We can use the utility-maximizing rule to determine whether consumers are doing the best they can. Suppose a firm has a fixed budget of $200 to spend on punch and cookies for its holiday party. The price of punch is $2 per cup and the price of cookies is $1 per cookie; both goods will, of course, be provided free of charge to workers at the party. The firm’s objective is to maximize the utility of the typical employee, and your job is to determine whether the company spent this year s party budget wisely. To simplify matters, assume that all employees have identical tastes for cookies and punch, so data from a single person will apply to every employee. You can ask the typical employee a single question. What s your question?
From the utility-maximizing rule, we know that when a consumer is maximizing utility, the marginal rate of substitution equals the price ratio. You know the price ratio for the holiday party is 2.0 (the price of punch is twice the price of cookies), so the question for the typical employee is “What is your marginal rate of substitution?” Or in more familiar language, “How many cookies would you be willing to trade for one cup of punch?”
If the answer is two cookies per cup of punch, the MRS equals the price ratio, and the firm did the best it could. On the other hand, if the answer is five cookies per cup of punch, the MRS exceeds the price ratio, and the firm could have generated higher utility with its $200 by providing more punch and fewer cookies.