10 Principals of Econimics

8/2/2019 10 Principals of Econimics

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ECONOMICS A TO ZGOUTAM BUCHHA

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1INTRODUCTION


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Ten Principles of Economics


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Economy. . .

. . . The word economycomes from aGreek word for one who manages ahousehold.


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TEN PRINCIPLES OFECONOMICS

A household and an economyface many decisions:

Who will work?

What goods and how many of them should beproduced?

What resources should be used in

production? At what price should the goods be sold?


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Society and Scarce Resources:

The management of societys resources isimportant because resources are scarce.

Scarcity. . . means that society has limitedresources and therefore cannot produce allthe goods and services people wish to have.


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Economicsis the study of how societymanages its scarce resources.


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How people make decisions.

People face tradeoffs.

The cost of something is what you give up toget it.

Rational people think at the margin.

People respond to incentives.


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How people interact with each other.

Trade can make everyone better off.

Markets are usually a good way to organizeeconomic activity.

Governments can sometimes improveeconomic outcomes.


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The forces and trends that affect how theeconomy as a whole works.

The standard of living depends on a countrys

production.

Prices rise when the government prints toomuch money.

Society faces a short-run tradeoff betweeninflation and unemployment.


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Principle #1: People Face Tradeoffs.

There is no such thing as a free lunch!


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Making decisions requires tradingoff one goal against another.

Principle #1: People Face Tradeoffs.

To get one thing, we usually have to give upanother thing.

Guns v. butter

Food v. clothing

Leisure time v. work

Efficiency v. equity


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Principle #1: People Face Tradeoffs

Efficiency v. Equity

Efficiencymeans society gets the most that itcan from its scarce resources.

Equitymeans the benefits of those resourcesare distributed fairly among the members ofsociety.


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Principle #2: The Cost of Something IsWhat You Give Up to Get It.

Decisions require comparing costs andbenefits of alternatives.

Whether to go to college or to work? Whether to study or go out on a date?

Whether to go to class or sleep in?

The opportunity costof an item is whatyou give up to obtain that item.


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Principle #2: The Cost of Something IsWhat You Give Up to Get It.

LA Laker basketballstar Kobe Bryant

chose to skip collegeand go straight fromhigh school to thepros where he hasearned millions ofdollars.


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People make decisions by comparingcosts and benefits at the margin.

Principle #3: Rational People Think atthe Margin.

Marginal changesare small, incrementaladjustments to an existing plan of action.


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Principle #4: People Respond toIncentives.

Marginal changes in costs or benefitsmotivate people to respond.

The decision to choose one alternativeover another occurs when thatalternatives marginal benefits exceed itsmarginal costs!


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Principle #5: Trade Can MakeEveryone Better Off.

People gain from their ability to trade withone another.

Competition results in gains from trading.

Trade allows people to specialize in whatthey do best.

P i i l M k A U ll


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Principle #6: Markets Are Usually aGood Way to Organize Economic

Activity. A market economyis an economy thatallocates resources through thedecentralized decisions of many firms and

households as they interact in markets forgoods and services.

Households decide what to buy and who to

work for. Firms decide who to hire and what to

produce.

P i i l 6 M k A U ll


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Principle #6: Markets Are Usually aGood Way to Organize Economic

Activity. Adam Smith made the observation thathouseholds and firms interacting inmarkets act as if guided by an invisiblehand.

Because households and firms look at priceswhen deciding what to buy and sell, they

unknowingly take into account the social costsof their actions.

As a result, prices guide decision makers toreach outcomes that tend to maximize thewelfare of society as a whole.


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Principle #7: Governments CanSometimes Improve Market Outcomes.

Market failureoccurs when the market failsto allocate resources efficiently.

When the market fails (breaks down)

government can intervene to promoteefficiency and equity.


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Principle #7: Governments CanSometimes Improve Market Outcomes.

Market failure may be caused by

an externality, which is the impact of oneperson or firms actions on the well-being of a

bystander. market power, which is the ability of a single

person or firm to unduly influence market

prices.


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Principle #8: The Standard of LivingDepends on a Countrys Production.

Standard of living may be measured indifferent ways:

By comparing personal incomes.

By comparing the total market value of anations production.


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Almost all variations in living standards areexplained by differences in countriesproductivities.

Productivityis the amount of goods andservices produced from each hour of aworkers time.


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Standard of living may be measured indifferent ways:

By comparing personal incomes. By comparing the total market value of a

nations production.


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Principle #9: Prices Rise When theGovernment Prints Too Much Money.

Inflation is an increase in the overall levelof prices in the economy.

One cause of inflation is the growth in thequantity of money.

When the government creates largequantities of money, the value of themoney falls.

P i i l #10 S i t F Sh t


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Principle #10: Society Faces a Short-run Tradeoff Between Inflation and

Unemployment. The Phillips Curve illustrates the tradeoffbetween inflation and unemployment:

InflationUnemployment

Its a short-run tradeoff!


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Summary

When individuals make decisions, theyface tradeoffs among alternative goals.

The cost of any action is measured interms of foregone opportunities.

Rational people make decisions bycomparing marginal costs and marginal

benefits.

People change their behavior in responseto the incentives they face.


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Summary

Trade can be mutually beneficial.

Markets are usually a good way ofcoordinating trade among people.

Government can potentially improvemarket outcomes if there is some marketfailure or if the market outcome is

inequitable.


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On July 29, 2006 I was reading the Omaha World Herald. On this

Saturday morning my eye caught the car ads section. On the front

page of that section is a question and answer section by Click &Clack. I do not remember their real names. They also host (usedto, anyway, and maybe they still do) a PBS radio show about cars.

I rarely read this section, but I did this day.

The first question had to do with going on a long trip in a car. The

question was about washing and waxing the car before the trip and

then washing the car along the way. The person asking the

question felt the washing would help save on gas and so the

questioner wanted information from the experts.

The experts said that yes there is some benefit to the washing, but

so little benefit that the cost of the washing and waxing would be

larger than the benefits obtained. So, from a dollars and cents point

of view the washing did not pay off.


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I was all excited about reading the story because I thought it made

sense and maybe I could use the story in my classesso here weare. I would like to repackage the story to make a more general

point. I will make a little diagram to aid in my story.

Policy or actionor proposal

Benefits

Costs


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The policy in the example is

Wash car before, and while on, long car trips.

The benefit(s):

Better gas mileage and thus a cost saving.

The cost(s):

The cost of the car wash.

Economics is a science that when looking at policies the focal point

is on the benefits and costs of the policy.

In our personal lives, when a policy has benefits that clearlyoutweigh the costs, many people engage in what the policy

recommends.

Examples: Brushing your teeth everyday, washing your hands after

using the restroom, and the list goes on and on.


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We have government in our world. Policies are recommended in

this arena. Every policy that gets mentioned has benefits. But

every policy also has costs. Please remember this.

