Theory of Consumer Choice

AP EconomicsMr. Bordelon

Utility and Consumption

• Utility. Measure of satisfaction.• Utils. Unit of utility.• Utility function. Shows relationship between

consumer’s utility and combination of goods and services (consumption bundle) he consumes.

• Assumption: Individuals try to maximize some personal measure of satisfaction gained from consumption.

• Cassie likes to eat clams at an all-you-can-eat buffet.

• Her utility function slopes upward, but gets flatter as the number of clams increases, eventually turning downward.

• Why?• Should she stop

eating clams, and if so how many?

• Adding each additional clam makes Cassie worse off—it lowers her total utility.

• Acting rationally, Cassie will stop at 8.

• To make this decision, she must consider the change in her total utility from consuming one more clam.

• Key point: To maximize total utility, consumers most focus on marginal utility.

Diminishing Marginal Utility

• Ashley (whining): “But Bordelon, you haven’t said anything about marginal utility. What are you talking about?”

• Marginal utility. Change in total utility generated by consuming one additional unit of a good or service.

• Marginal utility curve. Shows how marginal utility depends on quantity of a good or service consumed.

• Looking at the table, marginal utility per clam changes with the consumption of each additional clam.

• According to this table, at what number should Cassie stop consuming clams? Why?

• She should stop at 8. Each each clam consumed, her marginal utility decreases more and more. After her 8th clam, she actually sees a negative marginal utility in clam consumption.

• What would be an example of a negative marginal utility in clam consumption?

• The marginal utility schedule can be graphed as the marginal utility curve.

• The curve slopes downward because each clam decreases the total utility than the previous one.

• Consumption of most goods and services is subject to diminishing marginal utility.

Diminishing Marginal Utility

• Principle of Diminishing Marginal Utility. The additional satisfaction a consumer gets from one more unit of a good or service declines as the amount of that good or service consumed rises.– The more you have, the more you’re likely to be

satisfied until you reach a point where having one more does nothing for you.

Budgets and Optimal Consumption

• It costs some additional resources to consume more of a good, and consumers must take that cost into account when making choices.

• The fundamental measure of cost is opportunity cost. Because the amount of money a consumer can spend is limited, a decision to consume more of one good is also a decision to consume less of another good.

Budget Constraints and Budget Lines

• Sammy likes both clams and potatoes. Whatever he chooses, the cost of his consumption bundle can not exceed the amount of money he has to spend.

• Budget constraint. Limits cost of a consumer’s consumption bundle to no more than the consumer’s income.

Expenditure on clams + Expenditure on potatoes ≤ Total Income

Budget Constraints and Budget Lines

• Consumption possibilities. Set of all consumption bundles that affordable given the consumer’s income and prevailing prices.– Possibilities depend on consumer’s income and

prices of g/s.

This better look familiar to you...

Budget line. Shows consumption bundles available to a consumer who spends all of his income.

We assume that consumption bundles are made along the budget line so long as his marginal utility from consuming either good is still positive.

Optimal Consumption Bundle

• Optimal Consumption Bundle. Consumption bundle that maximizes consumer’s total utility given his budget constraint.

6 possible combinations, why?

The more of either good he consumes, the higher Sammy’s utility. However, Sammy’s got a limited budget, so he’s got to make a trade off between clam and potato consumption.

Why are the utils inverse for clams and potatoes?

What do you think is happening around consumption bundle C?

Huh. I wonder if we can graph this stuff.

• Panel (a) is the budget line concept we introduced earlier.

• Panel (b) shows Sammy’s utility function, or how his total utility affects the choice he makes in his budget line.

• Why do you think we can use the x-axis for both clams and potatoes for Sammy’s utility function?

• We can use the same axis because Sammy’s constrained by the budget line.

• The more clams he consumes, the less potatoes, and vice versa. Inverse relationship.

• Why ultimately is C the optimal consumption bundle?

Marginal Utility per Dollar

• Marginal Utility per Dollar. Dollar spent on a g/s is the additional utility from spending one more dollar on that g/s.– How to allocate an additional dollar between g/s

in a way that maximizes utility.

Marginal utility per dollar for each good is found by dividing the marginal utility of the good by its price in dollars.

What’s causing the marginal utility of clams to decrease? How does that affect the marginal utility per dollar?

Marginal Utility per Dollar

• Marginal utility per dollar spent on a good

• Notice that the two curves, MUc/Pc and MUp/Pp intersect at the optimal consumption bundle, point C, consisting of 2 pounds of clams and 6 pounds of potatoes.

• When Sammy consumes 2 pounds of clams and 6 pounds of potatoes, his marginal utility per dollar spent is the same for both goods: 2.

• At the optimal consumption bundle, MUc/Pc = MUp/Pp = 2

• How do we know this is right?

• Assume Sammy’s marginal utility per dollar for clams is higher than potatoes. He can fix this by spending $1 less on potatoes and $1 more on clams.

