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Lesson overview - Total utility and marginal utility

One of the questions that economists are interested in is how people decide to spend their money, a field of economics known as consumer theory. This study of how people decide to allocate their income to spending on goods has a few key assumptions that lead to some important conclusions about how a consumer will decide to allocate their income to spending on goods and services.
Key assumptions about consumer motivation:
  • A rational consumer is a utility maximizer. A consumer will seek to have as much benefit or satisfaction as possible. In economics, the term utility refers to the happiness, benefit or value a consumer gets from a good or service. In other words, consumers are not satisficers who will settle for "good enough". This happiness or satisfaction is measured in a unit called a util.
  • Most goods provide diminishing marginal utility. According to the law of diminishing marginal utility, as the consumption of good increases the additional amount of happiness the good provides the consumer decreases. So while having three scoops of ice cream makes you happier than two scoops, the second scoop doesn't make you as happy as the first one did, and the third one doesn't make you as happy as the second one did.
These assumptions lead us to several conclusions about how consumers go about deciding how to spend their money. Consumers will therefore consider
  • the marginal utility of another unit of a good they are considering buying
  • the prices of a good and alternative goods they are considering buying
  • their budget for consuming goods and services
Because consumers derive less satisfaction from consuming additional units of a good, they will only be willing to buy more of a particular good if the good's price decreases. In this way, the law of diminishing marginal utility helps explain the law of demand.

Total utility

If we consider how an individual experiences utility when consuming ice cream, we can make some important observations how total utility changes as the consumption of a good increases.
To express utility, we will use a unit called the util, which is simply a measure of how happy someone is. For instance, we might say that the first scoop of ice cream provides Axel with 7 utils of happiness. The table below shows how Axel's utility changes as he consumes additional scoops of ice cream.
Quantity consumedTotal utility
0scoops0 utils
1scoop7 utils
2scoops12 utils
3scoops15 utils
4scoops16 utils
5scoops15 utils
6scoops12 utils
Notice that additional scoops provide Axel with more utility up until the 4th scoop, at which point Axel's utility is maximized. Beyond 4 scoops we can see that Axel is actually experiencing less and less total happiness.
Axel's total utility from ice cream can be graphed in a utility function, as seen in Figure 1:
Figure 1: Axel's total utility for ice cream

Marginal utility

If we look more closely at Axel's total utility we can observe how it changes as he consumes more ice cream. The change in a consumer's total utility when he consumes one additional unit is the marginal utility.
Quantity consumedTotal utilityMarginal utility
0scoops0 utils
1scoop7 utils7 utils
2scoops12 utils5 utils
3scoops15 utils3 utils
4scoops16 utils1 utils
5scoops15 utils1 utils
6scoops12 utils3 utils
Notice that Axel's marginal utility decreases as he consumes more ice cream. This is explained by the fact that the second, third and fourth scoops of ice cream were less satisfying to him than the first scoop.
Notice also that beyond 4 scoops his marginal utility is negative, meaning that Axel is actually made worse off by the fifth and sixth scoops of ice cream.
Axel's marginal utility function can be added to his total utility function, as shown in Figure 2
Figure 2: Axel's total and marginal utility from ice cream
Note that the marginal utility for a particular quantity of consumption is actually in between two quantities. For instance, the marginal utility of the 1st scoop is actually his change in total utility between 0 and 1 scoops, which explains why MU=7 between 0 and 1 scoops in Figure 2.

Marginal utility per dollar spent

A good first step in determining how a consumer will decide to allocate their income is knowing the satisfaction they get from a good. But before the optimal amount to buy of any good the price must also be considered. In other words, what is the "bang per buck" that a buyer will get from the good?
We can determine the "bang per buck" a buyer gets using the marginal utility per dollar spent, or MU/$. To determine the MU/$ we divide the marginal utility a consumer gets at a particular level of consumption by the price of the good.
Assume ice cream costs $0.50 per scoop. The marginal utility per dollar can then be calculated by dividing the MU at each level of consumption by the price of $0.50.
Quantity consumedMarginal utilityMarginal utility per dollar spent
2scoops5 utils10u/$
3scoops3 utils6u/$
4scoops1 utils2u/$
5scoops1 utils2u/$
6scoops3 utils6u/$
The use of the marginal utility per dollar spent in making decisions is fairly straightforward. Suppose Axel is currently consuming two scoops of ice cream and is thinking about getting a third scoop of ice cream or a soda. Suppose he knew that his bang per buck for a soda was 10 utils/$. He would only get 6 utils/$ on a third scoop of ice cream. Since he would be getting a better "bang per buck" from a soda, he would purchase the soda and not a third scoop of ice cream.
Considering the marginal utility per dollar spent on a good will help consumers spend their limited budgets in a way that maximizing their total utility, as we will develop further in the next lesson.

Diminishing marginal utility and the law of demand

The law of diminishing marginal utility helps us understand the law of demand. Because consumers will derive less happiness or benefit from additional units of a good, they will only be willing to buy a larger quantity if the price decreases.
This is true on an individual level, as with Axel's utility schedule for ice cream, but will be true on a market-wide level as well. Society as a whole's marginal utility diminishes as more of a good or service is provide, therefore in order for more units to be sold the price society must pay has to decrease. In other words, there is an inverse relationship between a good's price and the quantity society is willing and able to buy.

Key terms

consumer theorythe study of how buyers decide to allocate income toward consumption
utility maximizersomeone who seeks to achieve the highest possible satisfaction or happiness
utilitythe happiness or benefit consumers derive from a good's consumption
utilan imaginary unit of measurement representing the amount of utility a good provides
total utilitythe total amount of happiness a consumer derives from a good at any particular level of consumption
marginal utilitythe change in total utility that a consumer experiences when one more unit of a good is consumed
law of diminishing marginal utilitythe observation that as more units of a good are consumed the amount of happiness derived from each additional unit decreases as consumption increases
marginal utility per dollar spent MU/$the "bang per buck" that a consumer gets from consuming a particular quantity of a good at a given price.

Key models

A consumer's or society's utility schedule can be graphed using total and marginal utility functions.
Figure 4: Total and marginal utility
Notice that at a quantity of 4, total utility is maximized at 15 units. Notice also that at a quantity of 4, marginal utlity is equal to zero. According to this graph, once this person has consumed 4 units of this good they no longer get additional enjoyment from the good. Consuming the 5th unit actually makes them worse off.

Key calculations

Marginal Utility =ΔTUΔQ
Marginal Utility per dollar =MU$

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