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General assumptions
Starting points 2
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Summary on the utility approach
We have begun this chapter on demand theory with the utility approach, an early response of neoclassical economists to the “paradox of diamonds and water” that had set Adam Smith and his contemporaries on a wrong turn. While there are some problems with it, the utility approach teaches some important lessons.
- It focuses our attention on marginal rather than total utility, solving the “paradox of diamonds and water.”
- It gives a reason why the demand curve is downward sloping, namely, the law of diminishing marginal utility. It turns out that that’s not quite the whole story — but we will have to save that complication for intermediate microeconomics.
- It gives us an approach to the whole problem of “efficient resource allocation,” and a key principle of “efficient resource allocation,” the equimarginal principle.
- It gets us started on practical cost-benefit analysis, with the fundamental concept of “consumers’ surplus.”
But for many of these purposes, we do not really need the central idea of utility theory, that subjective benefits from consumption can be directly measured in numerical terms. Instead, we can measure the benefits from consumption indirectly, in money terms. We measure the benefits from consuming a particular good by the market value of the other goods the consumer is willing to give up to get the particular good. The benefits, like the utility, increase at a decreasing rate as the quantity consumed increases; so we have a “law of diminishing marginal benefit.
In order to maximize the net benefits from consumption of a good or service — or, in other terms, to realize 100% of the potential benefit — the consumer will adjust the quantity consumed so that the marginal benefit is just equal to the price paid. Economists regard this maximization as “rational” choice among consumer goods. This leads to the
Fundamental Principle of Consumers’ Demand:
The demand curve for any product or service is identical with the marginal benefit curve for that good or service.
Using this principle, and applying it to market demand as well as individual demand, we can better understand many aspects of demand. As an example, we use the concept of consumers’ surplus — the area between the price line and the demand curve in a demand diagram — as a measure of the consumers’ net benefits in cost-benefit analysis.
Benefits and Costs
Whether we think in terms of the utility approach or the preference approach, a consumer will buy one more unit of a good or service only if she or he gets a benefit from it. The benefit is subjective — getting something she prefers, or increasing her utility — but that subjective benefit is the motivation for buying. The rational consumer will want to balance that benefit against the cost, and buy accordingly.
The cost of any purchase is an opportunity cost. For example, to get a diamond, I have to give up a number of gallons of water. It is equally correct to say that I give up a certain number of slices of pizza, of hamburgers, of subway rides and of movie tickets. When I hand over the money, I give up the goods that money would buy — whether I spent it on pizza, bottled water, movie tickets or whatever.
This is the key to translating from utility or preference to money. We can measure the subjective benefit a person gets from buying (for example) four hamburgers a week. Here is the way we do it. The benefit from four hamburgers is the market value of the most valuable goods the person would give up to get the four hamburgers. Suppose, for example, that I would give up three movie tickets to get the four hamburgers, and the movie tickets would cost me $6 each. And suppose there are no other goods I would give up to get my four hamburgers that would cost more than $18. Then we can say that the four burgers bring me a total benefit of $18. The market value of the goods I would give up is the measure of the benefit I get from the burgers.
Economists call this the “doctrine of revealed preference.” The idea is that, by choosing the burgers over the movie tickets, I have “revealed” that I prefer four burgers a week to three movies a week, ceteris paribus. Of course, I would prefer to have both! But, when I have to choose — perhaps because of a limited income — my choice “reveals” which of these I most prefer. Preference in this sense is, of course, relative!
From here on, we’ll explore demand theory in terms of benefits and costs, measured in money terms by that method. As usual, we will begin with an example — this time the demand for hamburgers.
Marginal Benefit
In demand theory, we can treat “benefit” approximately as “utility” expressed in money terms. As usual, we will be interested in the marginal benefit. We can define the marginal benefit in parallel as we did the marginal utility: the marginal benefit from burgers is the increase in total benefit as a result of consuming one more burger (per week). In algebraic terms:
That is, as near as we can approximate, the marginal benefit is the additional benefit from increasing consumption by one unit. For example, using the table in the previous overhead, when consumption of burgers is incresed from 2 burgers to 4, we have total benefit = 18-15 = 3 and burgers = 4-2 = 2, so the marginal benefit for the range of 2 to 4 burgers is 3/2=1.5.
Dollars of “benefit” parallel “utility” in another way: marginal benefit declines with increasing consumption of a good, ceteris paribus. We will see that the marginal benefit of burgers is smaller, in our example, the more burgers the consumer has. Here is the information we need in a table.
Maximum Net Benefit
This example illustrates several key themes of neoclassical demand theory.
- It is a theory of rational consumer decisions, in a special sense.
- Remember, our consumer kept increasing the consumption of burgers as long as one more burger would increase his net benefits. In other words, he maximized net benefits in consumption of burgers. Economists speak of “utility-maximizing” decisions, using the older terminology, or just of “maximizing” decisions, and understand decisions of that kind as “rational” decisions.
- According to the theory, consumers really do make decisions that are rational, in the sense of “maximizing.”
- Some economists, and many non-economists, doubt that real human beings are capable of “maximizing net benefits” in real-world decisions that can be much more complex than the “how many burgers” example. But neoclassical economist argue that, even though people do not consciously “maximize” anything, they act on the average “as if” they were maximizing. That’s “positive economics” — a question of fact — and neoclassical economists offer a wide range of evidence in favor of it.
- The example also gives us some hints about how to maximize net benefits.
- Recall, the consumer balanced the marginal benefit of one more burger against the price, and kept increasing his consumption until the marginal cost was very nearly equal to the price. The general rule is, to maximize net benefits, a consumer should adjust consumption so that MB=p, as nearly as possible.
Utility of Diamonds and Water
The explanation of the Paradox of Diamonds and Water will need a little special terminology. We will use the concept of marginal utility, and marginal utility will play an important part in some of the sections to follow.
