DEMAND

FOURTH LECTUREFebruary 14, 2012

William R. Eadington, Ph.D.Professor of Economics, College of Business

Director, Institute for the Study of Gambling and Commercial GamingUniversity of Nevada, Reno

www.unr.edu/gaming

PROBLEM OF THE WEEKREQUEST: PLEASE SUBMIT HARD COPIES FOR

HOMEWORKS FROM NOW ON.

Suppose there has been a storm in Nebraska that has destroyed part of the corn crop in the field. The demand curve for corn has not changed. As a result, the market clearing prices and quantities before and after the storm are: Pb = 50, Qb = 2000; Pa = 100, Qa = 1500. (The subscripts a and b refer to “after the storm” and “before the storm”.)

a. Assume a linear demand curve for corn, i.e. P = α + β Q. Calculate α, β with the provided information, and draw the demand curve with P on the y-axis and Q on the x-axis. Label the intercept and the slope on the graph.

b. The supply curve for the period after the storm is P = (1/15) Q, and it is parallel to the supply curve before the storm. Is the supply curve before the storm above or below that after the storm? Calculate the slope and the intercept of the supply curve before the storm. Draw both supply curves on a new graph with P on the y-axis and Q on the x-axis. Add the demand curve (calculated in part a) to the graph.

c. Suppose consumers care only about corn consumption and apple consumption (they live in a two-good world). How would the change in the price of corn affect the budget constraint of the typical consumer? Show graphically. How would the change in relative prices affect the typical consumer’s consumption of corn versus apples? Is this result consistent with your observation from the demand and supply framework (i.e. an increase in price of corn is associated with a decrease in the equilibrium quantity)? Explain.

We see the dots, but nothing else. Can we derive the D, Sa and Sb curves?

SPECIFIC KNOWLEDGE• Examples

• idiosyncratic knowledge of particular circumstances (i.e. the kinds of food products purchased in a particular neighborhood, clothing tastes in an ethnic part of the city, etc.)

• scientific knowledge (i.e. how a particular software system can be modified to bring about desired results, how to apply recent findings to a regimen for a disease)

• assembled knowledge (i.e. the value of a team who have worked together for some time; accumulated knowledge from experience and mutual understandings)

• Free markets make superior use of specific knowledge dispersed among many participants– It is not important for participants in the market to

understand all the factors that drive markets through specific knowledge; they just respond to general knowledge available in the marketplace based on their own self interest

– Prices and profits represent general (not specific) knowledge

FREE MARKETS VERSUS CENTRAL PLANNING: THE ROLE OF KNOWLEDGE

• Centralized decision-making versus decentralized, controlled by market prices and personal incentives– Challenge for the 2009 Stimulus Package in terms of

efficiency => Where should the dollars have been spent?– Was that the point of the Stimulus Package?

• General knowledge (i.e. prices) is freely transferable• Specific knowledge (i.e. scientific expertise, local

understanding of a particular marketplace, understanding of local political issues and challenges or of industries) is expensive to transfer

• Centrally planned economies fail because it is difficult to gather and use enough specific knowledge in the planning process

EXTERNALITIES AND THE COASE THEOREM

• Externalities occur when the actions of one party impose a benefit or cost on another party not involved in the exchange• Pollution, noise, graffiti, nice lawns & architecture• Foreclosed houses on the value of other houses in the

neighborhood• If Externalities are present, markets may not be efficient (Too

much or too little of the product is being produced)– tax or subsidize externalities to get closer to efficiency

• Ronald Coase argued market exchange will be efficient if: – Property rights are well defined– Property rights can be traded– Transactions costs are sufficiently low

• Example: Your neighbor at work smokes, and you object – Pass a law => could be inefficient (Why?)– Property rights? Course of action? Bribe or exemption purchase

EXTERNALITIES AND PROPERTY RIGHTS

• Consider the example of the train car with a smoker and non-smoker– Value of clean air: $100;

value of smoking: $50– Property rights vested in the smoker (1950)– Property rights vested in the nonsmoker (2012)

• Consider the example of the bee keeper and the fruit tree grower– Definition of Property rights and passage of laws

v. Entering into Mutually Advantageous Trade

AN EXAMPLE OF THE COASE THEOREM (1)

• Consider two business next door to one another: a doctor's office and a candy maker. The candy maker uses machinery which grinds up ingredients and which produce a low rumbling noise. The doctor needs to be able to hear quiet sounds like heartbeats and joint movements. The doctor desires to start treating patients in the room right next to the wall between his office and the candy maker, but the grinding noise makes it difficult for the doctor to carry on his business in that one room.

• A lawsuit is filed, based on either:– Law #1: It is impermissible for noises to pass from one

establishment to another.– Law #2: A business is allowed to do anything it wants on its own

property as long as it doesn't endanger the health of anyone else. • What would be optimal for society? If the scarce resource goes

to producing the more valuable (socially desired) output.• Conflicting parties should be allowed and encouraged to work

out some mutually advantageous agreement. Assume this can be done at relatively low cost (TRANSACTIONS COSTS)

AN EXAMPLE OF THE COASE THEOREM (2)

• Suppose that value added of output produced by the candy maker in the disputed location is $20,000 per year and that the doctor would produce value added of $15,000. A judicial decision that would force the candy maker to shut down would clearly create an inefficient allocation of resources.

