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

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 thirst 1st sip - much utility 2nd sip - less so eventually - 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&Ms

Marginal Utility with Multiple Choices Different activities will have different MU lines

2.4 Constructing a decision rule

2.4.1 Initial Decision Rule MU 1 =MU 2 =MU 3 =…=MU n =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

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

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=60

What you now have is a new rule 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: MU 1 =MU 2 =MU 3 =…=MU n =0 (consumption of free goods) MP 1 = MP 2 = MP 3 =…=MP n =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

You need a marginal utility schedule

Calculating V

2.6.9 Why Value Marginal product eventually falls V eventually falls because MU falls from unit 1 MP eventually falls

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

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 Time is perfectly divisible, so you can always reconfigure with smaller units of time until this works out

The General decision rule V1=V2=V3=…=Vn=X X>0

Changing constraints Assume winter comes, so no berries are available And there is only 7 hours of daylight

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

Should I go to college?

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

College Demographics Why is college full of year olds? Opportunity cost is higher for older students Retirees discount the future more because they have less time left

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 EPV 1 =EPV 2 =…=EPV n

2.8.3 Risk and Choice PV parachuting > PV movie But EPV parachuting < EPV movie

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

Gender perceptions and choice Mrs. Seigel Billy Tipton

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

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

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