Is the following good social policy from an economic point of

view? Every person in northeast Nebraska should give Chuck

Parker $1 each time they drive by Dairy Queen .

Hey, businesses have policies too. Most organizations havepolicies. The economic approach to viewing the world is looking

at the benefits and costs of the policy.

It seems that a lot of restaurants have a policy that if you buy a pop

you can get free refills. Is this a good business policy? Thebenefits are.

The costs are..


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Well, here is my little story triggered by my reading the Click &Clack article.

Should I make it a policy as a professor at WSC to bring in currentevents and other items I find in the paper?


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Overview

In consumer theory we started with the x and y axes both referring to a good orservice, with each axis representing a different specific good. Sometimes,though, we only want to focus on one good against everything else we couldbuy.

If we think of the Y good as a composite commodity then we can say the price of

the good is $1 per unit and the commodity is really then how much we spend onall goods except good x.

The budget line and indifference curves we saw before are essentially the sameas we saw before.


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Budget line

Y

X

Before we said the budget line wasPxX + PyY = I, with vertical intercept= I/Py, horizontal intercept = I/Pxand slopePx/Py.

In the context of the compositecommodity we have PxX + Y = I,with vertical intercept = I (ourincome amount), horizontal intercept= I/Px still and slope = -Px

I

I/Px


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Utility max

X

Y

X1

I PxX1

With the composite good ourutility max story is the same asbefore except when we seepoint X1 the Y point is theamount of income we have leftafter buying X1 units of X.

The point of the compositecommodity idea is we canfocus on the x good andeverything else in a lumped upamount.


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Consumer SurplusWhen consumers buy products inthe market they may pay less thanthe full amount they are willing to

pay they receive consumersurplus.


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Do you want to buy some eggs?

Who here would buy a dozen eggs for $1.59?

Who would pay $1.29?

Say the actual price of the dozen is $0.89. Do you think thebuyers would pay the $1.29 to the grocer when the grocer has

a sign out that says $0.89?

So if consumers are willing to pay, in this example, more than

$0.89, then they receive an extra benefit in the market calledconsumer surplus.


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consumer surplusConsumer surplus is an idea people I know have a hardtime accepting. Consumer surplus equals the maximumamount you are willing to pay for an item minus whatyou have to pay. It seems the hard part is

distinguishing between what you have to pay and whatyou would be willing to pay.

The amount you would be willing to pay is on thedemand curve for each unit of the product. In fact the

law of demand is an expression that you are not willingto pay as much for additional units as you did forprevious units.The amount you have to pay is market determined.


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Willing to pay

P

21

18

1512

1 2 3 4

24a

b c

d e f

g h i j

k l m n

When the price is 24, 0 unitsare demanded. At P=21, 1unit is demanded. 21 is the

maximum price this personwould pay for the first unit.Lets say the market price is10. Then the surplus on thefirst unit is 11. The surpluson the2nd....................,3rd....................... units is?

Q


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willing to pay

You will notice on the previous screen at price 21, thequantity demanded is 1. The area b + d + g + k equalsthe $21 the consumer would pay for the 1st unit. Thearea a is under the demand curve but not part of whatthe consumer would be willing to pay for the first unit.We will add in area a to calculate the consumer surplus.It makes the calculation easier.The second unit would be demanded if the price is 18.

The area e + h + i = $18. The area c is under the demandcurve but not part of what the consumer would bewilling to pay for the second unit.


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willing to pay

The point I am getting to on the previous screen is if we

add in areas like a and c, that are really not a part of what

consumers are willing to pay, we have an easier

calculation to find out what consumers are willing to pay

for a certain number of units. It is simply the area underthe demand curve out to a quantity.

P

QQ1

What consumers arewilling to pay for the Q1

units


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Consumer surplus again

P

25

10

300 Q

A

B

Area A = .5(300)(25-10)=2250

Area B = 10(300)= 3000

Note consumers would bewilling to pay 3000 + 2250

for 300 units.But the consumers only have to pay 3000 for the 300units.So the consumer surplus is area A and equals 2250.

Say with S & D we get theP = 10 and Q = 300.


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Refresher on areas

The area of a triangle is of the base times the height.

The area of a rectangle, of which the square is a special case,

is the base times the height.

We use these ideas from time to time because they assist in

the development of economic ideas.


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consumer surplus again

What do consumers do with the surplus received?

They may spend it on more units of the item in question, they

may spend it on other items, or they may save it for a rainy

day.

The point here is that the surplus is useful to the consumer!


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Market Demand from

Individual Demand


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In this section we want to think about market demand as theresult of adding up demands from many individuals.Remember individual demand is the result of each

consumer going about utility maximization.

Lets do an example with 3 people. qi is the demand fromthe ith consumer. Say,

q1 = 10 - p, q2 = 15 - 2p, and q3 = 18-3p.Often the demand is written in inverse form (where weisolate the p term). We have

p = 10 - q1, p = 15/2 - (1/2)q2, and p = 18/3 - (1/3)q3

We usually express demand in inverse form when we wantto graph the demands in the P, Q graph. I have a graph onthe next screen with each demand in it.


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P

Q

10

7.5

6

10 15 18

Note at a price above 10 no one demandsany units. At a price above 7.5 only person1 demands units. At a price above 6 only

person 1 and person 2 demand units. Ifprice is below 6 all three people demandunits.

The dashed line here is the marketdemand. It is found by looking at eachprice and adding the quantities eachperson would demand.


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To get the market demand we horizontally add the demandfrom each person. This amounts to saying q1 + q2 + q3 =

Q.We saw before the demand from each person was

q1 = 10 - p, q2 = 15 - 2p, and q3 = 18-3p.To get the market demand we add

q1 + q2 + q3 to get (10 - p) + (15 - 2p) + (18 -3p) = (10 +15 + 18) - (p + 2p + 3P), or

Q = 43 - 6P, but this is only true when price is less than or

equal to 6. In other words all three people demand unitswhen the price is less than 6.

Note if P = 1 q1 = 9, q2 = 13, q3 = 15 and Q = 37, or

if P = 2 q1 = 8, q2 = 11, q3 = 12 and Q = 31.

Remember if the price is above 6 but


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P

Remember if the price is above 6 butless than or equal to 7.5 the demandcomes from only the first two people

and the demand curve isq1 + q2 = Q = 25 - 39, andif the price is above 7.5 the demand isonly from the first person and thedemand curve is

q1 = Q = 10 - p.

So the market demand curve we havecome to know and work with is reallythe addition of the demand from manypeople as they have gone aboutmaximizing their utility.

Q


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Price elasticity of demandOften in economics we look athow the value of one variable

changes when another variable

changes. The concept calledelasticity is a summary statement

about those changes.


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Elasticity

The law of demand or the law of supply is a statementabout the direction of change of the quantity demanded,or supplied, respectively, when there is a price change.

