Constrained Utility Maximization
Now we require Joe to pay a price Pcfor additional cups of coffee. With a fixed daily income
and a price that must be paid, this individual is now a constrained utility maximizer. Joe
must ask himself: “Does the next cup of coffee provide at least $Pcworth of additional hap-
piness?” If Joe answers “yes” to this question for the first three cups of coffee, he maximizes
his utility by stopping at three cups. If his answer is “no” to the fourth cup, he does not
consume it.
Does this sound familiar? It should, as it is another example of how a consumer never
does something if the marginal benefit (in this case, utility) gained is exceeded by the mar-
ginal cost incurred.
- When required to pay a price, the utility maximizing consumer stops consuming when
MB =P.
Demand Curve Revisited
Using the logic outlined above as an example, what would happen if the price of coffee fell?
If Joe was facing a new lower price, you should expect that Joe would rationally increase his
daily consumption of cups of coffee. Have you heard this behavior described before? Sure!
It’s the law of demand, and it has a tight connection to the law of diminishing marginal
utility.
Imagine you are a consumer who has already paid for and consumed the first pint of
ice cream this week. Would you pay the same price for the second pint of ice cream?
Doubtful, because the second pint does not provide the same marginal utility as the first.
In order to entice you to purchase and consume additional pints of Cherry Garcia ice
cream, the price must fall to compensate you for your falling marginal utility.
This law of diminishing marginal utility is the backbone of the law of demand. To con-
vert the relationship between marginal utility and quantity consumed at any price, we
might ask you how much you are willing to pay to consume successive pints of ice cream.
Because of diminishing marginal utility, you offer to pay less for additional units. Thus, we
can then construct your monthly demand curve for ice cream. Figure 7.21 illustrates how
diminishing marginal utility from consumption of a good can be converted to a demand
curve for that good.
Elasticity, Microeconomic Policy, and Consumer Theory ‹ 95DMU
PriceMUHow much
would I pay for
the next unit?Q QFigure 7.21