2.0
Modeling Individual Choice
Robinson Crusoe - Why?
2.1
This chapter is about individual choice
Crusoe is alone
He makes his choices independently
Once we understand independent choice,
we can move to more complex,
interdependent choice
2.21 Assumptions
No scarcity
No production is necessary
No future or sense of time passing
No risk or uncertainty
2.2.2 Definitions
Utility Satisfaction
Consume the act of deriving utility
Note: not always using up.
Consume pizza - gone
Consume art - still there
Goods tangible, can be stored
Ex. Food, sneakers
Services intangible, cannot be stored
Ex. Haircut
2.2.3 More Assumptions
people know what gives them utility, and
can rank items by the utility they receive
from an item
Rational behavior utility maximizing
Assumption - people are rational
Rational households consume
goods and services in order to
derive the maximum utility
2.3 Diminishing Marginal Utility
New assumption
Ceteris paribus, the utility one derives from
the consumption of a good decreases with
each successive unit consumed
Ex. Dying of thirst
1st sip - much utility
2nd sip - less so
eventually - no utility
More clearly stated:
Ceteris paribus, the utility one derives from
the consumption of a good decreases with
each successive unit consumed
or
one experiences diminishing marginal utility
2.32 Marginal and Total Utility
We can make up a unit of utility
we’ll call it a util
Chart on page 20
Eventually, as you keep eating
you get to the point where you derive no
satisfaction
At this point, MU=0
Example - Big Bowl of M&Ms
M&M
Marginal
Utility
Total
Utility
1
50
50
2
49
99
3
48
147
4
47
194
5
46
240
JESSE
ABBY
Utils
Utils
Marginal
Utility
Marginal
Utility
Utils
Utils
Total
Utility
51
Figure 2.3.1 - Abby's and Jesse's Total and Marginal Utility Graphs.
Total
Utility
41
Marginal Utility with Multiple
Choices
Different activities will have different MU
lines
Activity 2
Activity 1
Utils
Activity 3
Utils
Utils
MU
Units
MU
Units
Figure 2.3.3 - MU's from three different way to spend time
MU
Units
2.4 Constructing a decision rule
2.4.1 Initial Decision Rule
MU1=MU2=MU3=…=MUn=0
If you can get to the point where you have
totally satisfied yourself in all dimensions
of consumption,
That is called a bliss point
Absolute maximum utility has been attained
This rule is valid only
given the strong assumptions we have chosen
While not totally realistic, it gives us a
starting point from which to build
2.5 Relaxing the “No Scarcity”
Assumption
If time were not scarce,
You could think of the decision rule as
MU 1
MU 2
MU 3
MUn


 ... 
0
UnitofTime UnitofTime UnitofTime
UnitofTime
We will now assume time to be
scarce
This is much more realistic
Can’t do everything to satiate yourself
Suppose the only things you have time to do
are study and play, and you only have ten
hours
An initial allocation
7 hours of play – MU=50
3 hours of study – MU=70
PLAY
STUDY
UTILS
UTILS
70
70
60
60
50
50
40
40
30
30
20
20
MU
MU
10
10
1
2
3
4
5
6
7
8
HOURS
1
2
3
4
5
6
7
Figure 2.5.1 - Marginal Utility of Study and Play - An Optimization Problem, Step 1.
8
HOURS
How to optimizethe optimal allocation is the one which
maximizes utility
Do another hour of the choice which gives
you the higher marginal utility
A new allocation
6 hours of play – MU=60
4 hours of study – MU=60
PLAY
STUDY
UTILS
UTILS
70
70
60
60
50
50
40
40
30
30
20
20
MU
MU
10
10
1
2
3
4
5
6
7
8
HOURS
1
2
3
4
5
6
7
Figure 2.5.2 - Marginal Utility of Study and Play - An Optimization Problem, Step 2.
8
HOURS
What you now have is a new
rule
MU 1
MU 2
MU 3
MUn


 ... 
X
UnitofTime UnitofTime UnitofTime
UnitofTime
Where X can be >0
This new rule describes how
people solve
a constrained optimization problem
In other words, how do people maximize
utility in the face of scarcity?