The concept of elasticity adds to these concepts byindicating the magnitude of the change in quantity,given the price change. The magnitude of the change isreported inpercentage terms.


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own price elasticity of demand

Ed = (% change in Q)/(% change in P)

As an example, if Ed = -2 we say for every 1 % changein the price of the good the quantity demand changedin the opposite direction by 2 %.


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absolute value

You may recall a function in math called the absolute value.

Basically this function makes negative values positive and

leaves positive values positive.

In the notes I will write abs( ) to mean take the absolute

value.

The own price elasticity of demand is a negative number, so

we will take the absolute value to describe some conceptsabout it.

Elasticity can have three basic


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Elasticity can have three basicvalues

If abs(Ed) > 1 we say demand is elastic. This means the% change in the Qd is greater than the % change inprice.

If abs(Ed) = 1 we say demand is unit elastic. Thismeans the % change in the Qd is equal to the % changein price.

If abs(Ed) < 1 we say demand is inelastic. This meansthe % change in the Qd is less than the % change inprice.


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Elasticity again

P

Q

P1P2

Q1 Q2

In the upper left of thedemand curve the %change in the Qd is

greater than the %change in the P andthus the Ed > 1 .

Without a real formal proof of the above statement, wecan see the % change in Qd is about 100 % and the %change in P is less than 100 %. Demand is elastic here.


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Elasticity has several ranges

of valuesP

Q

P1P2

Q1 Q2

In the lower right ofthe demand curve the% change in the Qd is

less than the % changein the P and thus theEd < 1.

Without a real formal proof of the above statement, wecan see the % change in Qd is less than 100 % and the %change in P is about 100 %. Demand is inelastic here.


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Elasticity has several ranges

of valuesP

Q

P1P2

Q1 Q2

In the middle of thedemand curve the %change in the Qd is

equal to the % changein the P and thus theEd = 1.

Without a real formal proof of the above statement, wecan see the % change in Qd is about equal to the % changein P. Demand is unit elastic here.


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Calculation point slope method

P

11

10 Q

If we know the slope of the demand

curve the elasticity at a point is found

by using the Q and P value of the

point and the slope in the following

way:

(P/Q)(1/slope).

Example say the slope here is -1.

The elasticity is (11/10)(1/-1) = -1.1When we take absolute value we get

1.1. Elastic in this case.


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Own price elasticity and total

revenue changesTotal revenue (TR) is price timesquantity. Along the demand curve P

and Q move in opposite directions.Knowledge of Ed assists in knowinghow TR will change.

Elasticity and total revenue


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Elasticity and total revenuerelationship

When we look at the collection of consumers in themarket, at this time in our study we assume eachconsumer pays the same price per unit for the product.

Also at this time in our study the total expenditure ofthe consumers in the market would equal the totalrevenue (TR) to the sellers.

So, here we look at the whole demand side of themarket in general.



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P

Q

P1

Q1

TR in the market isequal to the price in the

market multiplied bythe quantity traded inthe market. In thisdiagram TR equals thearea of the rectangle

made by P1, Q1 andthe horizontal and vertical axes. We know from math thatthe area of a rectangle is base times height and thus herethat means P times Q.



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We will want to look at the change in values of avariable and in order to do so we want to have aconsistent measure of change. In this regard lets say

the change in a variable isthe later value minus the earlier value.

Thus if the price should change from P1 to P2, then thechange in price is

P2 - P1, or similarly if the TR shouldchange the change in TR is

TR2 - TR1.


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relationshipP

Q

P1P2

Q1 Q2

Now in this graphwhen the price is P1the TR = a + b(adding

areas) and if the priceis P2 the TR = b + c.

The change in TR if

the price should fallfrom P1 to P2 is (b + c) - (a + b) = c - a.Similarly, if the price should rise from P2 to P1 the changein TR is a - c. I willfocus on price declines next.

a

b c


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relationshipP

Q

P1P2

Q1 Q2

Since the change in TRis c - a, the value of thechange will depend onwhether c is bigger orsmaller, or even equalto, a. In this diagramwe see c > a and thusthe change in TR > 0.

This means that as the price falls, TR rises. I think youwill recall that in the upper left of the demand thedemand is price elastic. Thus if the price falls in the elasticrange of demand TR rises.

a

b c


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Elasticity and TR

You will note on the previous screen that I had c - a. Inthe graph c is indicating the change in TR because weare selling more units. The area a is indicating thechange in TR when there is a price change. We have tobring the two together to get the change in TR.

Thus a lower price has a good and a bad.Good - sell more units.

Bad - sell at lower price.


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relationshipP

Q

P1P2

Q1 Q2


areas) and if the priceis P2 the TR = b + c.In this diagram we seec < a and thus the

change in TR < 0.I think you will recall that in the lower right of thedemand the demand is price inelastic. Thus if the price

falls in the inelastic range of demand TR falls.

ab c


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relationshipP

Q

P1P2

Q1 Q2


areas) and if the priceis P2 the TR = b + c.In this diagram we seec = a and thus the

change in TR = 0.I think you will recall that in the middle of the demandthe demand is unit elastic. Thus if the price falls in the unitelastic range of demand TR does not change.

a

b c


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Elasticity and TR

P

Q

TR

Q

D

When the price falls the quantity

demanded always rises. As the

quantity demanded rises

(because of the price change)

the TR is first rising in the

elastic range, levels off when

demand is unit elastic and TR

falls in the inelastic range.


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Marginal revenue

Marginal revenue is defined as the change in total revenue asthe number of units cold changes. In the demand graph we

have seen that in order to sell more the price has to be

lowered. So, there is a relationship between elasticity and

marginal revenue.

If price falls and demand is elastic we know TR rises so MR

is positive.

If Price falls and demand is inelastic we know TR falls and so

MR is negative.

If price fall and demand is unit elastic we know TR does not

change.


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Other demand elasticities

There are other elasticitiesbesides the own price elasticity of

demand. Lets see a few here.


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demand shifters

We saw that things like taste and preference, price of other

goods, income and the number of buyers shift the demand

curve if they change. How much do they shift the demand

curve?We use other elasticity concepts as an indication of how much

the curve will shift given a change in one of these factors.


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cross price elasticity of demand

Edxy = % change in Qdx / % change in Py.

The bigger the value the more the demand shifts.

If the value is negative we have complements and if positivewe have substitutes.

If the absolute value is between 0 and 1 the cross elasticity is

inelastic, if = 1 unit elastic and if greater than 1 elastic.


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income elasticity of demand

Edxm = % change in Qdx / % change in M.

The bigger the value the more the demand shifts.

If the value is negative we have an inferior good and ifpositive we have a normal good.

