Social Sciences and History / Unit 13 SSH 1226 worked example, 60 to 90 seconds
The Rule MU/P = MU/P: Finding the Best Bundle
The idea
The exam gives prices and marginal utilities and asks the best bundle, and the anchor gives three routes to it, the third a rule. First, add up total utility for each affordable bundle on the budget line and take the highest. Second, start anywhere and move toward neighbors that raise utility until none does. Third, compare marginal utility per dollar: at the optimal choice the ratio of marginal utility to price is equal across goods, MU one over P one equals MU two over P two, the consumer equilibrium, where the ratio of prices equals the ratio of marginal utilities. If one good yields more utility per dollar, shift spending toward it; diminishing marginal utility lowers its ratio as you buy more, until the ratios meet.
In practice
Given "coffee costs two and its next cup is worth eight; tea costs one and its next cup is worth three", coffee gives four per dollar, tea three: buy more coffee. Given "the ratios are equal", stop. Given "a good's price falls", its utility per dollar rises, so buy more, which is the law of demand from the inside. Ask, for each good, how much satisfaction the last dollar bought.
Where people slip
The trap is comparing marginal utilities without dividing by price. The second trap is expecting equal quantities; the rule equalizes utility per dollar, not units.
Your place on the trail
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