Total And Marginal Utility
- Why is the fear of losing money in an investment greater than the desire of earning the same amount of money?
- Why, as some studies have shown, does the desire for greater income drop off sharply when a person is already earning at least $75,000 annually?
- Why would someone pay over $100 million for a painting or $35,000 for a purse?
- Why do richer people value experiences over acquiring more goods or services?
- If a poor person earning $20,000 a year pays 20% of their income in taxes and a rich person making $1 million per year pays 90% of their income in taxes, who has the greater tax burden?
You can gain insight into the answers to these questions by understanding marginal utility, especially the marginal utility of money.
Utility is the satisfaction a person derives from the consumption of a good or service. Total utility is the total satisfaction received from consuming a given total quantity of a good or service, while marginal utility is the satisfaction gained from consuming an additional quantity of that item. Sometimes, economists like to subdivide utility into individual units that they call utils. However, because utility is subjective, meaning that it differs from person to person, and because it varies continuously, depending on the quantity consumed, an util cannot actually be measured, but is simply a heuristic device that allows economists to talk about the degree of satisfaction for a product or service.
Marginal utility always declines for each successive quantity of consumption. If you like ice cream, and you eat one scoop, the first scoop will provide the greatest satisfaction. If you eat another scoop, you'll probably enjoy that also, but the satisfaction will be less than for the first. At some point, you will not want any more ice cream. The marginal utility will drop to zero and may even become negative. This illustrates the law of diminishing marginal utility. Marginal utility declines for everything, including money. Although many people want to amass great wealth, each dollar accumulated becomes worth less and less, because the marginal utility of what it can buy declines.
| Quantity | Marginal Utility | Total Utility |
|---|---|---|
| 1 | 10 | 10 |
| 2 | 8 | 18 |
| 3 | 6 | 24 |
| 4 | 4 | 28 |
| 5 | 2 | 30 |
| 6 | 0 | 30 |
| 7 | -2 | 28 |
As can be seen in these diagrams, total utility increases with increasing quantity of a single item until marginal utility = 0; thereafter, total utility declines when marginal utility becomes negative.
A person or firm has limited resources, so total utility is maximized by apportioning those resources to products and services where the marginal utility of each is equal. In terms of money, if buying a greater quantity of 1 item yields a smaller marginal utility than if the money were spent to acquire another item, then total utility will be less than if that other item was purchased. Thus, total utility is maximized when the marginal utility of the last dollar spent on any product or service equals or exceeds the marginal utility of any other purchase that could have been made.
Declining marginal utility explains why the demand curve slopes downward as the supply quantity is increased, and why people will only consume more if the price declines, since people's willingness to pay also declines.
Marginal utility is also related to the elasticity of demand. If demand is inelastic, then the quantity demanded drops off slowly as the price increases, indicating that the marginal utility of the product or service is high; with elastic demand, demand quantity drops off sharply, indicating a low marginal utility for the product, so the consumer is not willing to pay a higher price.
Consumer Choice
Consumer choice is guided by preferences for specific products, budget constraints, prices, and the marginal utility of products. A budget constraint exists because the consumer only has so much money, so only so much can be spent; therefore, even among desirable things, a choice must be made. This choice will depend on the marginal utility of the product and its price. Because marginal utility declines with quantity, while the price does not vary, a consumer tends to buy as much product until the marginal utility of the product falls below the marginal utility of other products the consumer can buy. Hence, the consumer stops buying more of a product when the marginal utility of an additional amount is less than its price. In this way, the total utility of what the consumer can purchase within his budget is maximized. So the marginal utility of each type of product divided by its price will roughly equal the marginal utility of the other products that the consumer purchased divided by their prices. This is called the law of equal marginal utility per dollar, since dollars are spent for each good or service until the marginal utility of each good or service is equal.
| Marginal Utility of Product A | Marginal Utility of Product B | |
| ÷ | = | ÷ |
| Price of Product A | Price of Product B |
Indifference Curve Analysis
How consumer choice varies with marginal utility is sometimes depicted with indifference curves. Each point on an indifference curve represents a combination of products that yields the same total utility for the consumer. Because each consumer's purchasing power is limited, this budget constraint, represented by a budget line, limits the choices consumers make.
Indifference curve analysis is simplified by assuming that the consumer spends all their money on 2 products. For instance, suppose the consumer has $12 to spend on cantaloupes and apples. Each cantaloupe costs $2 apiece and each apple costs $1 apiece. The following table shows what can be purchased:
| Apples | Cantaloupes |
|---|---|
| 0 | 6 |
| 2 | 5 |
| 4 | 4 |
| 6 | 3 |
| 8 | 2 |
| 10 | 1 |
| 12 | 0 |
This yields the above budget line.