If the absolute value is between 0 and 1 the income elasticity

is inelastic, if = 1, unit elastic, and if greater than 1, elastic.

f


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Elasticity of supply

The elasticity of supply is used to indicate the percentage

change in the quantity supplied given a percentage change in

price.

The elasticity of supply is calculated in a manner similar to theother elasticities we have seen and has a similar interpretation

in terms of the range of values the elasticity might take, i.e.

elastic, inelastic and unit elastic.


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Decisions under uncertainty

A Different look at Utility Theory

O i


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Overview

The author says that economic decisions made under

uncertainty are essentially gambles. Lets first look at somegambles, and then come back to decisions under uncertainty.

Initially, our gamble will be to flip a fair coin (one where the

probability of a head is .5 and the probability of a tail is .5).

The payout will depend on which side of the coin is showing

when the coin lands at rest.

E l


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8080

Facts about several gambles with a fair coin:

Gamble 1heads means you win $100 and tails means you lose$0.50

Gamble 2heads means you win $200 and tails means you lose$100

Gamble 3heads means you win $20000 and tails means you lose

$10000

Note what a person would lose on each gamble. Many people

would say the loses in gambles 2 and 3 make them uneasy and

they wouldnt take those gambles. But, some folks out there might

take gambles 2 and 3.

Examples

Di h


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Digress the mean

What is the mean or the average of the numbers 4 and 6? You

probably said 5 and you are right. This could be written

(4+6)/2 = (4/2) + (6/2) = (1/2)4 + (1/2)6, wherein this last form you see each number multiplied by . In this

context the mean is said to be a simple weighted average, with

each value weighted by . What would the weights be if we

wanted the average of 4, 5, and 6? 1/3! In general with nnumbers the weight is 1/n.

In other situations we may look at a weighted average (not

simple), though the weights are found in a different way.

B k t l


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Back to example

The expected value of a gamble is a weighted average of the

possible payout values and the weights are the probabilities of

occurrence of each payout. We talk about EVi as the expected

value of gamble i.

EV1 = .5(100) + .5(-0.50) = 500.25 = 49.75. (Notice whenyou lose the loss is subtracted out.)

EV2 = .5(200) + .5(-100) = 10050 = 50EV3 = .5(20000) + .5(-10000) = 100005000 = 5000

E l


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Example

In our example the EV for each gamble is positive. The EV isthe highest for gamble 3. But, remember we said not many folks

would probably like it because of the uneasiness they would feel

by losing the 10000.

A couple of guys named Von Neumann (both names are just thepersons last name) and Morgenstern created a model we nowcall the expected utility model to deal with situations like this.

They indicated folks make decisions based not on monetary

values, but based on utility values. Of course the utility valuesare based on the monetary values, but the utility values also

depend on how people view the world.

E t d Utilit


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Expected Utility

Say we observe a person always buying chocolate ice creamover vanilla ice cream when both are available and both cost

basically the same, or even when chocolate is more expensive

and always when chocolate is the same price or cheaper. So by

observing what people do we can get a feel for what is preferredover other options.

When we assign utility numbers to options the only real rule we

follow is that higher numbers mean more preference or utility.

Even when we have financial options we can study or observe

the past to get a feel for our preferences.


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Expected Utility Theory is a methodology that incorporates our

attitude toward risk (risk is a situation of uncertain outcomes,

but probabilities are known) into the decision making process.

Utility

value

Monetary

value

It is useful to employ a graph like this

in our analysis. In the graph we will

consider a rule or function that

translates monetary values into utility

values. The utility values are oursubjective views of preference for

monetary values. Typically we

assume higher money values have

higher utility.


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In general we say people have one of three attitudes toward

risk. People can be risk avoiders, risk seekers , or indifferent

toward risk (risk neutral).

Monetary

value

Utility

valueRisk avoider

Risk indifferent

Risk seeker

Utility values are assigned

to monetary values and the

general shape for each typeof person is shown at the

left. Note that for equal

increments in dollar value

the utility either rises at adecreasing rate(avoider),

constant rate or increasing

rate.


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Utility

$

X1 X2

U(X2)

U(X1)

Here we show a

generic example with

a risk avoider. Twomonetary values of

interest are, say, X1

and X2 and those

values have utilityU(X1) and U(X2),

respectively

E t d Utilit


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Expected Utility

In expected utility theory we want to focus on wealth values and

utility values. Gambles will lead to adjustments in wealth.

Lets call W the initial wealth which can always be retained if no

gamble is taken, and call the wealth at a loss X1 = Wloss, and thewealth at a win X2 = W + win.

The expected value of wealth from a gamble is then (p1 is the

probability of a loss and p2 is the probability of a win)

EV = p1X1 + p2X2

Note we called the expected value of a gamble EV and I now have

the expected value of wealth with a gamble being EV. EV will

mostly stand for expected value of wealth, unless otherwise stated.

E t d Utilit


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Expected Utility

The following is what needs to be considered to get the expected

utility of a gamble:

1) Start with a persons initial wealth W,

2) If the gamble is taken identify X1 and X2,

3) Assign to each wealth value in 2) the respective utility value

U1, and U2 and in a graph connect the U1 and U2 values with a

chord.

4) Calculate the expected value of wealth with the gamble EV.

5) Calculate the expected utility of the gamble as EU where EU =

p1U1 + p2U2, and find the value on the chord above the EV.


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Utility

$

X1 EV X2

U2

U1 EU

Example continued


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9191

Example continued

Say utility is assigned by the function U = sqrt(wealth) and a

person has initial wealth 10000. Then for the three gambles

we had before the EUs would be

EU1 = .5sqrt(9999.5) + sqrt(10100) = 100.248

EU2 = .5sqrt(9900) + sqrt(10200) = 100.247

EU3 = .5sqrt(0) + sqrt(30000) = 86.603

So in terms of EUs the preferred order of gambles for thisperson is gamble 1, then 2, and the 3. When we looked at

EVs the order was 3, 2, and 1. So expected utilities ofgambles may have a different rank ordering than when

looking at the EVs.

Fair gambles


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Fair gambles

A fair gamble is one where the expected value of the gamble is

zero, i.e., p1(-loss) + p2(win) = -p1(loss) + p2(win) = 0.

This implies that the expected value of wealth with the gamble

is equal to the value of wealth when not gambling at all, which

you might call your certain wealth.

For fair gambles

EV = p1(Wloss) + p2(W + win)

= p1W +p2Wp1(loss) + p2(win) = (p1+p2)W + 0 = W, sincep1+p2=1.

Risk averse fair gamble


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wealth

Utility

X1 X2EV

= W

Uw

EU

In this graph I have the generic

view of a risk lover. With the fair

gamble we have the EV and the

EU is on the chord above the EV.

If the person does not gamble

wealth will be W and the utility

there is just read off the utility

function here as Uw (note a risk

averter has diminishing marginalutility of wealth.)

