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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
1U
2U
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 Want
Fredo, 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
CP
PF
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
r
II
r
XXPV
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
1U
2U
A
E
B
*C
*FF
C
F
C
P
P
MU
MUMRS
F
F
C
C
P
MU
P
MU
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
CFC
FMRS
2
2
First, equate your MRS to the price ratio
Second, substitute for F in your budget line
502
25
10022
1002
**
*
CF
C
CC
CF
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
1U
2U
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