Utility theory is a useful way of analyzing how a consumer makes choices. But in the real world we do not observe a consumer’s utility, either total or marginal. Instead, his or her behaviour in the marketplace is observed through the demand curve. How are utility and demand related?
Demand functions relate the quantity of a good consumed to the price of that good, other things being equal. So let us trace out the effects of a price change on demand, with the help of this utility framework. We will introduce a simplification here: goods are divisible, or that they come in small packages relative to income. Think, for example, of kilometres driven per year, or liters of gasoline purchased. Conceptualizing things in this way enables us to imagine more easily experiments in which small amounts of a budget are allocated one dollar at a time. In contrast, in the snowboard/jazz example, we had to reallocate the budget in lumps of $30 or $20 at a time because we could not “fractionalize” these goods.
The effects of a price change on a consumer’s demand can be seen through the condition that describes his or her equilibrium. If income is allocated to, say, three goods {a, b, c}, such that
, and the price of, say, good
b falls, the consumer must reallocate the budget so that once again the MUs per dollar spent are all equated. How does he do this? Clearly, if he purchases more or less of any one good, the MU
changes. If the price of good b falls, then the consumer initially gets more utility from good b for the last dollar he spends on it (the denominator in the expression 
falls, and consequently the value of the ratio rises to a value
greater than the values for goods a and c).
The consumer responds to this, in the first instance, by buying more of the cheaper good. He obtains more total utility as a consequence, and in the process will get less utility at the margin from that good. In essence, the numerator in the expression then falls, in order to realign it with the lower price. This equality also provides an underpinning for what is called the law of demand: More of a good is demanded at a lower price. If the price of any good falls, then, in order for the equilibrium condition to be re-established, the MU of that good must be driven down also. Since MU declines when more is purchased, this establishes that demand curves must slope downwards.
The law of demand states that, other things being equal, more of a good is demanded the lower is its price.
However, the effects of a price decline are normally more widespread than this, because the quantities of other goods consumed will also change. As explained in earlier chapters, the decline in the price of good b will lead the consumer to purchase more units of complementary goods and fewer units of goods that are substitutes. So the whole budget allocation process must be redetermined in response to any price change. But at the end of the day, a new equilibrium must be one where the marginal utility per dollar spent on each good is equal.
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