Risk Averse fair gamble


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Risk Averse fair gamble

For the fair gamble we again know EV = W, but for a risk averse

person Uw > EU. Thus we can conclude risk averse folks will

not accept fair gambles.

On the next slide you can see I thickened part of the horizontal

axis and the chord connecting the two points on the utility

function associated with the wealth values under the gamble.

The probabilities of the gamble could be changed (and the

gamble would no longer be fair) and the only way the person

would accept the gamble over having the certain wealth W is ifthe EV was greater than W*.

So, a risk averse person may gamble, but it has to be at favorable

odds.



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wealth

Utility

X1 X2EV

= W

Uw

EU

If the EV of a gamble is above

W* (and is no longer a fair

gamble, but a favorable one),

then the person will end up on the

chord segment that has not beenthickened and thus only then have

EU>Uw.


W*

Risk Seeker fair gamble


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U

WX1 X2EV

=W

EU

Uw

In this graph I have thegeneric view of a risk seeker.

With the fair gamble we have

the EV and the EU is on the

chord above the EV.If the person does not gamble

wealth will be W and the

utility there is just read off

the utility function here as

Uw (note a risk seeker has

increasing marginal

utility of

wealth.



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9797


For the fair gamble we again know EV = W, but for a risk

seeker person Uw < EU. Thus we can conclude risk seeker

folks will always accept fair gambles.

On the next slide you can see I thickened part of the horizontal

axis and the chord connecting the two points on the utility

function associated with the wealth values under the gamble.

The probabilities of the gamble could be changed (and the

gamble would no longer be fair) and the only way the person

would NOT accept the gamble over having the certain wealth

W is if the EV was less than W*.

So, risk seeker may NOT gamble, but it has to be at

unfavorable odds.



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U

WX1 X2EV

=W

EU

Uw

If the EV of a gamble isbelow W* (and is no longer a

fair gamble, but an

unfavorable one), then the

person will end up on thechord segment that has not

been thickened and thus only

then have EU


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Risk Neutral fair gamble

U

W

Uw = EU

X1 EV

=W

X2

The risk neutral person

is indifferent between a

fair gamble and not

gambling at all. If oddsare switched to favorable

gambles will be favored

and if switched to

unfavorable gambles

will not be taken.

Certainty Equivalents


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Certainty Equivalents

In a more general sense we could talk about gambles that are fairor unfair. The certainty equivalent of a gamble will be the sum of

money or wealth for which the individual would be indifferent

between the certain sum and the gamble. We will examine these

certainty equivalents for folks with risk aversion, neutrality and

risk seeking prefrences.

Risk averse certainty


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Utility

$

X1 X2

U2

U1

The decision makermay have an option

that is certain. If so,

the EU is simply the

utility along the utilitycurve (I called it Uw

before). So in this

diagram we see that

any sure bet greater

than Y has an expected

utility greater than the

expected utility of the

risky option.

EV

EU

Y

equivalent

Another Example


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Another Example

Say Utility U = square root of X, where X is a dollar amount the

person ends up with,Then U(4) = 2 and U(16) = 4, for example.

Say a risky option will result in 4 50% of the time and 16 50%

of the time. The expected value is 10 because.5(4) + .5(16) = 10 and the expected utility is 3 because

.5U(4) + .5U(16) = .5(2) + .5(4) = 3.

Now, if there is an option that will pay more than 9 withcertainty, than the certain option is better. So, 9 is the certainty

equivalent of this uncertain gamble. Lets see this on the nextslide.


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4 9 10 16 x

U(x)

U(16)=4

EU = 3

U(4)=2

U(x)

Any certain option above 9 gives a utility

value greater than the expected utility of

the uncertain option.

Risk seeker certainty


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equivalent

U

WX1 X2EV

EU

Uw

In this graph I have thegeneric view of a risk seeker.

With the fair gamble we have

the EV and the EU is on the

chord above the EV.Y is the certainty equivalent

of the gamble. Any certain

option above Y would be

preferred to the gamble

shown by the risk seeker.

Y


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Reducing Risk

In a previous section we mentioned that sometimes we face an


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p

uncertain situation with regards to monetary values. We saw

1) The expected monetary value, EV, of the uncertain situation(what I will now call a gamble) is the sum of some numbers,

where each number is a monetary value multiplied by its

probability of occurring,

2) The expected utility of a gamble (what I will now write asEU) is the sum of some numbers, where each number is the

utility of a monetary value multiplied by its probability of

occurring,

3) The expected utility of a gamble does not occur on the utilityfunction (unless the person is risk neutral), but on the chord or

line segment that connects utility values of each part of the

gamble and directly above the EV of the gamble.

Say we have a risk lover and the gamble Gleaves Y1 p1 % of the time and Y2 p2% of the


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U

Y

Y1 EMV Y2

U(Y1)

U(Y2)

EU

leaves Y1 p1 % of the time and Y2 p2% of thetime.

EV =p1Y1 + p2Y2

EU = p1U(y1) + p2U(Y2)

Say we have a risk avoider and the gamble GleavesY1 p1 % of the time and Y2 p2% of the


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U

Y

Y1 EMV Y2

U(Y1)

U(Y2)

EU

leavesY1 p1 % of the time and Y2 p2% of thetime.

EMV =p1Y1 + p2Y2

EU = p1U(y1) + p2U(Y2)

On the last few slides I show you generic cases of a risk lover and


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a risk avoider. You see a gamble with monetary values Y1 and

Y2, with associated probabilities p1 and p2 (where p2 = 1- p1).

I now want to show something we saw in the previous section, but

I want to be more precise in my language.

Sometimes we may have an opportunity that is known with

certainty. The utility of the opportunity will be on the utility

function for the individual and will be noted U(C).

The decision rule for choosing between a gamble and a certain

payoff is

-choose the certain option when U(C) > E[U(G)], and

-choose the gamble when U(C) < E[U(G)].

Of course, when the two are equal the individual would be

indifferent between the two.

Back on the slides I have some vertical dashed lines. I put them


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there on purpose. I want you to think of the location as values of

a certain payoff, I now call C, and then we can see that

U(C) = EU. The payoff C is called the certainty equivalent of the

gamble.

Say we have a risk avoider and the gamble Gleaves Y1 p1 % of the time and Y2 p2% of the


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U

Y

Y1 EV Y2

U(Y1)

U(Y2)

EU

p ptime.

The risk premium, rp, of agamble is the EV of thegamble minus the certaintyequivalent of the gamble.

rp = EV - C and will alwaysbe positive for a risk avoider.

The risk premium for a risklover will be negative and itwill be zero for a risk neutralperson.

C

A Gamble of no fire insurance Say Y2 is value of property ifno fire and Y1 is the value of


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U

Y

Y1 EV Y2

U(Y1)

U(Y2)

EU

C

the property with a fire.

The EV = p1Y1 + p2Y2.

