How To Calculate Marginal Utility (With Examples)

December 06, 2021, 09:16:15
How To Calculate Marginal Utility (With Examples)

Marginal utility describes the increase in utility or satisfaction that a consumer receives from consuming a good. In principle, the marginal utility can be calculated by calculating the change in total utility due to the change in the number of goods consumed. 

Marginal utility definition with example

The marginal utility (often abbreviated to MU) is the benefit that the consumer has from consuming another unit of the good in question.

For example, marginal utility is the utility of the third apple when you've already eaten two. It is obvious that the marginal utility decreases with increasing consumption (the 5th apple brings less utility, maybe even leads to stomach problems).

The marginal utility can be calculated as the 1st derivation of the utility function according to the considered good (e.g. MU1 for the marginal utility of good 1).

Decreasing marginal utility example

The law of diminishing marginal utility can best be represented in the case of food consumption because saturation occurs after a while. For example, consuming additional chocolate from a certain point in time increases the level of benefit less and less. The increase in benefit for each additional chocolate decreases.

Assume that x_1 stands for chocolate. If you haven't eaten that much chocolate yet, you're more likely to be willing to pay more for another bar. But if you've already eaten a lot of chocolate, the desire for another bar will decrease. 

The law of decreasing marginal utility applies here. If this is equal to 0, one speaks of saturation. A negative increase in benefit is also possible and occurs in our example if the person eats too much chocolate. Then you get sick. The benefit is then even negative and the chocolate harms it.  

Calculating marginal utility with example

In the example of the utility function, let’s start with: U (x, y) = x + 3 × y with x for the consumed amount of good 1 (liters of milk) and y for the consumed amount of good 2 (kg of bread).

The marginal utility of good 1 corresponds to the 1st derivative of the utility function with respect to x, which results in MU1 = 1 

If you derive the function U (x, y) = x + 3 × y from x, the first term x derived from x then results in 1, and the second summand 3 × y results in derived from x - as the derivative of a "from the point of view of x" constant - 0, so in total 1 + 0 = 1; it is a partial derivative.

If the household had, for example, previously 1 liter of milk and 1 kg of bread, the benefit was: U (1, 1) = 1 + 3 × 1 = 4.

If a liter of milk is added, the benefit is: U (2, 1) = 2 + 3 × 1 = 5. The difference corresponds to the marginal benefit of 1.

Similarly, the marginal utility of good 2 is the 1st derivative of the utility function with respect to y, which results in MU2 = 3.

If, based on the original consumption (1 liter of milk and 1 kg of bread with a benefit U (1, 1) = 1 + 3 × 1 = 4), one kg of bread is added, the benefit is U (1, 2) = 1 + 3 × 2 = 1 + 6 = 7. The difference of 7 - 4 = 3 corresponds to the marginal utility of bread of 3.

As a linear function, the utility function was such that the marginal utility does not decrease. Every liter of milk more brings a constant marginal utility of 1, every kg more bread brings a constant marginal utility of 3. 

In most realistic scenarios and the utility functions developed from them, however, a decreasing marginal utility would occur, as described earlier in the article.

More examples of calculating decreasing marginal utility

Almost all beneficial functions have a decreasing marginal utility. For example, imagine you are studying for an exam. In the first week, you will learn a lot of new formulas and concepts, but the learning effect decreases with increasing time. 

If you study for an exam for six weeks instead of five weeks, the difference is significantly smaller than if you study for two weeks instead of one week. 

The increase is very large at first, but the further you go into detail, the less the amount of new learning material you can keep. 

Another example is the clothes in your closet. If you only have very, very few clothes, you will be very happy about a new shirt. But as soon as you have a wardrobe full of clothes, a new shirt doesn't really matter because you can't put it on often because of all the other clothes.


What does marginal utility measure?

The marginal utility is the marginal increase in utility of a household that arises from a further unit of the consumed good. As a rule, it is a matter of decreasing marginal utility according to Gossen's first law. Mathematically, this is to be determined via the derivation of the utility function.

How marginal utility is linked to marginal benefits and marginal costs?

The economic sciences know many compounds such as marginal yield, marginal costs, marginal utility, marginal price, or marginal product, which have in common that it is about the increase that is achieved or expended through the use of another unit of an economic variable.

What do you mean by the use of a good?

Consumption of a good or service triggers the satisfaction of needs or the enjoyment in the consumer. Both the subjectively perceived measure of the degree of need satisfaction and the properties of the material good or the service itself are viewed as benefits.

Is the marginal utility of a glass of water large or small?

How can it be small? The marginal utility of a glass of water is great because water has an important benefit for us (survival, hydration) and in most civilized countries, tap water only costs 0.02 cents for a liter.