To Buy or Not To Buy
4. From marginal utility to the demand curve

The influence of price on demand

Back to Maria's choice of gasoline. If the price of gasoline is $3.00 per gallon, then Maria can be viewed as facing this problem: "How many gallons do I want to own, considering the price is $3.00?" Notice how the question has been turned around. So far our discussion has asked what she would be willing to pay for the Nth gallon of gasoline (the first, the second, and so on). The turned-around question looks at the same table of marginal utilities but starts with the second (value) column and moves back to the first (quantity). The same table and same diagram apply (refer to Table 5.1 and Figure 5.3).

Figure 5.4. A rational person chooses the quantity that brings marginal utility down to price

This is the same graph as in Figure 5.3. The vertical axis measures the marginal utility in dollar terms. The price is given at $3.00. Maria chooses to buy the number of gallons where the marginal utility (of the last gallon bought) equals or just barely exceeds the price.

Maria buys four gallons of gasoline because (as shown in Table 5.1) the last, fourth gallon is worth (in utility to Maria) $1.10, which just exceeds the going price. What is being applied here is the Rule of Rational Life:

Do what's best - and you can do it by equalizing marginal benefit and marginal cost.

When Maria buys her first gallon, she adds $10.00 in utility to her total utility, because $10.00 is the value in use of the first gallon. She has to give up only $3.00 to acquire the $10.00-worth of utility. A good deal. In total her utility goes up by the difference ($10.00 - $3.00 = $7.00). On balance she feels better. And so it goes until that third gallon, which nets her only ***$0.10 on the deal. To go further, and buy five gallons, would give her a marginal benefit of $0.90 but would have a marginal cost, still, of $3.00. Not a good idea. Stop at four gallons.

The step from here to the demand curve is simple. Translate the marginal utility curve into dollar values---as we've already done so in the example. That's called the marginal valuation curve. You might as well call it the "marginal value in use" curve. It's just Maria's demand curve. It says that at $3.00 she buys a certain number of gallons of gasoline, namely three. But it also says that at a lower price she would buy more. Try it out. If the Going Price in the diagram were lower, it would obviously cross the Marginal Utility curve at some larger quantity. But buying more at a lower price is merely the Law of Demand, familiar from Chapter 3. In other words, the Law of Demand can be derived from thinking about diminishing marginal utility. If you believe that the 74th tortilla at a sitting would not be quite so tasty as the first, then you also believe in the Law of Demand.

Figure 5.5. The buyer's marginal utility curve is also a marginal valuation (demand) curve

The graph is the same as the graph in Figure 5.4 with one difference: now you read "price" on the vertical axis instead of "marginal utility expressed in dollars." At a lower price she buys more gallons because it will take more gallons to get marginal utility equal to that lower price.

Now we're getting somewhere. The Law of Diminishing Marginal Utility links the Law of Demand to sensible behavior by individuals. If Maria has a demand for gasoline, so does Alan, and so do millions of other people. Taken together their little demand curves make up the Market Demand Curve. The market demand curve depends on how individuals value the next gallon of gasoline or carat of diamonds they are thinking of buying.

Figure 5.6. Individual demand curves add up to the total (market) demand curve

At each separate price determine the quantity of chocolate gallons that individuals demand for that price. Add those quantities up horizontally and you get the total market demand for the price. Do so for each price and you have derived the total demand for gallons of gasoline.

A solution to the water-diamond paradox

The analysis of marginal utility thoroughly resolves the water-diamond paradox. True, the total utility that a person gets from having all the water he or she uses is greater than the total utility he or she gets from having diamonds. Without water the person would be dead; without diamonds he or she would be a little less ornamented. It's not the total utility, though, but the marginal utility that matters for markets. The marginal valuation of the last ounce of water is what figures in the demand curve, not the earlier marginal valuations. Fresh water is so abundant that its marginal utility is low, and so it is priced low, and so it is used a lot, for watering lawns and flushing toilets. Diamonds are so rare that they are reserved for high-value, high-marginal-utility uses, as for instance tokens of marital affection. Their total utility is probably quite small beside the total utility of water. But marginal utility runs the markets.

