The rule
is best thought of as a diagnostic rule, in a double-negative sense. If MB=p is not satisfied, then we don't have a maximum. When neoclassical economists assume that people are acting "as if" they maximized net benefits, what the neoclassical economists mean is that they are assuming that MB=p (or an equivalent rule) applies. The evidence they cite in support of the claim that consumers act as if they were maximizing is mostly evidence that MB=p or an equivalent rule does apply.
The formula MB=p is an example of a very general principle in economics, which we may call the "equimarginal principle." In this case the consumer is seen as balancing the benefits from consuming one additional burger against the cost of consuming one additional burger, and choosing the number of burgers per week so that (as nearly as possible) they are equal. To do this he makes the marginal benefit from the purchase equal to the price he pays for one more unit, which we might call the marginal cost of the purchase. The equimarginal principle is to make the benefits and the costs "equal at the margin." We will apply the same approach throughout the field of microeconomics in the chapters to follow.
Does it seem strange to say that the rational consumer tries to make marginal benefit and price equal? Many students do find it strange, but here is a way to understand it: we are making a distinction between potential and realized net benefits. To maximize, the consumer wants to realize 100% of the potential, as nearly as possible. The difference, marginal benefit minus price, is a measure of unrealized potential net benefit. Total benefit minus total spending on burgers is the realized net benefit. To make the realized benefit as near 100% as possible, we want to make the unrealized potential -- MB-p -- as small as possible. The best is to make unrealized potential benefit, MB-p, zero, so that MB=p. It is the absolute value of MB-p that measures the unrealized potential, so making MB-p negative would not help: MP-p=0 is the target.
Finally: in our burger example, the consumer is limited to choosing 1, 2, 3, or 4 burgers. MB-p=$.02 was as close as he could get to MB-p=0. But remember, we are really talking about the average number of burgers per week. So the consumer could consume a fraction of a burger by buying, for example, four burgers one or two weeks of the year, and three the other weeks. Then his burger consumption would average out to a fraction more than four burgers a week. That means he could to MB=p exactly by consuming fractional burgers. So we'll get rid of the simplifying assumption that people consume whole numbers and, after we finish with the burger example, we'll just say that
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