Nobody needs a fourth latte before noon. That simple fact, that each cup is worth a little less than the one before, is where the downward-sloping demand curve comes from.
Learning objectives. After this week you can (1) compute marginal utility from total utility; (2) apply the rule of equal marginal utility per dollar; and (3) explain why diminishing marginal utility makes demand slope down.
Remember this: customers spend where their next dollar brings the most satisfaction.
1) Utility and marginal utility
Utility is satisfaction, counted in made-up units called utils. Marginal utility (MU) is the extra satisfaction from one more unit.
Marginal Utility = change in Total Utility ÷ change in Quantity
| Cups | Total utility | Marginal utility |
|---|---|---|
| 1 | 20 | 20 |
| 2 | 36 | 16 |
| 3 | 48 | 12 |
| 4 | 56 | 8 |
| 5 | 60 | 4 |
The 4th cup adds 56 − 48 = 8 utils. Each cup adds less than the one before: the law of diminishing marginal utility. Total utility still rises while MU is positive, just more slowly.
2) Spending a budget well
MU of coffee ÷ Price of coffee = MU of muffin ÷ Price of muffin
A coffee giving 20 utils at $2 delivers 20 ÷ 2 = 10 utils per dollar. A muffin giving 30 utils at $3 also delivers 10. Equal, so the budget is well spent. If coffee gave 10 per dollar and tea 5, moving a dollar from tea to coffee would raise total utility. The rule compares utility per dollar, not utility alone.
3) Where demand comes from
Because each extra cup is worth less to a buyer, they buy more only if the price falls. That is the downward-sloping demand curve, seen from the customer's side.
Your customers make this choice every morning: your latte, your drip, Common Grounds' latte, or no coffee at all. The lattes and drips on your Daily Report are their answer at your two prices.
Quick self-check
(a) Total utility goes from 20 (1 cup) to 36 (2 cups). What is the 2nd cup's MU? (b) A latte gives 40 utils at $4.00 and a drip gives 15 utils at $2.50. Which gives more per dollar? (Answers: 16 utils; the latte, 10 per dollar against the drip's 6.)
Common mistakes
- Comparing utils, not utils per dollar. A good twice the price needs twice the MU.
- Thinking total utility falls when MU falls. It still rises while MU is positive.
- Treating the drink mix as fixed. Change one price and customers rebalance.
This week in the arena
Pick one Daily Report and find the line that reads lattes, drips and pastries. Work out what share of your drinks were lattes (lattes ÷ customers served), then compare your latte and drip prices. When the gap between those prices changes, watch whether the mix moves the way utility per dollar says it should.