2.6 Relaxing the “No production
necessary” assumption
In reality,
Stuff doesn’t just appear like magic for you to
consume
Endowment- all the natural and human resources
from which all goods and services are produces
Endowment may not be fixed, but it is finite, so
scarcity is an issue
(We discover new oil all the time, but there is an
ultimate limit)
More new terms
Factors of production are allocated to and
then combined in processes of production
that apply techniques chosen from
available technology in order to produce
goods and services
2.6.2 On factors
Factors of production – basic inputs we use
to produce, such as
Natural resources – in, on or around the earth
Labor- human work
Together, these first two are called the
natural endowment
Another factor is capital
“a produced means of production”
More properly called production capital
Physical capital –tools, machines
Human capital – inside yourself, allows you
to be more productive – education
2.6.3 Allocation, Techniques,
and Technology
Allocated – we decide how to use the factors
Process of production – transforming the
inputs into an good, or service
Technique- one way of combining inputs
Technology – set of all available techniques
Types of techniques
Labor-intensive technique- uses primarily
labor
Capital-intensive technique – uses primarily
capital
Firms usually choose the cheapest way
2.6.5 Scale of Production
Refers to the size of the process of production
Returns to scale – how does a change in scale affect
output?
Ex. If double inputs – less than doubles the output
–decreasing returns to scale
If double inputs – doubles the output – constant
returns to scale
If double inputs - more than doubles the output –
increasing returns to scale
We assume decreasing returns to scale
2.6.6 Marginal Productivity
The additional output that comes from an
additional unit of input is called
the marginal product
While MP can increase for a while,
It will eventually diminish
If inputs were free, to maximize production
you would use inputs until
MP=0 for all inputs
2.6.7 Value from the marginal
product – V
So far, we have two independent rules:
MU1=MU2=MU3=…=MUn=0 (consumption
of free goods)
MP1= MP2 = MP3=…=MPn=0 (use of free
inputs)
Now we need to bridge the two
To connect the two sides,
we must find out what the utility is for the
last unit of labor towards a given product
this is called the Value of the Marginal
Product, or
V
2.6.8 How to calculate V
You need a marginal product
schedule
Labor
(hrs)
1
2
3
4
5
6
Marginal
Product
(rabbit)
1
2
3
2
1
0
Total
Product
(rabbit)
1
3
6
8
9
9
You need a marginal utility
scheduleMarginal
Rabbit
Utiliy
1
2
3
4
5
6
7
8
9
100
90
80
70
60
50
40
30
20
Calculating V
Labor Rabbits and MU of each
st
1
2nd
3rd
4th
5th
th
6
1 @ 100
2 @ 90 + 3 @ 80
4 @ 70 + 5 @ 60 + 6 @ 50
7 @ 40 + 8 @ 30
9 @ 20
0
UMP
100
170
180
70
20
0
Total
UMP
100
270
450
520
540
540
2.6.9 Why Value Marginal
product eventually falls
V eventually falls because
MU falls from unit 1
MP eventually falls
2.6.10 V and optimization
If R.C. had V schedules for each activity,
he could decide on the “optimal” or best
allocation of his labor
Because he is rational, he chooses activities
that give him the maximum utility
V schedules
Labor
(hrs)
1st
2nd
3rd
4th
5th
6th
7th
8th
Hunting
V
100
170
180
70
20
0
0
0
Fishing
V
50
60
180
170
70
5
0
0
Berries
V
50
70
40
10
5
0
0
0
Water
V
180
70
5
0
0
0
0
0
How many hours
To get every last util?
23
What if there was a time
constraint of 13 hours of
daylight?
Answer:
Hunt - 4 hours
Fish - 5 hours
Pick Berries - 2 hours
Pump Water - 2 hours
Decision rule
V1
V2
V3
Vn


 ... 
UnitofTime UnitofTime UnitofTime
UnitofTime
Time is perfectly divisible, so you can
always reconfigure with smaller units of
time until this works out
2.6.11 The General decision rule
V1=V2=V3=…=Vn=X
X>0
2.6.12
Changing constraints
Assume winter comes,
so no berries are available
And there is only 7 hours of daylight
2.6.13 Conclusion on V
We are trying to build a model to describe
how people make choices
Whether it is done consciously or not, people
do allocate their scarce resources according
to some process
Given our assumptions, people will follow
the rule we have developed
2.7 Relaxing the No Future
Assumption
2.7.1 Missiles are on the way
Would this alter your choices?
