Practice

Marginal utility per dollar

Choose the combination of two goods that maximizes total utility on a budget, by comparing marginal utility per dollar.

The skill

A consumer gets the most total utility from a fixed budget by buying where the last dollar spent on each good brings the same marginal utility. Divide each unit's marginal utility by its price to get utils per dollar, then buy units in order from the highest value down until the budget is spent. Check that the combination costs exactly what the consumer has. The usual mistake is ranking units by marginal utility alone, which ignores that one good costs more than the other.

A worked example

Jordan has $18 to spend on pretzels, which cost $2 each, and smoothies, which cost $4 each, and wants the most total utility from it. The table shows the marginal utility of each unit.

Marginal utility (utils) of each unit
UnitMU of pretzelsMU of smoothies
12656
22044
31632
41424
51216
61012

How many smoothies should Jordan buy?

Solution

  1. Divide each marginal utility by the price to get utils per dollar: pretzels 13, 10, 8, 7, 6, 5; smoothies 14, 11, 8, 6, 4, 3.
  2. Buy units in order of utils per dollar until the $18 is spent. That gives 3 pretzels and 3 smoothies, which costs $2 × 3 + $4 × 3 = $18.
  3. At this combination the last dollar spent on each good brings the same marginal utility, 8 utils, and every unit left out brings less.
  4. Total utility = 26 + 20 + 16 + 56 + 44 + 32 = 194 utils.

Answer: 3

Your turn

Lessons behind these problems