# Total Utility

Total utility refers to the overall or total level of happiness or satisfaction that a consumer experiences by consuming a certain amount of a good or service. While marginal utility measures the change in (total) utility of consuming one additional unit, total utility measures the total level of happiness associated with the consumption of a certain quantity of the good.

Utility is an important concept in economics, because the neoclassical economic theory is based on the premise that rational individuals maximise their utility. This implies that all (economic) decisions and interactions can be analysed by studying the utility maximisation problem of the people involved. Utility is usually described by a utility function, i.e., a mathematical function that assigns a value to the level of happiness an individual experiences when consuming a certain bundle of goods and services. This utility function represents the preferences of a consumer over a set of alternatives. Commonly, we assume that utility can be measured in monetary units meaning that utility is a cardinal concept for us. The total utility of consuming a good is equivalent to the amount of money that would make the consumer equally as happy as when they consume the good. For example, the level of happiness or satisfaction you obtain from a chocolate bar can be measured by the amount of money that would give you the same level of happiness as consuming the chocolate bar. Cardinal utility means that the number we associate with the utility of the consumption of a good has a meaning and we can use it for comparisons. For example, if the consumption of 1 chocolate bar gives me a total utility of 1 and the consumption of 1 piece of cake gives me a total utility of 2, then we can conclude that not only do I prefer cake to a chocolate bar, but I like cake twice as much as a chocolate bar.

When studying economics, you cannot get around the term marginal utility, which describes the increase in utility from consuming one additional unit. The difference between marginal and total utility is that total utility refers to the overall level of utility from consuming a certain quantity, while marginal utility only measures the change in happiness associated with the last unit that was consumed. This means that total utility of consuming a certain quantity is equivalent to summing up the marginal utility of all units. Marginal utility can be positive or negative depending on whether consuming one additional unit increases or decreases total utility. If the marginal utility of the last unit is positive, then total utility is increasing. In case the marginal utility of the last unit is negative, total utility is decreasing.

Let us look at an example to better understand the difference between total and marginal utility. In the table below we can see the total utility as well as the marginal utility that an individual, let us call her Anne, obtains from consuming a certain number of cups of coffee. Consuming one cup of coffee gives Anne a total utility of 5 and as this is also the increase or change in total utility from consuming the first cup. That is, the marginal utility of the first cup is equal to its total utility.

 Nr of cups of coffee 0 1 2 3 4 5 Total utility (measured in monetary units) 0 5 7 8 8 5 Marginal utility 5 2 1 0 -3

Drinking two cups of coffee gives Anne a total utility of 7, whereas her marginal utility is equal to 2 (the change in total utility from the first to the second cup). In other words, the second cup of coffee still increases Anne’s happiness or wellbeing, although the increase is smaller than from the first cup. For the fourth cup, the marginal utility is equal to zero and we see that the total utility of Anne from the third to the fourth cup does not change. Anne’s total utility of consuming five cups is lower than her utility of consuming two, three or four cups and this means that marginal utility is negative. As mentioned above, the total utility of a certain quantity is equal to the sum of the marginal utilities. For example, the total utility of the second cup is equal to the increase in utility from consuming the first cup (5) plus the increase in utility from consuming the second cup (2), which is equal to 7.

Some economists argue that (total) utility should not be interpreted as a cardinal concept, but rather on an ordinal scale. Ordinal utility means that the value associated with the utility of the consumption of a good can only be used to make comparisons telling us which consumption bundles are preferred to others, but nothing more. If for example, a chocolate bar gives you a utility of 1 and a piece of cake a utility of 2 then according to ordinal utility we can only infer that you prefer cake to a chocolate bar. The actual numbers cannot be interpreted, i.e., we cannot say that a piece of cake makes you twice as happy as a chocolate bar. G. Debreu, in Representation of a preference ordering by a numerical function, 1954, established the conditions under which a preference ordering can be represented by a utility function. You may already have seen ordinal utility in the form of indifference curves. All consumption bundles that are on the same indifference curve give the individual the same total utility. Consumption bundles on higher indifferences curves are preferred, but the difference in the total level of utility is meaningless.

## Good to know

The consumption of a good that increases happiness has a total utility that is positive. Some goods, those that actually reduce utility or give you disutility are called bads. For example, air pollution is clearly a bad. And here we encounter difficulty. How can we measure the decrease in utility a person experiences from having to consume polluted air? To measure the disutility of bads we can ask an individual how much he or she would be willing to pay in order to not have to consume the bad or alternatively, how much money we would have to give to the person consuming the bad in order to keep his or her utility unchanged.