• He becomes better off and stays within his budget.

• If Sammy has chosen the optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal.

Marginal Utility per Dollar

• Optimal Consumption Rule. When a consumer maximizes utility in the face of a budget constraint, the marginal utility per dollar spent on each good or service in the consumption bundle is the same. That is, for any two goods C and P, at the optimal consumption bundle

Marginal Utility per Dollar

• This applies no matter how many g/s a consumer buys: the marginal utilities per dollar spent for each and every good or service in the optimal consumption bundle are equal.

Billy’s Budget

• Billy’s income: $50• Price of Notebook: $5• Price of CDs: $10• $50 = $5N + $10CD

– Billy’s income must equal the amount of money he spends on notebooks plus the amount he spends on CDs.

– He’s constrained because he can not afford a bundle that exceeds $50 of total spending.

Billy’s Budget

• Discuss the following:– Point A– Point B– Point C

Billy’s Budget

• Point A– Inefficient.– Points inside budget line

are affordable, but don’t maximize utility/spend all of consumer’s income.

– 2 notebooks + 1 CD = $20

Billy’s Budget

• Point B– Efficient.– Points along the budget

line are affordable, and maximizes utility/spends all of consumer’s income.

– 6 notebooks + 2 CDs = $50

Billy’s Budget

• Point C– Impossible.– Points outside the

budget line are unaffordable.

– 6 notebooks + 5 CDs = $80

Billy’s Budget

• Slope = -2– Remember, slope in a

PPC is the opportunity cost.

– To buy one more CD, Billy has to give up two note books. (Opportunity cost of a CD).

Billy’s BudgetQty of Notebooks Utility from

NotebooksQty of CDs Utility from CDs

0 0 0 0

2 70 1 80

4 130 2 150

6 180 3 210

8 220 4 260

10 250 5 300

What should he consume?

Billy’s Budget#N #CDs Total Utility?

0 5 300

2 4 330

4 3 390

6 2 330

8 1 300

10 0 250

As a matter of total utility, Billy should consume 4 note books and 3 CDs.

Billy’s Budget

• MU = ΔTU/ΔQ• MU per dollar = MU/P

Qty Notebooks

Utility Notebooks

MU/$ spent on N

Qty CDs Utility CDs MU/$ spent CDs

0 0 0 0

2 70 1 80

4 130 2 150

6 180 3 210

8 220 4 260

10 250 5 300

Billy’s BudgetQty

NotebooksUtility

NotebooksMU/$ spent

on NQty CDs Utility CDs MU/$ spent

on CDs

0 0 0 0

2 70 7 1 80 8

4 130 6 2 150 7

6 180 5 3 210 6

8 220 4 4 260 5

10 250 3 5 300 4

Marginal utility per dollar is equal for both goods. This is the optimal consumption/utility maximization rule.

Billy’s Budget

• Optimal Consumption/Utility Maxmization:– Consumer should spend all of his income on two

goods such that:

Billy’s Budget

• Optimal Consumption/Utility Maxmization:– Consumer should spend all of his income on two goods

such that:

– 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.

Billy’s Budget

P

P

C

C

P

MU

P

MU

– 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.

– What if:

Billy’s Budget

• In this case, you’re getting more bang for your buck with good X, so you’ll consume more.– This also means you’ll decrease your consumption

of Y.

• What happens to MUX when you come more?

Billy’s Budget

• In this case, you’re getting more bang for your buck with good X, so you’ll consume more.– This also means you’ll decrease your consumption

of Y.

• What happens to MUX when you come more?– Decreases. And as you consume less Y, MUY

increases.

Billy’s Budget

• Billy’s now consuming 8 notebooks and 1 CD.• MUn/Pn = 4; MUcd/Pcd = 8.• What’s happening in terms of utility?

Billy’s Budget

• Billy’s now consuming 8 notebooks and 1 CD.• MUn/Pn = 4; MUcd/Pcd = 8.• The last dollar Billy spent on notebooks only

gave him 4 utils. With CDs, 8 utils.– He’s spending too little on CDs.

Billy’s Budget

• Suppose Billy buys one more CD at $10. This gives him 70 utils for 150 total.

• He has to give up 2 notebooks each to afford the 2nd CD though.

• Going from 8 notebooks to 6 notebooks lowers his total utility by 40 utils.– He gains 70 and loses 40. Total utility increased by

30 utils.

Billy’s Budget

• New combo:– MUn/Pn = 5; MUcd/Pcd = 7

• He should buy more CDs still and fewer note books and his total utility will continue to rise until maximized.– MUn/Pn = MUcd/Pcd = 6

Angry Ashley

• Ashley: “Bordelon, seriously, I hate you so much right now. Why did you show us this?”

• Two words: substitution effect, baby.• Substitution effect explains ultimately why the

demand curve obeys the law of demand.• Marginal analysis explains more precisely how

an increase price leads to less marginal utility per dollar and therefore a decrease in the quantity demanded.