EU = p1u(Y1) + p2U(Y2)

C is the certaintyequivalent of thegamble.

If a person buys insurance it changes the risky situation


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into a certain situation.

If Y2 - C = fee paid for insurance the individual will haveC with certainty. To see this we note

If no fire the individual has Y2 - fee = C, and

If fire the individual gets restored to Y2 and has still paid

the fee so the certain property value is C.

SOOOOOO

Y2 - C is really the maximum fee the person would pay

for insurance and they would like to pay less. Y2 C iscalled the reservation price for insurance.

Lets take the point of view of the insurance company - and


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we do not have to look at the graph here.

They pay claim of Y2 - Y1 p1% of the time and they pay 0p2% of the time for an expected claim of

p1(Y2 - Y1) + p2(0) = p1(Y2 - Y1)

This is called the actuarially fair insurance premium -

meaning this is the minimum they have to charge to beable to pay out all the claims.

Now look in the graph - here is an amazing result:

Y2 - EV = Y2 - (p1Y1 + p2Y2) = Y2(1 - p2) -p1Y1= p1(Y2 - Y1), so Y2 - EV is the actuarially fair premium

Review


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Y2 - EMV = least insurance company will charge,

Y2 - C = Most person will pay,

(Y2 - C) - (Y2 - EMV) = EMV - C is the room the personand the insurance company have to negotiate for theinsurance. Before we said EMV - C was the riskpremium and now we see it is the most the person wouldpay over the actuarially fair premium to insure againstthe gamble.

Now insurance companies pay out claims and payemployees and electricity and other admin. expenses.The company has to get some of EMV - C to pay theseexpenses.

People wont buy the insurance if the insurance company


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p y p yneeds more than EMV - C to cover its other expensesbecause the person would have more utility without it in

that case.

Next lets look at how information can be beneficial in

reducing risk.

U

situation without


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Y

Y

U

Y1 C EMV Y2

Y1 c EMV Y2

situation withoutinformation

situation withinformation

On the previous slide I show two graphs. Both have thesame utility function for an individual The top graph is a


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same utility function for an individual. The top graph is asituation where the individual has no information and the

bottom graph shows what happens when more informationis obtained.

Note more information may not eliminate risk, but it canreduce it. Lets study an example to show context.

Say an individual can buy a painting and if it is a realmaster painting the wealth of the individual will be Y2. Ifthe painting is a fake the individual will lose some of hisexpenditure because the painting is no big deal - wealth is

Y1. We see the certainty equivalent of the gamble is C.Presumably the individual will buy the painting if thecertainty equivalent of the gamble is better than his wealthby not buying the painting at all.

Now say the person can hire a painting expert to see if thepainting is a fake or not If the expert says the painting is a


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painting is a fake or not. If the expert says the painting is afake then you will not buy it and will not lose on the low end.

But if it is a real painting you will have the same high endwealth because you will buy the painting.

So information from an expert in this case gives you thesame high end value but makes your low end value better

than without information.

But, the expert is going to want to charge you for theinformation. How much should you pay?

Since C is the certainty equivalent with information and C isthe certainty equivalent without the information, the personwould pay up to C - C for the information and the utility ofthe person would be improved.


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Game Theory

Here we study a method forthinking about oligopoly situations.

As we consider some terminology,we will see the simultaneous

move, one shot game.

Simultaneous Move, One ShotG


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Games

We will again assume there are only two decision makers. For

now we assume both have to make their decisions at the same

time. This is a simultaneous move game. The main point about

a simultaneous move game is that although I may know all the

information about what the other guy might do, I do not

actually see what is done before I do my thing.

Games could be sequential, where one player follows the other.

Some games have only one decision by each player involved.Other games involve repeated rounds of play. Here we focus

on the one shot games.

Normal Form


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Normal Form

In the normal form of a game, information about the options of

each player is presented in a matrix. The row playersoptions are described in each row and the payoff is the first

number in each cell.

The column players options are described in each columnand the payoff is the second number in each cell.

Since we have a simultaneous move game each player will

choose its options without knowing what the other player willchoose. But the choice of the other player may be anticipated.

Lets check out an example on the next few screens.

Column player

left right


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g

Row up a, A c, C

Player down b, B d, D

Lets make sure we understand this table. Here we have twoplayers: the Row Player and the Column Player (Miller and Bud,

if you want).

This is a generic game for now and all the Row Player can do ischoose up or down (in rock, scissors, paper you can choose one

of the three, but for the Row Player here the choice is up or

down.)

The Column Player can only choose left ofright.

Now, lets say the row player picks up and the column playerpicks left.

Column player

left right


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g

Row up a, A c, C


Now, lets say the row player picks up and the column playerpicks left just as an example to see what each would get.

If the game ended at up, left, the row player would get a andthe column player would get A.

Note all these letters usually are dollar amounts for us and can be

negative amounts. But, sometimes the letters represent other

concepts besides dollars. As an example the numbers couldrepresent jail time.

Column player

left right


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g

Row up a, A c, C


If the game ended at down, right, the row player would get dand the column player would get D.

Caution: If as ROW Player you pickdownthinking you get bremember that what you get is also influenced by Column Player.

So, you could actually get d if the Column Player picks right.

Next we want to think about how each player should decide what

strategy to pick.

Row player should think this way: (As the row player) I do not

know what the column player will do But I can look at each


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know what the column player will do. But, I can look at each

option of the column player, one strategy at a time.

If the column player picks left my choices are

up a

down b

As the row player I would pick the option that has the highest

value: pick up if a > b, or pick down if a < b.

If the column player picks right my choices are

up cdown d

As the row player I would pick the option that has the highest

value: pick up if c > d, or pick down if c < d.

For the row player the choice of strategy is up or down.


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A strategy is called a dominant strategy for a player if it has a

higher payoff no matter what the other player chooses.

So, up would be a dominant strategy for the row player if both

a > b and c > d.

Down would be a dominant strategy for the row player if both

a < b and c < d.

Example


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p

column player

left right

Row up 10, 20 15, 8

Player down -10, 7 10, 10

The row player will think in the following way(look at each

column). If column man picks left I can have 10 if I go up and

10 if I go down. So I will go up. If column man goes right I

can have 15 if I go up and 10 if go down. So I will go up.In this example the row player sees it is best to go up no matter

what the column player is doing. In this sense we say up is adominantstrategy for the row player.

E l


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Example

column player

left right

Row up 10, 20 15, 8


This is the same slide as before, but I show in each column

what the ROW player will look at. If the highest value in each

column is in the same rowthe person has a dominant

strategy.Again, up is a dominant strategy here for the row player.

Column player should think this way: (As the column player) I do

not know what the row player will do But I can look at each


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not know what the row player will do. But, I can look at each

option of the row player, one strategy at a time.

