In this chapter we will demonstrate that THE MARKET PRICE OF A GOOD TELLS US THE WILLINGNESS TO PAY VALUE OF THE MARGINAL CONSUMER. By "market price" we mean the prevailing price of a good in a given city, town, or market. By "marginal consumer" we mean the consumer who would end up with a good if one more unit of that good were distributed to that market. In the context of our T-shirt example, if the price of T-shirts in a given market is $10, that means that if one more T-shirt were shipped to that market, the consumer who would end up with that T-shirt would have a willingness to pay for T-shirts right around $10.

Recall from the previous chapter that at a price of $10, Consumers B and C would choose to purchase the T-shirt, while Consumers A, D, and E would not. Let's assume that once a consumer buys a good, their willingness to pay falls to zero. That is, once they have the good, they wouldn't get any pleasure from having another unit of that good. (This is what we call a simplifying assumption. It's not necessary to get our result, but it greatly simplifies the analysis of the problem.) Now our table of willingness to pay values looks like this.

Suppose we were to distribute one more T-shirt. What would be the willingness to pay value of the person who would receive it? Clearly, the answer to that question depends on who gets the additional T-shirt. If Consumer A was given the T-shirt, then the answer to the question would be $3.50. Alternatively, if Consumer E received the T-shirt, then the willingness to pay value of the person who receives the extra T-shirt would be $7.90. To get us over this hurdle we will make the assumption that a market guided by the price system will tend to direct goods to those who value them most. In a little bit we will explain this. For right now you have to take it on faith.

Of the three consumers who would not buy T-shirts at the price of $10 (A, D, and E), clearly Consumer E would derive the greatest happiness from having one. Assuming the market would direct this additional T-shirt to the one who valued it most, Consumer E would end up with it. Consumer E is then the "marginal consumer." Using the information from the table, we see that the willingness to pay value of the marginal consumer is thus $7.90.

Hold on here! Didn't we just get done saying that the price of a good tells us the willingness to pay of the marginal consumer? We did. But isn't the price of the good $10, while the willingness to pay value of the marginal consumer is only $7.90? That's true, but we aren't done yet.

Let's add five more consumers to our market and repeat the analysis from above. These new consumers have the willingness to pay values reported in the table below.

At a price of $10 per T-shirt, how many T-shirts get bought and who buys them? There are now six consumers who decide to buy T-shirts (B, C, F, H, I, and J) and four who decide not to buy a T-shirt (A, D, E, and G). After the six buy T-shirts, and assuming that they have no interest in another T-shirt, we get the following table of willingness to pay values.

What would be the willingness to pay value of the marginal consumer if we were to distribute an extra (seventh) T-shirt? Once again we assume that the extra T-shirt will go to the consumer who values it most (we really will explain this later). Since Consumer G values it more than A, D, and E, he becomes the marginal consumer to whom the market directs the extra T-shirt. Thus, with ten consumers in our society and a T-shirt price of $10, we can say that the marginal consumer has a willingness to pay value of $8.90.

Now we know that $8.90 is still not $10, but consider what just happened as the number of consumers in the market increased. When there were 5 consumers, the willingness to pay value of the marginal consumer was $7.90. When there were 10 consumers in the market, the marginal consumer's willingness to pay value was $8.90. What do you think would happen if there were 50 consumers in the market? 500 consumers? 500,000? Don't you see as there are more and more consumers in the market, there is a greater likelihood that one of those consumers will have a willingness to pay value a little less--but very close--to the market price of the good. Thus, the marginal consumer's willingness to pay value approaches the market price as the size of the market increases.