MUi = Marginal Utility for Good i

Di = Change in Consumption of Good i

Pi = Price of Good i

Then we have:

$$0=MU_F(D_F)+MU_C(D_C)$$

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:

$$-(\frac{D_C}{D_F})=\frac{MU_F}{MU_C}$$

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

$$MRS=\frac{MU_F}{MU_C}$$

The marginal rate of substitution (MRS) measures how much of one good a consumer will sacrifice to get more of another good.

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:

$$MRS=\frac{MU_F}{MU_C}$$

We have:

$$\frac{MU_F}{MU_C}=\frac{P_F}{P_C}$$

We can rearrange the expression once again to get:

$$\frac{MU_F}{P_F}=\frac{MU_C}{P_C}$$

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.

Want to know more about the marginal rate of substitution? Read our article: The Marginal rate of Substitution.

## 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:

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

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.

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.

Saturation occurs when 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.

Consumers are limited by budget constraints!

- Budget Constraint;

## Marginal Utility - Key takeaways

• Utility is defined as the level of satisfaction, or happiness, a consumer attains from consuming a certain good or bundle of goods. It has no value other than to compare goods and bundles of goods.
• Total utility is defined as the total amount of satisfaction, or happiness, a consumer attains from consuming a certain amount of a good or bundle of goods.
• Marginal utility is the additional utility, or satisfaction, obtained from the consumption of one additional unit of a certain good.
• Diminishing marginal utility is a concept that says the more of a good a consumer has, the less of that good the consumer wants, hence the less marginal utility they will obtain as consumption of that good increases.
• The marginal rate of substitution (MRS) measures how much of one good a consumer will sacrifice to get more of another good.

#### Flashcards in Marginal Utility 81

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What is the difference between marginal utility and diminishing marginal utility?

The difference between marginal utility and diminishing marginal utility lies in their essence.

Marginal utility is the additional utility, or satisfaction, obtained from the consumption of one additional unit of a certain good.

Diminishing marginal utility says the more of a good a consumer has, the less of that good the consumer wants, hence the less marginal utility they will obtain as consumption of that good increases.

How does marginal benefit impact consumers choices?

Marginal benefit impacts consumers' choices because it informs them what the actual benefit from continued consumption is.

Why is diminishing marginal utility important?

Diminishing marginal utility is important because it shows how the satisfaction from consuming each additional unit of product decreases.

Why is marginal utility more useful than total utility in consumer decision making?

Marginal utility is more useful than total utility in consumer decision making because marginal utility informs consumers whether it is worth it to continue consuming.

Why does marginal utility decrease as more is consumed?

Marginal utility decreases as more is consumed because consumers gain less satisfaction from consuming additional units of a good.

## Test your knowledge with multiple choice flashcards

If the probability of a stock return of 20% (Outcome A) is 30% (PA) and the probability of a stock return of 40% (Outcome B) is 70% (PB), then the expected return would be:

A less-risky stock should be priced _____ than a riskier stock.

Risk and return are _____ correlated.

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