If the row player picks up my choices are

left right

A C

As the column player I would pick the option that has the highestvalue: pick left if A > C, or pick right if A < C.

If the row player picks down my choices are

left right

B DAs the column player I would pick the option that has the highest

value: pick left if B > D, or pick right if B < D.

For the column player the choice of strategy is left or right.


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A strategy is called a dominant strategy for a player if it has a

higher payoff no matter what the other player chooses.

So, left would be a dominant strategy for the column player if

both

A > C and B > D.

Right would be a dominant strategy for the column player if

both

A < C and B < D.

Example


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p

column player

left right

Row up 10, 20 15, 8


The column player will think in the following way(look at each

row). If row man picks up I can have 20 if I go left and 8 if I go

right. So I will go left. If row man goes down I can have 7 if I

go left and 10 if go right. So I will go right.In this example the column player does not have a dominant

strategy. What to do? If the other player has a dominant

strategy, assume he will play it and then do the best you can.

Column player should go left.

E ample


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Example

column player

left right

Row up 10, 20 15, 8


This is the same slide as before, but the column player looks at

his possibilities in each row.

Nash Equilibrium


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q

A set of choices by the players would be considered a Nash

equilibrium if each player would NOT want to change their

choice given the choice of the other player. The choices up

and left represents a Nash equilibrium because neither would

choose to change given the choice of the other.

The row player saysif the column player will be at left, thenit is best for me to stay at up.

The column player says - if the row player will be at up, thenit is best for me to stay at left.

Lets pick a different cell than up, left to see why another cell


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might not be a Nash equilibrium.

Lets look at up, right.The row player says - if the column player is at right then I want

to stay at up (Nash Equilibrium may still be in the running).

The column player saysif the row player is up, then I want tochange from right to left.

Because the column player wants to change, the cell considered

is not a Nash Equilibrium.

Note: You look for dominant strategies before the game isplayed and you see if you have a Nash equilibrium after the

game is played.


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Applications

Here we look at severalapplications. We will see a classic

example of a dilemma that can arisein such games.

Pricing Example


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g p

column player

low price high price

Row low price 0, 0 50, -10

Player high price -10, 50 10, 10

The numbers in the matrix represent profit. The row player has

a dominant strategy of a low price (0 is better than -10 and 50

is better than 10) and the column player has a dominant

strategy of a low price as well (similar numbers). And, lowlow is a Nash equilibrium.

A dilemma that arises here is that both could be better off if

they both went with a high price

Prisoner Dilemma Games


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The game we just saw has the characteristic that has come to be

known as the prisoners dilemma. When the players actseparately (competitively) the outcome is worse than if they

cooperated.

Dont be taken advantage ofIn the pricing example each might be tempted to get together and


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In the pricing example each might be tempted to get together and

both charge the high price and both do better than the low price

strategy. The problem of the high, high solution is that it is not aNash equilibrium and thus each would have the incentive to change

to the low price strategy. Your stockholders would not want you to

be taken advantage of by a double crosser. Dont collude here, for it

is not likely to pay off. Lets see why.Say you are the row player and you agree (illegally) to set priceshigh with the column player. After you finish the meeting you will

note 1) if you as the row player see the column stay at a high price

the it is better for you to have a low price (this is part of why high,

high is not a Nash equilibrium), and 2) perhaps more importantlyyou will note the column player also has the incentive to switch to

low (this is the other part of high, high not being a Nash

equilibrium). So, if you stay at high you will look bad!

Advertising Example


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column player

ad no ad

Row ad 4, 4 20, 1

Player no ad 1, 20 10, 10

Profits are in the matrix. Each player has a dominant strategy

of advertise. This outcome is a Nash equilibrium.

A similar dilemma arises here as before. No ads would bebetter but each does not want to get taken advantage of in this

situation. If you dont have ads when the other does youwont be on the minds of the consumers and thus you will not

make enough

Coordination example


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column player120 volt 90 volt

Row 120 volt 100, 100 0, 0

Player 90 volt 0, 0 100, 100

In this example say you have consumer appliance

manufacturers who have the choice between making the

appliances run on 120 or 90 volt plugs. If they both do not

use the same plug they will earn less profit because

consumers will have to spend on different plugs and thus

not be willing to spend as much on the appliances. The

game has two Nash equilibriaboth doing the same plug.The next question is how do they get the same plug?

Coordination Example


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In this example, the firms need to figure out a way to get on

the same page. Agreements to coordinate may be looked at

negatively legally, so maybe companies lobby the government

to set the standard for a product.


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Hawks and Doves

Tastes


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In economics we largely take the tastes and preferences of the

consumer to be a given piece of information. Within that

context, the consumer attempts to maximize utility also given

prices and income. We have spent some time thinking about

how the consumer changes their actions when income or prices

change. But we leave preferences stable.

Biologists assume (I am told) an organisms tastes are forged by

the pressure of natural selection to help the organism solve

important problems in their environment.

Please read the book example about out tastes for sweets.

Strategic Preference


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A strategic preference helps the individual solve important

problems of social interaction and the usefulness of having the

preference depends on the fraction of the population who share

them.

What we will look at next is a model of preference formation.

The example is taken from biology, but put into the language ofeconomics. Note how there are basic assumptions and then

conclusions are reached.

On to the example of hawks and doves a model of the taste foraggressive behavior.

The Model


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Say people are all the same except for some are hawks (have a

strong preference for aggressive behavior) and some are doves

(prefer to avoid aggressive behavior).

Whenever two individuals come into conflict over an important

resource (food, a mate, and so on) the hawks strategy will be toalways fight for it while the doves strategy will be to never fight.

Remember economics is about using scare resources. Hawks

may kill doves and get the resources, but hawks might kill eachother for the resource. Doves do not fight each other, but share

resources.

The Model


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Say a food unit has 12 calories.

When two doves meet close to a food unit they share it and each

gets 6 calories.

When a hawk and a dove meet close to a food unit the dovedefers and the hawk gets all 12 calories.

When two hawks meet close to a food unit there is a battle. The

winner gets the 12 calories and the loser gets none. Also, eachspends 10 calories in the fight. So, the winner has a net gain of 2

calories and the loser has a net gain of -10 (sometimes called a

lose). If over time a hawk wins half of the encounters with other

hawks and loses the other half the average payoff is -4.

The Model


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The average payoffs can be put in tabular form as:

Individual Y

hawk dove

Individual X hawk -4 each 12 for X, 0 for Y

dove 0 for X, 12 for Y 6 each.

So you can see, for example, if 2 doves meet each will get 6

calories on average.

Say h is the proportion of the population that is hawk and thus 1-

h is the proportion that is dove. Then a hawk would meet

another hawk h of the time and the payout would be -4 and

would meet a dove 1-h of the time and the payout would be 12

for an average payoff of Ph = h(-4) + (1-h)12.