It is best to begin with an example. In the example, we will assume that a person can buy water or diamonds or both. We assume that the satisfactions she gets from diamonds and from water can be measured in money terms. Following a long tradition in economics we will speak of the amount of satisfaction as the “utility” of diamonds and water. We assume:
- that her total satisfaction is the sum of the utility of water and the utility of diamonds,
- that the utility of diamonds increases as she consumes more diamonds,
- that the utility of water increases as she consumes more water, and
- that she tries to spend her income in such a way as to get the most satisfaction that she can — that is, that she “maximizes” utility.
Marginal Utility
This example makes several points.
First, the consumer’s decision is not an all-or-nothing one. Instead, it is a decision to buy or not to buy just one more unit. That means it is a mistake to look at the total utility of the two goods as the basis for demand. The total utility is irrelevant to the decision to buy or not to buy one more unit of the good. What is relevant to any decision is what is gained or lost depending on how the decision is made; and only a part of the total utility is gained or lost as a result of the decision to buy, or not to buy, one more unit of the good. Economists call the part of utility that is gained or lost (in the decision to buy one more unit) the marginal utility.
So we should not look at the total utility but at the “marginal” utility of the good or service. Marginal utility is defined as the increase in utility as a result of consuming one more unit of the good. In other — algebraic — terms,
MU = U/Q approx = dU/dQ
where U is utility and Q is the quantity of the good. In the numerical example, the MU of water is 1 and the MU of diamonds is 15, so the consumer is willing to pay 15 times as much for a diamond as for a gallon of water. (This example is, of course, not “realistic.”) Despite that, the person gets about 67000 times as much total utility from water as from a diamond.
Let’s see how the marginal utility of diamonds and water vary depending on how much of each good the person has.
Diminishing Marginal Utility 1
This illustrates a general principle that has much wider application in economics. In economics, we speak of a law or principle of diminishing marginal utility.
The “Law of Diminishing Marginal Utility” states that for any good or service, the marginal utility of that good or service decreases as the quantity of the good increases, ceteris paribus. In other words, total utility increases more and more slowly as the quantity consumed increases.
This is “diminishing returns” from the viewpoint of the consumer, and is a general principle of economics. There might be a threshold before the principle applies. For example, the marginal utility of golf clubs might increase until you have a fairly full set. But beyond some threshold, marginal utility will diminish with increasing consumption of any good.
There are other applications of “diminishing (marginal) returns” in other branches of microeconomics.
Marginal Utility and Demand
The marginal utility approach resolves the “paradox of diamonds and water.” There is no paradox: the scarcer good, diamonds, have the higher marginal utility, even though water gives the greater total utility. This opens the way to develop a theory of demand based on utility. But we aren’t there yet.
Demand is a relation between money price and quantity purchased. So far, using our example, we have seen why a person might give up a large amount of water to get a diamond. That’s not quite the same as giving up a large amount of money for a diamond. So one step we need to take is to translate from the barter of goods for goods to the exchange of goods for money. We won’t go into detail, but, if you are interested, here is a sketch of how to do that in terms of utility.
Once we have translated from barter to money exchange, we can move ahead with the theory of demand. We’ll be getting to that real soon now. But first, there are some problems with the whole utility approach — at least, some economists believe there are.
Demand in General
This illustrates a general principle that applies to all consumer demand. In fact, it is so important and general that we might call it the fundamental principle of consumers’ demand. Here it is:
Fundamental Principle of Consumers’ Demand:
The demand curve for any product or service is identical with the marginal benefit curve for that good or service.
We remember the Law of Demand: a higher price means a lower quantity demanded, ceteris paribus. We also remember the Law of Diminishing Marginal Utility: each additional unit of consumption adds less to utility than the previous one. Since benefits are approximately utility in money terms, that also applies to benefits — each additional unit of consumption adds less to total benefits than the previous one. So we have diminishing marginal benefits, and we can now see that the Laws of Demand, Diminishing Marginal Utility, and Diminishing Marginal Benefits all really are the same law, looked at from different points of view.
Marginal Benefit and Consumer’s Surplus
Now, let’s see how to put these ideas to work in cost-benefit analysis. The first step will be to restate the relationship between the demand and the consumers’ benefits. The consumer will buy just enough of any good so that the marginal benefit of the good is equal to its price. Conversely, the individual’s demand curve is also her marginal benefit curve for the good.
The burgers example illustrates this. Let’s forget about the pennies and suppose that the consumer bought three burgers at a price of $2, so that the price is exactly equal to the marginal benefit of the third burger.
But notice that the total benefit from three burgers is $17, while the consumer has paid only $6.00 for the three burgers. He has gotten a net benefit of $17-$6.00=$11.00 from the three burgers. This net benefit of $11.00 is called the “consumer’s surplus.”
How has this happened? The customer got a marginal benefit of $10 for the first burger, but paid only $2, for a net of $8. For the second burger, he got a marginal benefit of $5, but paid only $2, for a net of $3. The consumer’s surplus is the sum of the net benefits on the successive units bought: $8+$32=$11.
Price is equal to marginal benefit, which means the marginal benefit of the “last” unit bought. If the price had been higher, he would have bought fewer units. The “last” unit does not mean the last unit in time or space, but the unit the consumer would not have bought if the price were just a little higher. For the “previous” or “inframarginal” units, the person would be willing to pay more if he had to. They must be worth more to him — but in a competitive market, he gets these “previous” or “inframarginal” units at the same price as the “last” unit. So he gets a net surplus on the “previous” or “inframarginal” units. In the example the surplus is $8 of benefits on the “first” burger and $3 on the “second” burger. This “consumers’ surplus” is the benefit the consumer gets from buying in a competitive market
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