An indifference curve for this example would yield every combination of apples and cantaloupes that yield the same total utility. Indifference curves are convex to the origin because of the law of diminishing marginal utility — when there is a predominance of cantaloupes, then the marginal utility of an additional cantaloupe is less than the marginal utility of an additional apple, and vice versa. In other words, consumers like variety. A tangent line to an indifference curve represents the marginal rate of substitution (MRS) of one product for the other that maintains total utility.
An indifference map can be created by several indifference curves representing an increased budget for apples and cantaloupes that allows the consumer to buy more of each product for a greater total utility. Generally, consumers with higher incomes will have larger budgets for specific items. In the above diagram, for instance, I1 represents the indifference curve at the lowest total utility of the 3 displayed in the diagram. The consumer would not choose any point on this curve because their higher income with the correspondingly increased budget for cantaloupes and apples would allow the achievement of greater total utility by choosing a point on indifference curve I2 that would still be affordable. When the consumer's budget line is superimposed on the indifference map, the point where the budget line is tangent to the highest indifference curve is the highest attainable total utility, given the consumer's budget, and represents the consumer's equilibrium position. Although curve I3 offers higher utility, the price of any combination of cantaloupes and apples on this indifference curve is outside of their budget.
Explaining the Real World Using the Marginal Utility of Money
The marginal utility of goods and services directly affects the marginal utility of money, for if the additional value of goods and services falls, so does the money used to buy those items. Marginal utility explains a lot in our economy, including the answers to the questions posed at the beginning of this article.
Why do investors fear loss more than they desire gain? Investors are more fearful of losing money than their desire to gain the same amount of money, if the probability of the gain or loss is equal. So if someone has $100,000 to invest, where the investment will yield, with a 50% probability per option, either a $50,000 gain or $50,000 loss, most investors, especially risk-averse investors, would forgo the investment, because the loss of the $50,000 has more value — greater marginal utility — than the gain of an additional $50,000, as shown in the above schematic diagram. Of course, if the gain had a sufficiently greater probability, then the investor will be more likely to invest. How much more likely would depend on the perceived probability of the gain or loss and on the risk profile of the investor. Thus, the marginal utility of money explains risk aversion, since a given amount of loss always has a greater marginal utility than the same amount potentially gained.
- The desire for higher income drops off significantly after $100,000 (this will increase with inflation) because the marginal utility of money declines significantly. In most locations, it is a sufficient income to pay for a decent living, which is why other things become more important, such as time off.
- A painting is just an array of colors on a canvas, earns no income, costs money to store and insure, so the only hope for profit is if someone else will pay even more for it later. So why would someone pay $100 million for a painting? Obviously, someone rich enough to afford the finest things in life, so the marginal utility of the $100 million to the buyer is small. If the investment results in a loss, then it is not a loss that would have much consequence for the buyer. After all, no one would spend $100 million for a painting if that is all they had! It also explains why rich people pay $35,000 for a purse or over $1 million for car. Of course, many rich people like to show off their wealth; it is how the rich measure themselves among themselves — it represents their status. For someone who only has $35,000, they certainly would not use it to buy a purse, since many other things will have much greater marginal utility, including food, shelter, and healthcare.
- The poor person needs the money to buy essential goods and services: food, shelter, health insurance, and so on, and even the whole $20,000 would not cover it. On the other hand, the rich person earning $1 million annually still has $100,000 after paying the 90% tax, which still allows her to buy all these essential necessities of life. In fact, her after-tax income would still be almost twice the median household income — before taxes! — in the United States (2015 median income: $55,775), and at least 3 times more after that average income is taxed. If she only paid the 20% rate that the poor person paid, then she could buy a nicer house, a nicer car, and many other things, but the improvements would have less marginal utility. Although the marginal utility cannot be quantified in these cases, it's not unreasonable to assume that the poor person paying a 20% rate has a much greater tax burden than the rich person paying the 90% rate, because the rich person can still live well, even if not as well as she could if she paid the 20% rate.
- Some studies have found that people prefer spending money on experiences rather than goods, which seems perplexing, since goods can last a long time, while experiences are fleeting. A recent study has shown that most people value experiences more than buying material goods, but only if their income exceeds $25,000; otherwise, low-income people prefer to buy material goods. What explains this? Marginal utility, of course. The marginal utility of products is greater when a person has fewer of them, but as the accumulation of goods increases, the marginal utility of additional goods declines, thus making experiences more desirable, especially since there are many more experiences than there are unique products. Moreover, people can enjoy their memories of experiences, especially since such enjoyment is enhanced by the fading of boring or bad memories and by the embellishment of good memories, making the memories better than the actual experiences.
The above are not complete explanations, but marginal utility does provide insight into the economic behavior of people.