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?