The Law of Diminishing Marginal Utility
It's a hot day in Mexico City and you've just finished soccer practice. The first bottle of water tastes amazing. The second one, very good. The fourth... you're just drinking it to drink it. Why does the same product give you less and less satisfaction? And, above all, what does that have to do with what you're willing to pay? In this section you'll be able to measure it.
Total utility: the satisfaction you get from consuming
In consumer theory, utility doesn't mean "profit in pesos" (as it does for a business), but satisfaction: how much well-being you get from consuming something. Since satisfaction can't be weighed, economists measure it with an invented unit: utils.
Diego writes down how much satisfaction he gets from steamed tacos (tacos de canasta). With 0 tacos, TU is 0. With 1 taco, 10 utils. With 2 tacos, 18 utils in total (not 18 for each one: it's the accumulated amount).
Notice that the curve goes up, but less and less steeply. That clue is the key to this section.
Diego keeps track of the satisfaction he gets from eating basket tacos, measured in «utils»: | Tacos | Total utility (utils) | | --- | --- | | 0 | 0 | | 1 | 10 | | 2 |…
Diego keeps track of the satisfaction he gets from eating basket tacos, measured in «utils»:
| Tacos | Total utility (utils) |
|---|---|
| 0 | 0 |
| 1 | 10 |
| 2 | 18 |
| 3 | 24 |
| 4 | 28 |
| 5 | 30 |
- a) Compute the marginal utility of each taco, from the first to the fifth, and show it in a table.
- b) Does the law of diminishing marginal utility hold? Back up your answer with your results.
Marginal utility: what one more unit adds
When you decide whether to order another taco, you don't think about all the ones you've already eaten, but about what one more gives you. That is marginal utility.
You subtract because what unit $n$ adds is exactly the difference between what you had with it and what you had without it.
You can also go the other way: if you know the MU, TU is the running total. With MU of 12, 9, 6, 3, the TU with 3 units is $12 + 9 + 6 = 27$.
Fill in the following table, which shows the total utility and marginal utility a consumer gets from buying elotes at the fair: | Elotes | Total utility (utils) |…
Fill in the following table, which shows the total utility and marginal utility a consumer gets from buying elotes at the fair:
| Elotes | Total utility (utils) | Marginal utility (utils) |
|---|---|---|
| 1 | 12 | 12 |
| 2 | ? | 9 |
| 3 | 27 | ? |
| 4 | ? | 3 |
| 5 | 31 | ? |
Copy the table with the four missing values and point out from which elote the law of diminishing marginal utility shows up.
The law of diminishing marginal utility
Look at Diego's series: 10, 8, 6, 4, 2. Each extra taco gives him less satisfaction than the one before. It's no coincidence: it's a regularity of human behavior.
The reason is intuitive: the first unit meets your most urgent need (hunger, thirst); the following ones meet needs that are less and less urgent. Notice that TU keeps rising as long as MU is positive, just more slowly.
When MU reaches zero or becomes negative
Mariana is drinking agua de jamaica (hibiscus water) on a hot day. Her TU is 0, 14, 26, 34, 38, 38, 35.
| Glass | TU | MU |
|---|---|---|
| 1 | 14 | 14 |
| 2 | 26 | 12 |
| 3 | 34 | 8 |
| 4 | 38 | 4 |
| 5 | 38 | 0 |
| 6 | 35 | −3 |
At glass 5, MU is zero: TU has reached its maximum (the saturation point). At glass 6, MU is negative: so much water is making her feel sick and her total satisfaction drops.
On a hot day, Mariana drinks glasses of jamaica water and records her total utility: | Glasses | Total utility (utils) | | --- | --- | | 0 | 0 | | 1 | 14 | | 2 | 26 | |…
On a hot day, Mariana drinks glasses of jamaica water and records her total utility:
| Glasses | Total utility (utils) |
|---|---|
| 0 | 0 |
| 1 | 14 |
| 2 | 26 |
| 3 | 34 |
| 4 | 38 |
| 5 | 38 |
| 6 | 35 |
- a) Compute the marginal utility of each glass.
- b) At which glass is the marginal utility zero? And starting from which one does it turn negative?
- c) Explain in your own words what it means that total utility falls even though Mariana keeps drinking.
MU and willingness to pay
Since MU falls with each unit, willingness to pay also falls. After practice, you gladly pay $\$25$ for the first bottle of water: it gives you a lot of satisfaction. The fourth gives you very little, so you wouldn't pay more than, say, $\$8$. That's why stores lower prices when you buy several items ("3 for 2" promotions).
The first bottle of water after working out is worth a lot to almost anyone; the fourth one, much less. a) Explain this fact using the concept of marginal utility. b)…
The first bottle of water after working out is worth a lot to almost anyone; the fourth one, much less.
- a) Explain this fact using the concept of marginal utility.
- b) Connect it to willingness to pay: why would a rational consumer gladly pay $\$25$ for the first bottle but not for the fourth?
How many units should you buy?
The decision rule is simple: buy one more unit as long as what it is worth to you (MU in pesos) is greater than or equal to its price. When the price exceeds what it is worth, stop.
Going back to the beginning: the fourth bottle gives you little satisfaction because MU decreases, and that is why you value it less and no longer pay the same for it.
At a fair, each glass of flavored water costs $\$18…
At a fair, each glass of flavored water costs $\$18$. Mariana values each glass in pesos, according to the satisfaction it gives her (her marginal utility measured in pesos):
| Glass | Marginal utility |
|---|---|
| 1 | $\$30$ |
| 2 | $\$24$ |
| 3 | $\$20$ |
| 4 | $\$16$ |
| 5 | $\$12$ |
- a) How many glasses should she buy if she wants the highest possible net satisfaction? Justify your answer by comparing the marginal utility of each glass with its price.
- b) Compute the total net gain of that decision: the difference between what she values the glasses she buys and what she pays for them.