In a way, the surprise is that anything at all can be said about this, in general. The obvious guess is that people have a wide variety of motives, and that different things motivate different people to buy different things, so that nothing can be said in general. All that these motivations have in common is that the item bought gives satisfaction -- or, as we will say, "utility" -- of some sort. This may seem pretty vague, but, surprisingly, we can do a good deal with it.
However, Smith saw a difficulty with this argument. The problem Smith posed has come down to us as the "Paradox of Diamonds and Water."
The Labor Theory of Value came to play a key role in Marxism, and has a history of its own. We will have to leave this history for the study of Marxist economics, and for now go on to show how the New Economists of 1880 answered Smith's paradox.
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 numerical terms. Following a long tradition in economics we will speak of the amount of satisfaction as the "utility" of diamonds and water. We assume:
| Water | Diamonds | ||
|---|---|---|---|
| Gallons | Utility | Carats | Utility |
| 1 | 1,000,000 | 1 | 15 |
| 2 | 1,000,100 | 2 | 29 |
| 3 | 1,000,110 | 3 | 42 |
| 4 | 1,000,111 | 4 | 54 |
| 5 | 1,000,111 | 5 | 64 |
3 gallons of water but no diamonds. The fourth gallon of water would give her only one additional unit of utility. However, the first diamond would give her 15 units of utility. Thus, she would be willing to spend 15 times as much for a one-carat diamond as for a gallon of water..
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.
For that reason, we should not look at the total utility but at the "marginal" utility of the good or service. Marginal utility is defined as
MU = U/Q ‰ U/Q
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.
Second, it follows that when one commodity is very common, and the other is very scarce, it is not so surprising that a person would pay more for the scarce good.
| Water | Diamonds | |||
|---|---|---|---|---|
| Total Utility | Marginal Utility | Total Utility | Marginal Utility | |
| 0 | 0 | 0 | ||
| 1,000,000 | 15 | |||
| 1 | 1,000,000 | 15 | ||
| 100 | 14 | |||
| 2 | 1,000,100 | 29 | ||
| 10 | 13 | |||
| 3 | 1,000,110 | 42 | ||
| 1 | 12 | |||
| 4 | 1,000,111 | 54 | ||
| 0 | 10 | |||
| 5 | 1,000,111 | 64 | ||
We observe that for each good, the marginal utility decreases as the quantity of the good increases. 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.
The utility theory works OK as an example, to show how the "paradox of diamonds and water" can be resolved. But some economists -- and many other people -- are pretty doubtful that consumer satisfaction can really be measured in a number.
In more advanced economics, we have an alternative: "preference theory." It turns out that all we really need is consistent preferences. That is, suppose the consumer prefers five gallons of water and one diamond to fifty gallons of water and two diamonds. As long as those preferences are consistent, we can just use the preferences -- no utility numbers -- to get a theory of demand.
Whether we think in terms of the utility approach or the preference approach, a consumer buys 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. How can we measure a subjective benefit?. We can measure the subjective benefit by using the idea of opportunity cost. Let's measure the 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."
For the example, we'll assume that a consumer's benefit from burgers increases with the number of burgers consumed as we see in Table 3.
| Burgers | Total Benefit in $ |
|---|---|
| 1 | 10 |
| 2 | 15 |
| 3 | 17 |
| 4 | 18 |
As usual, we will be interested in the marginal benefit. We can define the marginal benefit in parallel as we did the marginal utility:
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.
| Burgers | Total Benefit | Marginal Benefit |
|---|---|---|
| 0 | 0 | |
| 10 | ||
| 1 | 10 | |
| 5 | ||
| 2 | 15 | |
| 2 | ||
| 3 | 17 | |
| 1 | ||
| 4 | 18 |
We assume that a rational consumer will keep increasing the consumption of burgers until she has maximized net benefits The rule for this objective is That is, according to basic economic theory, consumers adjust their consumption of all goods and services so that MP=p for each good and service. MB=p
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:
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.
That's actually pretty easy. At any price, the market demand is the sum of the amounts demanded by each of the individuals at that price. That is, the market demand is the horizontal sum of the individual demands.
The diagram shows individual demand curves for Tom,
Dick and Harry. The thick gray line is the demand curve for a market consisting of Tom, Dick and Harry.
The burgers example illustrates this. Our consumer, in the example, buys three burgers. The marginal benefit of the third burger is $2, equal to the price.
But notice that the total benefit from three burgers is $17, while the consumer has paid only $6 for the three burgers. He has gotten a net benefit of $17-$6=$11 from the three burgers. This net benefit of $11 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+$3=$11.
In the figure, the demand for burgers is the stairstep, and the $2 price is the gray line. The lightly shaded area between the demand curve and the price line is the consumer's surplus.
The area under the demand curve is the consumer's total benefit, and the area between the demand curve and price line is her net benefit, that is, consumer's surplus.
Suppose D is the demand for VCR's and p is the price for which they sell. Before VCR's were introduced, consumers of course got no benefit from them at all. After they are introduced, consumers get a surplus indicated by the area of the shaded triangle. That is their net benefit from buying VCR's and is the consumers' benefit from the introduction of the new good.
Skeptic: I don't see how a "theory of demand" is possible. People demand different goods and services for all sorts of different reasons.
NE: The economist's strategy is to abstract from all that. What all goods and services have in common is that they give the consumer satisfaction -- "utility" -- and our theory of demand is built on just that.
Skeptic: That doesn't sound very promising! Can you say anything worthwhile at that level of abstraction?
NE: That's just what the utility approach does, and it shows that we can say important things without worrying about all the reasons why people buy things. Look what the utility theory tells us:
Skeptic: OK, I guess that proves the trick can be done -- but at what price, if you will excuse the expression! I have some problems with this whole utility approach.
NE: Tell me what they are.
Skeptic: Well -- the first one is small, but it bothers me. In your examples, the utility of cokes depends only on the consumption of cokes. What if the burgers make the consumer thirsty? Wouldn't that shift his marginal utility of cokes?
NE: Probably. That's just a simplifying assumption. We can get rid of it -- with a little math or geometry -- but we'll save that complication for intermediate microeconomics.
Skeptic: I'm supposed to trust you, huh?
NE: You could sign up for Econ 320.
Skeptic: I'll trust you.
Skeptic: OK -- I guess I can buy this as a first approximation with a lot of simplifying assumptions for us first-term students. But one other thing puzzles me. Is this positive or normative economics?
NE: A bit of both, all mixed up in complicated ways. For example: we can compute the consumers' surplus from an estimate of the demand curve. That's positive economics. We can use that to estimate the costs and benefits of some government policy. That's positive economics (although the use of terms like "benefit" has some normative connotations). But as soon as we say that the government policy ought to be this, or that, because of the costs and benefits -- that's normative economics.
Skeptic: OK! I've got a few ideas about demand. How about supply?
