1. Utility Maximization Module KRUGMAN'S MICROECONOMICS for AP* Micro: 1551
Module
Utility Maximization
KRUGMAN'S
MICROECONOMICS for AP*
Margaret Ray and David Anderson

2. What you will learn in this Module:
What are consumers trying to maximize, and why?
Why don’t rich people buy lots of rice? What doesn’t the income effect explain well?
How would a perfectly rational consumer spend their $100 at Walmart?
The purpose of this module is to introduce the concept of utility and the theory of consumer choice. Students will learn how utility-maximizing consumers choose to purchase bundles of goods and services, given a budget constraint.

3. Maximizing utility
How do you spend money? How do you choose what to buy?
Why do we demand particular goods and services? Because they make us happy and because we can afford them. Economists refer to this happiness as utility.

4. Utility
Utility: a measure of the satisfaction the consumer derives from consumption of goods and services.
Utility and Consumption
The principle of diminishing marginal utility
How to measure?
Utility is a subjective notion in economics, we don’t expect to really measure it, but consumers know when utility is rising or falling, and they know when one choice provides more utility than another.

5. Utility Pizza slices Utility 1 20 2 36 3 46 4 52 5 54 6 511 20 2 36 3 46 4 52 5 54 6 51
How many cokes can you drink?
Diminishing marginal utility: at some point, the happiness gained from obtaining one more unit decreases.
Marginal [adj]: at the edge, the limit
Diminishing [adj]: getting smaller and smaller
Marginal Utility 20 16 10 6 2 -3
Utility is a subjective notion in economics, we don’t expect to really measure it, but consumers know when utility is rising or falling, and they know when one choice provides more utility than another.

6. Utility Cokes Utility Marginal Utility X 1 20 2 35 3 45 4 50 5 53 6 52X 1 20 2 35 3 45 4 50 5 53 6 52
Now, assume you have about 10$ to spend. Cokes are 1$ each.
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

7. Utility
If we assume pizza is 2$ a slice and coke 1$ per can, and since we have 10$, how many of each should we buy to maximize our utility?
How can we relate money and utility?
[hint: use a similar mathematical method as our various elasticity formulae]
Now that we have our formula, remember that you want to maximize your happiness, your utility. Therefore, which amounts have the same marginal utility per dollar?
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

8. How much of each?
The rule of equal marginal utility per dollar spent : To maximize the total utility (given limited income), you should buy pizza and Coke up to the point where the last slice of pizza and the last cup of Coke give you equal increases in utility per dollar.
In short, marginal utility per dollar spent must be the same for both goods. Mu pizza/P pizza = MU Coke/P Coke
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

9. Don’t forget how much money we have to spend!
There’s about three combinations that satisfy the marginal dollar spent.
Don’t forget how much money we have to spend!
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

10. Budgets Good Y Good X The budget line, budget constraint
The optimal consumption bundle
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.
Good Y B A C
Good X

11. Summary We can summarize the two conditions for maximizing utility.
Marginal utility per dollar spent must be the same for both goods
MUpizza / Ppizza = MUCoke / PCoke
2) Spending on pizza + Spending on Coke = Income
(Ppizza × Qpizza) + (PCoke × Qcoke) = Income
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

12. Concept Check
1) What would happen if the price of pizza fell to 1.50$ [talk about “effects”]
2) The law of diminishing marginal utility
a. is another way of expressing the law of demand
b. states that people's inclination to consume basic goods falls as incomes increase
c. shows that goods lose their individual values as the total utility of all goods decreases
d. is the utility equivalent to the law of increasing costs
e. states that total utility rises at a decreasing rate as consumption increases
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

13. Concept Check
1) Given that you want to maximize utility per dollar, if MU1/P1 > MU2/P2,
a. the consumer should consume more of good 1 and less of good 2
b. the consumer should consume more of good 2 and less of good 1
c. total utility of good 1 is greater than total utility of good 2
d. total utility of good 2 is greater than total utility of good 1
e. the price of good 1 must fall
The consumer’s challenge is two-fold:
1. Find the bundles of goods that are affordable, given income and prices, and
Choose the bundle that provides the highest utility.
Consumers want to maximize utility, but must do so within a budget constraint.

14. Free Response
You have 2,000 RMB to spend. Headphones are 200 RMB each, and albums are 5 RMB each. Draw a budget constraint graph with labels.
If you get 380 utils from another pair of headphones, and 12 from another album, are you maximizing your utility? Why or why not?
What would happen to these things if you decided to just buy another pair of headphones?
total utility
marginal utility
[clue: you don’t need math]
The “utility maximization rule” says that the consumer should spend all of his income on two goods such that:
MU/P is equal for both (all) goods.
As long as one good provides more utility per dollar than another, the consumer will buy more of the first good; as more of the first product is bought, its marginal utility diminishes until the amount of utility per dollar just equals that of the other product.