To get a theory of demand, we have to answer the question: at a certain price of burgers (or any other commodity) how much will the consumer buy? And how will that amount change as the price changes?
We can think of this in terms of opportunity cost. The opportunity cost of a dollar spent on burgers is the utility that dollar would have obtained if it had been spent on any other good. The person will keep increasing his spending on burgers as long as the marginal utility per dollar spent on burgers is greater than the opportunity cost.
In other words, Joe cannot increase his spending on burgers without cutting back on his purchases of something else. So Joe will not increase his spending on burgers unless the next burger gives him more utility than the other goods and services he will have to give up to get it.
(By the way, saving is not an exception. If Joe saves, Joe is using the money he saves to buy something -- a financial asset that he can use to buy some consumer good in the future. So: if Joe cuts back on his saving to guy a burger, it must be because the burger, now, gives him more utility than the good or service he would otherwise buy in the future. Cutting back on cokes now or on saving, it's all the same -- Joe won't do it unless he gets more utility from the burger.)
Two more point follow from this. Joe may not buy any burgers at all. No burgers will be bought unless the marginal utility per dollar is greater than the opportunity cost for the first burger. On the other hand, Joe will almost certainly not spend all his income on burgers, either. Remember the law of diminishing marginal utility. Each additional burger will give Joe less utility -- and so, sooner or later, he will find that the utility he gets is less than the utility of the alternative he has to give up. Diminishing marginal utility assures us that the demand for burgers will be limited.
This leads us back to the equimarginal principle: spending on burgers will increase until the marginal utility per dollar spent on burgers is equal to the opportunity cost, that is, the marginal utility per dollar spent on other goods.
This opportunity cost is often called "the marginal utility of money" or the "marginal utility of income." Here's a reason: if Joe were to get his hands on one more dollar of income, and spend it on other goods and services, the utility he would get is the same as what he would give up if he cut back on spending on those other goods and services to buy more burgers. But for our purposes, it is the opportunity cost that matters -- the "marginal utility of income" is also the opportunity cost of an additional dollar spent on burgers -- or on any other good or service.
But now let's see what happens when the price of burgers rises.
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