Utility, Constraints, and Choices (Chapter 2)

What people wantConstraints

Choices

Utility: What do people want?

• Objective: maximize “utility”• Imagine your “utility” depends on just a couple of

things, say food and clothing

• The utility function ranks combinations of food and clothing

• What matters for choosing: total or marginal utility?

),( CFUUUtility

Indifference Curves

• An indifference curve represents a set of market bundles that a person equally prefers (or gives the consumer an equal amount of utility). If two bundles are on the same indifference curve, then the person is indifferent between the two bundles.

• The slope (ΔF/ΔC) tells you the marginal rate of substitution (MRS) between C and F

How are Indifference curves usually shape?

• Cannot cross• Downward Sloping- You are willing to trade one good for another• Convex- Averages preferred to extremes• Decreasing MRS =

(ΔF/ΔC)

F

C

Northeast is better; the combinations on U2 are preferredover those on U1

1U2U

C

F

Preferences for leisure• Indifference curves

illustrate how people rank things and prefer to trade them off

• Think about your attitudes toward some important choices – like working, saving and risk-taking, and even honesty and integrity?

• What are the tradeoffs and how do you weigh them?

X

L

Working trades off leisure (L) for consumption (X)

Preferences for “now” and risk

future return

risk

Risk-taking trades off lower risk for greater return

Saving trades off the present for the future

Risk is a “bad”, sonorthwest is better

present

Constraints—You Can’t Always Get What You WantFredo, you're my older brother, and I love

you. But don't ever take sides with anyone against the family again. Ever.

Michael Corleone, The Godfather

Budget constraints

• Introduce a Basic Model with 2 goods Food (F) and Clothing (C)

• One period decision—no borrowing or lending• Take income as a given • Prices of Food and Price of Clothing • Model is meant to introduce general principles

not to explain all of the world

)( CP)(I

)( FP

Budget constraints

• Go back to the food and clothing example• What determines your limits? • A budget set shows what is affordable:

• Focus on the boundary of the constraint, the budget line:

ICPFP CF

ICPFP CF

(Expenditures on food and clothing cannot exceed income)

Budget lines

• It is helpful to rewrite the budget line like this:

• What is the slope and what does it tell you?

F

C

Beyond the budget line is not affordable

IP

CPPF

FF

C 1

C

F

How Do Constraints Change When Income and prices change?

F

C

Decrease in the price of clothing

F

C

Increase in income

Other Budget Constraints

• Consumption and Leisure—We allow income to vary

• Consume now or in the future—We allow people to save and borrow

Budget line for leisure and consumption

• Budget Constraint

H = Hours of Work L = Leisure X = Consumption p = price of consumption (1)• How does the market

trade off leisure and consumption?

X

LT

X

How much consumption do you get for giving up an hour of leisure?

wslope

“endowment”

AwHpX

ALwpX )24(

Intertemporal budget line• You may save or borrow

at a market rate of interest (r)

• To every dollar of present consumption deferred to the future, r dollars are added to it:

• So, what does r measure?

2X

1X

How much future consumption do you get for giving up a unit of present consumption?

)1( rslope

1I

2I12 )1( XrX “endowment”

Present and Future Value

• Intertemporal budget line (2 periods)

• Work forward to calculate future values of $100

• Work backward to get the present values

rII

rXXPV

IIrXXrFV

11:

)1()1(:

21

21

2121

Date Value

0 100

1 100 + 100r = 100(1+ r)

2 100(1 + r) + 100(1+ r)r = 100(1 + r)2

T 100(1 + r)T-1 + 100( 1+ r)T-1r = 100(1 + r)T

Budget line for risk and return

• If risk is measured in terms of the standard deviation (σ) of returns

• Two possibilities are the market portfolio, with return rm and a risk-free asset, with return rf

)(returnE

How much does the market compensate investors for taking on extra risk?

mfm rrslope /)(

fr

mr

m

ChoosingOne's philosophy is not best expressed in words; it is expressed in the choices one

makes … and the choices we make are ultimately our responsibility.

Eleanor Roosevelt

Reconciling tradeoffs

• Why is neither A nor B the best you can do?

• At E:

• What does that mean?

F

C

Personal and market tradeoffs are reconciled at E-highest I curve

1U2U

A

E

B

*C

*FF

C

F

C

PP

MUMUMRS

F

F

C

C

PMU

PMU

You consume the right (optimal) amount of food and clothing• If you

– Have a budget of $100– Face prices of food ($1)

and clothing ($2) per unit– Have an MRS of (–F/C)

• What is the “right” amount of food and clothing for you?

• Consumer and “market” value goods in the same way

CFCFMRS

2

2

First, equate your MRS to the price ratio

Second, substitute for F in your budget line

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25

100221002

**

*

CF

C

CCCF

Optimizing in other decisions

return

risk

Remember, risk is a “bad” and northwest is better

• How are the tradeoffs reconciled in the other choices we studied?

• How about the investment decision?

• What does it mean to say that E is best? m

mr

fr

x

xrE

From choosing to demand

F

C

The price of clothes falls and you“re-optimize”, increasing your consumption of clothes

1U2U

E2

*2C

E1

*1C

cP

C

The demand curve traces outyour choices as price changes, holding other factors constant

1cP

D

2cP

*2C*

1C

Other views“The fundamental economic theory of motivation is based on assumptions of

effort aversion (people will not expend effort unless paid to do so), opportunism (people, in the pursuit of their own interests, will often misrepresent their true

preferences and engage in guile and deceit), and a lack of goal alignment (employees in organizations have different agendas than the owners and,

therefore, incentive systems need to be designed to force people to do what is right for the good of the organization). In the economists’ view, people are assumed to be lazy, dishonest, and at odds with the goals of the managers.

Although each of these assumptions may be valid in a specific situation, or for a particular individual (for instance, when managing economists themselves), none

is likely to be right in most settings with normal human beings.”

Charles O’Reilly & Jeffrey Pfeffer

Conclusions

• Self-interest matters – people are driven pretty much by their desire to better themselves (maximize “utility”)

• Constraints matter – people respond to incentives (changes in “relative prices”)

• Preferences and constraints are reconciled at the margin (when MB = MC)

• Standard model is the foundation for demand analysis• Apply to work, savings and risk-taking• These basic models illustrate general principles