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 - goneConsume art - still there

tangible, can be stored

Ex. Food, sneakers

Services -

intangible, cannot be stored

Ex. Haircut

Goods -

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

Ceteris paribus, the utility one derives from the consumption of a good decreases with each successive unit consumed

Ex. Dying of thirst1st sip - much utility2nd sip - less soeventually - no utility

New assumption

Ceteris paribus, the utility one derives from the consumption of a good decreases with each successive unit consumed

or

one experiences diminishing marginal utility

More clearly stated:

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&MsM&M Marginal

UtilityTotalUtility

1 50 50

2 49 99

3 48 147

4 47 194

5 46 240

Utils Utils

MarginalUtility

MarginalUtility

ABBY JESSE

51 41

UtilsUtilsTotalUtility

TotalUtility

Figure 2.3.1 - Abby's and Jesse's Total and Marginal Utility Graphs.

Marginal Utility with Multiple Choices

Different activities will have different MU lines

Utils Utils

MU

Activity 1

Units

Figure 2.3.3 - MU's from three different way to spend time

Utils

Units Units

MU MU

Activity 2 Activity 3

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

0...321

UnitofTime

MUn

UnitofTime

MU

UnitofTime

MU

UnitofTime

MU

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=70PLAY STUDY

Figure 2.5.1 - Marginal Utility of Study and Play - An Optimization Problem, Step 1.

UTILS

MU

1 3 76542 8

10

20

30

40

50

60

70

HOURS

UTILS

MU

1 3 76542 8

10

20

30

40

50

60

70

HOURS

How to optimize-

the 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=60PLAY STUDY

Figure 2.5.2 - Marginal Utility of Study and Play - An Optimization Problem, Step 2.

UTILS

MU

1 3 76542 8

10

20

30

40

50

60

70

HOURS

UTILS

MU

1 3 76542 8

10

20

30

40

50

60

70

HOURS

What you now have is a new rule

Where X can be >0

XUnitofTime

MUn

UnitofTime

MU

UnitofTime

MU

UnitofTime

MU ...

321

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 productionReturns to scale – how does a change in scale affect

output?Ex. If double inputs – less than doubles the output –

decreasing returns to scaleIf double inputs – doubles the output – constant

returns to scaleIf double inputs - more than doubles the output –

increasing returns to scaleWe 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 productWhile MP can increase for a while, It will eventually diminishIf inputs were free, to maximize production

you would use inputs untilMP=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

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

To connect the two sides,

2.6.8 How to calculate V

You need a marginal product schedule

Labor (hrs)

Marginal Product (rabbit)

Total Product (rabbit)

1 1 1 2 2 3 3 3 6 4 2 8 5 1 9 6 0 9

You need a marginal utility schedule

Rabbit

Marginal Utiliy

1 100 2 90 3 80 4 70 5 60 6 50 7 40 8 30 9 20

Calculating V

Labor Rabbits and MU of each UMP Total UMP

1st 1 @ 100 100 100 2nd 2 @ 90 + 3 @ 80 170 270 3rd 4 @ 70 + 5 @ 60 + 6 @ 50 180 450 4th 7 @ 40 + 8 @ 30 70 520 5th 9 @ 20 20 540 6th 0 0 540

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)

Hunting V

Fishing V

Berries V

Water V

1st 100 50 50 180 2nd 170 60 70 70 3rd 180 180 40 5 4th 70 170 10 0 5th 20 70 5 0 6th 0 5 0 0 7th 0 0 0 0 8th 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

UnitofTime

Vn

UnitofTime

V

UnitofTime

V

UnitofTime

V ...

321

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

2.6.12Changing 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

rateHigher discount rates diminish the future more than

lower onesThere 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 up5 minutes is forever to a little kidAdults are more willing than kids to wait

2.7.7 Present Value

what future utilities are worth right nowEx. $150 a year from now might have a present

value of $100depending 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=XNow, 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?

Utils

Figure 2.7.1 - Representing Intertemporal Choices: Net Utility of College Versus a Job

Time into Future

Now 1 3 7542 86 9 10

W

C

I

R

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 coordinatedHe’s the only one involved,so consumption and production, as well assaving and investing, are coordinated in his

own headNote : 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