Utility, Constraints, and
Choices (Chapter 2)
What people want
Constraints
Choices
Utility: What do people want?
• Objective: maximize “utility”
• Imagine your “utility” depends on just a couple of
things, say food and clothing
Utility  U  U ( F , C )
• The utility function ranks combinations of food
and clothing
• What matters for choosing: total or marginal
utility?
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?
F
• Cannot cross
• Downward Sloping
- You are willing to trade
one good for another
F
• Convex
- Averages preferred to
extremes
• Decreasing MRS =
(ΔF/ΔC)
Northeast is better; the
combinations on U2 are preferred
over those on U1
U2
U1
C
C
Preferences for leisure
• Indifference curves
illustrate how people
X
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?
Working trades off leisure (L)
for consumption (X)
L
Preferences for “now” and risk
future
return
Risk is a “bad”, so
northwest is better
risk
present
Saving trades off the present
for the future
Risk-taking trades off lower risk
for greater return
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 (I )
• Prices of Food ( PF ) and Price of Clothing ( PC )
• Model is meant to introduce general
principles not to explain all of the world
Budget constraints
• Go back to the food and clothing example
• What determines your limits?
• A budget set shows what is affordable:
PF F  PC C  I
(Expenditures on food and clothing cannot exceed income)
• Focus on the boundary of the constraint, the
budget line:
PF F  PC C  I
Budget lines
• It is helpful to rewrite
the budget line like
this:
F
PC
1
F  C
I
PF
PF
Beyond the budget line is
not affordable
F
• What is the slope and
what does it tell you?
C
C
How Do Constraints Change When
Income and prices change?
F
F
Decrease in the price
of clothing
Increase in income
C
C
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
pX  wH  A
X
How much consumption
do you get for giving up
an hour of leisure?
pX  w(24  L)  A
H = Hours of Work
L = Leisure
X = Consumption
p = price of consumption (1)
• How does the market
trade off leisure and
consumption?
slope   w
“endowment”
X
T
L
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:
X 2  (1  r )X1
• So, what does r measure?
X2
How much future
consumption do you get
for giving up a unit of
present consumption?
slope  (1  r )
I2
“endowment”
I1
X1
Present and Future Value
• Intertemporal budget line (2 periods)
FV : (1  r ) X 1  X 2  (1  r ) I1  I 2
PV : X 1
X2
I
 I1  2
1 r
1 r
• Work forward to calculate future values of $100
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
• Work backward to get the present values
Budget line for risk and return
How much does the market
compensate investors for
taking on extra risk?
E (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
rm
slope  (rm  rf ) /  m
rf
m

Choosing
One'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? F
• At E:
MU C PC
MRS 

MU F PF
F
A
*
Personal and market tradeoffs
are reconciled at E-highest I
curve
E
MU C MU F

PC
PF
B
U2
U1
• What does that
mean?
C*
C
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
First, equate your MRS to the price ratio
F
 2
C
 F  2C
MRS  
Second, substitute for F in your budget line
F  2C  100
2C  2C  100
 C *  25
 F *  2C *  50
Optimizing in other decisions
• How are the tradeoffs
reconciled in the other
choices we studied?
return
rm
• How about the
investment decision?
rx
E
rf
• What does it mean to
say that E is best?
x
m
Remember, risk is a “bad”
and northwest is better
risk
From choosing to demand
F
Pc
The price of clothes falls and you
“re-optimize”, increasing your
consumption of clothes
E1
E2
The demand curve traces out
your choices as price changes,
holding other factors constant
Pc1
U2
Pc2
U1
C1* C2*
C
D
C1* C2*
C
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