2.7.2 The future and choice
Intertemporal - across time
You have to decide now about things that
will have utilities in the future
2.7.3 Discounting the Future
Discount- to diminish value
Economists assume that ceteris paribus,
people discount the future relative to the
present
Ex. $100 now or a year from now
2.7.4 Discount rates
If $100 now equals $150 a year from now,
Your “waiting premium” is 50%
The name for that waiting premium is the discount
rate
Higher discount rates diminish the future more than
lower ones
There is no right or wrong rate, everyone has there
own based on that person’s attitude towards
waiting
2.7.5 Changing discount rates
Your discount rate changes as your perception of
the future changes
More immediate utility might be preferable
2.7.6 Discount rates and social
frames
discount rates are personal, but they are also
socially developed
Attitudes about waiting change as we grow up
5 minutes is forever to a little kid
Adults are more willing than kids to wait
2.7.7 Present Value
what future utilities are worth right now
Ex. $150 a year from now might have a present
value of $100
depending on your discount rate
All future utilities have a present value
2.7.8 An Intertemporal decision rule
Before, when we assumed no future, the rule was
V1=V2=V3=…=Vn=X
Now, since some choices have payoffs into the
future, the rule becomes
PV1=PV2=PV3=…=PVn=X
where PV means Present Value
2.7.9 Saving, Investing, and
Intertemporal choice
Decision to save or invest depends on
discount rates
High discount rates mean little present value
to future utilities, so
people with high personal discount rates rates
will be less likely to save or invest
2.7.10 Should I go to college?
C
Utils
R
W
I
Now
1
2
3
4
5
6
7
8
9
10
Time into Future
Figure 2.7.1 - Representing Intertemporal Choices: Net Utility of College Versus a Job
Explanation
C – College
W – work
I - Investment cost
R – Return
If present value of return is higher than the present
value of cost, go to school
If not, go to work
Doesn’t have to measured in dollars
2.7.11 College Demographics
Why is college full of 18-22 year olds?
Opportunity cost is higher for older students
Retirees discount the future more because
they have less time left
2.7.12 Conclusion on
intertemporal choice
When we relax our assumption of no future,
then the rule becomes
PV1=PV2=…=PVn
2.8 Relaxing the no risk and
uncertainty assumption
Risk
negative outcome that you can’t control but
can assign a probability to
Uncertainty
negative outcome you can not assign a
probability to
2.8.2 Building risk into the
decision rule
All utilities should be looked at as expected
utilities because of risks and uncertainties
EPV1=EPV2=…=EPVn
2.8.3 Risk and Choice
PVparachuting > PVmovie
But
EPVparachuting < EPVmovie
2.8.4 Uncertainty and Choice
Ex.
Falling objects in NYC
2.8.5 Risk and Learning
For kids, most all is uncertainty
Then when something bad happens, an
overestimation of risk,
Then eventually a more realistic assessment
2.8.6 Risk as perception
Perception of risk affect our choices
We rarely know the actual probability
Lower perception of risk leads to being more
likely to engage in unsafe behaviors
Drugs/alcohol affect your perception of risk,
usually diminishing or eliminating those
perceptions
2.8.7 Risk as perception – a
policy case
Police training tape
Why?
Raise perception of that risk of becoming a
crooked cop
Governments also try to alter perceptions to
promote ideas –
Rosie the Riveter during WWII
2.8.8 Perceptions, Choice and
the Media
Advertising – product will bring great utility
Shape our perceptions –beauty standards
Eating disorders – more prone if high
discount rate and low perception of risk
2.8.9- 2.8.11 Gender perceptions
and choice
Mrs. Seigel
Billy Tipton
2.8.12 On role models
Role models affect:
Preferences – without role models, might never
consider that career choice
Discount rate – if your role models have high
discount rates and value immediate gratification,
you might too
Risk – if others blaze the trail for you, less risk for
you, then the more likely you make that choice
2.8.13 Social Constructions and
Individual Choices
Understand that while choices are individual,
They do occur within a larger social frame
Other social sciences can help us understand
the construction of these frames
2.8.14 Perceptions, Individual
Choices, Challenge of Policy
The world is really complicated
A web of connections means
a change in one thing may have many other
effects
Ex. Drug Policy
Policy is never simple
2.9 Conclusion on Independent
Individual Choice
RC’s decisions are perfectly coordinated
He’s the only one involved,
so consumption and production, as well as
saving and investing, are coordinated in his
own head
Note : this doesn’t mean that they always
work out –
due to risks and uncertainty
This perfect coordination
separates
The RC world from the real one
Next, we look at a more complex world
which
Includes more realistic interdependent choice