Concept Check 4: What is the addition to Maria's utility from the first gallon of gasoline she buys? The second? The third? The fourth? Make a two columned table. Contrast successive subtotals with the marginal utility she gets from each gallon (1st, 2nd, 3rd, and so on). What is the total utility she gets from her purchase of the 3 gallons as a whole?
Technical workshop: Consumer surplus
The logic of Concept Check 4 can be extended a long way. It's one of the premier tools of applied economics, used for evaluating road projects, for example, and for showing the costs and benefits of price and wage controls. The total value in use is just the area under the marginal valuation:
Figure 5.7 Measuring total utility and the consumer surplus

Total utility is the summation of marginal utilities. The area of each rectangle measures the marginal utility of the last item demanded. Adding up the rectangles gives you total utility. This total is, by approximation, equal to the surface below the curve, namely the shaded areas Cost plus Surplus.

The area Cost under the price line measures the total opportunity cost of buying four gallons at the going price. It's of course just the value in exchange (namely, $4.00). The value in use exceeds the value in exchange by the red colored triangle Surplus. It's called consumer surplus. Formally, consumer surplus is the excess of value in use over value in exchange for the amount purchased.

You can also think of the total value in use as the most that Maria would be willing to pay for all gallons of gasoline if she had to. For the first gallon she would be willing to pay $3, $2 for the second, and so on. But she actually pays only $1. Accordingly, Maria the consumer gains when she buys four gallons of gasoline. The area Surplus is her "gain from trade" (which is still another name for the concept). It is the "profit" or surplus of happiness Maria the consumer got on all the gallons she actually bought.

It is obvious, actually, that there is a consumer surplus. When you buy anything you always pay less than the maximum amount you would be willing to pay. Why? Because otherwise you would not buy it! You are certainly not going to pay more than what you are, at most, willing to pay. So you pay less if you buy at all.

Notice that the point picked out by the Rule of Rational Life is the point of maximum consumer surplus. One could say "choose the point of maximum surplus" or "choose the point where marginal utility equals the cost of the next gallon." They lead to the same answer. If Maria bought too few gallons she would not get the whole Surplus. Or if she bought too many, say five, she would again be giving up surplus, because the area of loss on the additional purchases, Loss, would have to be subtracted from the area Surplus.

Heterdox Box: Conspicuous Consumption
Not every economist is impressed by the law of demand. In 1899 Thorstein B. Veblen published an unusual book, The Theory of the Leisure Class, arguing among other things that emulation, status, envy, the desire to make "invidious distinctions," not price, were the big drivers of demand. He coined a term-"conspicuous consumption"-to describe what the rich do when they go to market. Buying more when the price is high, especially for items that signal your status, such as bright trophies, green lawns, and even mistresses, said Veblen, makes sense. What better way to show off your great wealth and status? Veblen, and especially Veblen's many followers, such as John Kenneth Galbraith (1908-2006), thought that social pressures like status and advertising were more important than price.

Neoclassical economists don't believe that Veblen's critique of the law of demand cuts very deeply. For example, there are substitutes for everything, they say, including status and other forms of invidious distinction, and people economize on them just as they do bread and beer. A stranger or best friend will not be able to tell that your Prada purse came from T. J. Maxx in Peoria and not from Prada in Paris. But the contents of your purse prove the point. Fake status goods can be bought at a low price, and the lower the price, the higher the quantity demanded. Do all those wearers of Louis Vuiton handbags pay full retail price?

And does advertising really do what its critics think---"manipulate" consumers? That's you. The neoclassical economists doubt it. One among several warrants for their doubt is that if advertising were so powerful then advertiser would be rich. It's the $100 Bill Theorem again.

Economists subscribing to a school of thought called "Institutionalism"-to which Veblen largely contributed-persist in their disagreement with neoclassical economists. The status good in question will lose its status at a high volume of circulation, they reply, turning the neoclassical response on its head. Fake Vuiton's will cause people to shift to other signals of status and wealth. And on advertising theinstitutionalists, and many others, claim to the contrary that advertising is essential for late capitalism. And so on. Science, you see again, is a conversation about exactly where we agree and disagree.