The Model


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Similarly, the dove would have an average payoff of

Pd = h(0) + (1-h)6.

Whenever we consider a value for h, if hawk has a higher

average payoff then hawks will flourish and doves will diminish

and h will grow. For example, if h = .5,Ph = .5(-4) + .5(12) = 4 and Pd = .5(0) + .5(6) = 3 and thus hawks

will get most of the calories and thus they will have larger

families and that trait will grow. But, if at an h doves have a

higher average payoff then their families will grow and h will fall.For example, if h = .75,

Ph = .75(-4) + .25(12) = 0 and Pd = .75(0) + .25(6) = 1.53 and thus

doves will get most of the calories and thus they will have larger

families and that trait will grow.

Conclusion


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Now, if the average payoff is the same at an h that h will remain

and the family sizes will stabilize. We find this h by setting Ph =

Pd and solving for h. We have

h(-4) + (1-h)(12) = h(0) + (1-h)(6) and solving for x we get

-4h + 12 12h = 0 + 6 -6h, or

12 6 = 4h + 12h 6h, orh = 6/10, or .6

The average payoff is 2.4 for each.


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Income and substitution

effects

Here we want to explore some more of the detail of a priceh th d d f d H i th b i id


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change on the demand for a good. Here is the basic idea.

Say the price of x falls. When this happens we think twothings are at work: an income effect and a substitutioneffect.

The income effect: If initially we buy the same amount of x

as we purchased before, since x has a lower price we willhave more of our own income left and so it will feel like wehave more income. We saw when we have more income wewant more normal and less inferior goods. So, the incomeeffect of a price change means if the price is lowered we

could want more or less of the good.

The substitution effect: The sub effect is an indication that as


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the price of a good falls we want more of the good and we

use it in substitution for other goods.In economics we like to show the income and substitutioneffects in the diagram of consumer utility maximization.

change in price - optimal point


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changey

xx1

y1

Say the consumer starts out atx1, y1. If the price of x shouldfall the budget line rotates out

in a counterclockwise fashion.The dashed line above x1 issimilar to the one in the incomechange diagram. Except herewe do not think the consumer

will end up to the left of the dashed line when there is aprice decline.

change in price - optimal pointchange


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change

The reason we feel the consumer will not end up to theleft of the dashed line is twofold:when the price falls1) at the initial amount of x purchased the consumerfeels richer and we saw this may make them buy moreor less of x(income effect of a price change),2) x becomes relatively cheaper and we feel peoplemove toward now relatively cheaper products and

away from now relatively more expensiveitems(substitution effect of a price change).

change in price - optimal pointh


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changeSo, the income effect means more or less x given aprice decline, and the substitution effect means more xgiven a price decline.Now if the good is an inferior good1) the income effect says less x2) the substitution effect says more x.

The only way we could end up to the left of the dashed

line on the previous screen is if the income effectoperating with an inferior good is larger than thesubstitution effect. Economists have felt this rarely, ifever, happens if so we call it a Giffen good.


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income and substitution effect


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The movement from r to s highlights the substitutioneffect because the consumer had the income effect of theprice change taken away. The movement from s to t isthe income effect.

The demand curve


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P

x (usually we put Q)

P1

P2

Q1 Q2(r t)

From 2 screens ago we saw a pricedecline had us move from pointr to t. When we put this info intoa price, quantity graph we see the

demand curve is downwardsloping.

The demand curve


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You and I already knew the demand curve wasdownward sloping, but now we also know it isbecause we think substitution effects outweigh incomeeffects. Plus we know at each point along the demand

curve the consumer is maximizing their utility giventhe situation they find themselves in.We also know now that at lower prices the consumerreaches a higher level of satisfaction. This was not

always obvious along just the demand curve.



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y

xt s r

Focusing only on good x here, say westart at point r. With a price increase inx this consumer would end up at pointt. But I have also shown point s. Hereis how to think about this point: afterthe price increase think about theconsumer getting enough income so

that the initial

utility level could be obtained.

r to s subeffect

s to tincome

effect

To highlight the income and substitution effects of a priceh t i i t di t i t E ti ll h t


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change we put in an intermediate point. Essentially what

we did was say after the price change lets show ahypothetical change in income to get the consumer back tothe original indifference curve that they started with.

(Lower price, take income away, higher price, give income

back.)The movement along the original indifference curve is thenthe substitution effect. Then take the income change backout to see the income effect.


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Impact of Change in Income

Here we want to consider thechange consumers will make if

they experience a change inincome.


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change in income - budgetchange


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gy

x

Remember on the budgetline we are measuring theamount of x and y the

consumer can buy giventheir income and given thefact that prices must be paid.

x1

y1

I have illustrated one basket the consumer can buy. Withthe price of x = Px and the price of y = Py the consumerhere could buy x1, y1.

change in income - budgeth


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changey

x

There are many ways tothink about how the budgetline would change given an

income change, but one wayto think about it would be topick a given amount of x, sayx1. Before the incomex1

y1

change say that once x1 is bought that leaves only y1 ofy. Now if there is an income increase, after x1 is boughtthat would leave more money to spend on y and thus y2could be bought (I just say could it may not be bought).

y2

change in income - budgetchange


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g

From the previous screen we can see more y can bebought if there is more income available, but how muchmore depends on the prices of x and y and it depends onthe income change.

But, as income rises more y can be bought, given anamount of x is bought. Thus the budget line shifts out ina parallel fashion if income grows and by a similar logic

shifts in parallel if there is an income decline.

change in income - optimalpoint change


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p g

Now that we know how the budget changes given anincome change, lets see how the consumer optimumchanges(given that taste and preferences do notchange).



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point changey

x

Say the consumer starts out atpoint a - x1, y1 givesmaximum satisfaction. Note Ihave extended a line above

point x1.Now with more income thebudget line shifts out. Theconsumer will end up eitherx1

y1

to the right or the left of the dashed line. If the consumerends up to the right, more x is wanted with more income.If the consumer ends up to the left of the dashed linethen less x is wanted when more income is obtained.

a



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p g

A normal good is one where that as the consumer getsmore income more of the product is demanded (or lessincome means less of the good is demanded).

An inferior good is one where as the consumer getsmore income less of the product is demanded (or lessincome means more of the good is demanded).



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point changey

x

It just so happens here thatwhen income went up theconsumer moves to a pointwhere there is more x than

before. This is the case of anormal good.

x1

y1 a

change in income - optimalpoint changey


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point changey

x

It just so happens here thatwhen income went up theconsumer moves to a pointwhere there is less x than

before. This is the case of aninferior good.

x1

y1 a

Example: When you think of music CDs are probably normal andcassettes are probably inferior.

In general we are not sure if goods are normal or inferior until we

do a study. Here we show what happens in each case.

Income consumption pathy


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10 Principals of Econimics

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Transcript of 10 Principals of Econimics