• However, the cost to society of lost output is borne by the doctor in the form of the opportunity cost he faces by using that room. He might realize that it is worth any amount up to $20,000 to the candy maker for the right to run a grinding machine near that area. Thus, his using that room to treat patients would cost society $5,000. He could capture a portion of that through negotiation (a bribe to forego using the room in return for a payment of $15,000 to $20,000.)

WHY DO FIRMS EXIST?THE ROLE OF TRANSACTION COSTS

• Types of transaction costs• search and information costs• bargaining and decision costs• policing and enforcement costs• opportunity cost of inefficient resource allocation

• Optimal economic organization minimizes transaction costs– You work on contract rather than renegotiating

your salary each day or week

FIRMS CAN REDUCE TRANSACTION COSTS

• Advantages of firms over markets• fewer transactions• information specialization• reputational concerns

DEMAND FUNCTIONA mathematical representation of the relationship between the quantity demanded and all factors influencing demand:

Q = f(X1, X2,… Xn)

where Q is quantity demanded and the Xis are the factors influencing demand

DEMAND FOR THEATER TICKETS

Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I

where P is Theater ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income

VARIABLE VALUESSuppose the variables have the

following values:P = $30

Ps = $50

Pr = $40I = $50,000

How many tickets will the Theater Company sell?

THE DEMAND CURVESubstitute variable values (except for P)

into the equation and simplify:

P = 60 - 0.15Q

This is the equation for the demand curve.

Law of demand – as the price of a good rises, the quantity demanded falls

GRAPHING THE DEMAND CURVE

Quantity of Theater tickets Quantity of Theater tickets

606160

Income = 51,000

Income = $50,000

400 406.0

Tic

ket

pric

e (in

dol

lars

)

DD0

D1

$ $

Q Q

PRICE CHANGES AND TOTAL REVENUE

• Total revenue is P x Q

• For Theater Company, P=60-.15Q

• And TR = (60-.15Q)Q=60Q-.15Q2

• Marginal revenue, MR, is

TR/Q=60-.30Q

• General rule for derivatives: If Y = a*Xb, then dY/dX = b*a*Xb-1

PRICE ELASTICITY OF DEMAND• Measures the responsiveness of quantity

demanded to changes in price• Often referred to as elasticity of demand• “Inelastic demand” => buyers respond less

than proportionately to changes in price• “Elastic demand” => buyers respond more

than proportionately to changes in price• Helps firms determine the effect of price

changes on total revenue

DEMAND ELASTICITY

• The price elasticity of demand is the ratio of the percentage change in output divided by the percentage change in price

• It is computed as:

P

Q

%

%

CALCULATING ELASTICITYARC PRICE ELASTICITY

• Using two data points to estimate elasticity• Information requirements:• Quantity demanded before and after the price

change• Q1

• Q2

• Price before and after the price change• P1

• P2

CALCULATING ELASTICITYARC PRICE ELASTICITY

)(

)(

2)(

2)(

21

21

21

21

PPPQQQ

PPP

QQQ

Note definition as a ratio of percentage changes, & cause-effect where price influences quantity demanded

PRICE CHANGES AND TOTAL REVENUE

• If demand is elastic (>1), price and total revenue move in opposite directions– If P↑ then TR↓– If P↓ then TR↑

• If demand is inelastic (<1), price and total revenue move together– If P↑ then TR↑– If P↓ then TR↓

RANGE OF PRICE ELASTICITIES

Perfectly Inelastic Perfectly Elastic

Quantity Quantity

Pric

e (in

dol

lars

)

Pric

e (in

dol

lars

)

D

D

η = 0

η = ∞

$ $

Q Q

DETERMINANTS OF PRICE ELASTICITY

• Availability of substitutes– few substitutes for airplane trips, textbook for this

class– many substitutes for out-of-home meals

• Size of commodity in consumer budget– TV cable bill versus house payment or rent

• Time period for consumer adjustment– Durable goods cannot be quickly and frequently

replaced (i.e. SUVs, home heating systems)– over time, consumers will find alternative goods

ELASTICITY AND TOTAL REVENUES

DEMAND, TOTAL REVENUE, & MARGINAL REVENUE

Quantity of Theater tickets

Inelastic demand (n < 1)T

ota

l re

venu

e (in

dol

lars

)

200Q

6,000

$

$

Q

Tic

ket

pric

e (in

dol

lars

)

30

60Elastic demand (n > 1)

n = 1

OTHER DEMAND INFLUENCES

• Complements versus substitutes– Cross price elasticity of demand

21

21

yy

y

xx

x

xy

PP

PQQQ

or Ƞxy = dQx/dPy*Px/Qy

CROSS PRICE ELASTICITY

• For substitutes, ηXY > 0

• If the price of Pepsi rises, the demand for Coke rises

• For complements, ηXY < 0

• If the price of peanut butter rises, the demand for jelly falls

INCOME ELASTICITY• Income elasticity of demand

• Normal goods – demand rises as income increases (>0)

• Inferior goods – demand falls as income increases (<0)

• Luxury goods – demand rises more than proportionately as income increases (>1)

21

21

IIIQQQ

xx

x

I

or ȠI = dQx/dI*I/Qx

NETWORK EFFECTS

• Demand for a good increases as the number of users of the good increases– Telephone networks– Mail: The internet versus the postal system– Microsoft Outlook versus Netscape– Beta-Max versus VHS– High Definition DVD versus Blu-Ray

• Without critical mass, a product will die– FAX machines

PRODUCT ATTRIBUTES

• What product attributes are important to consumers?– Price => affordability; comparability; value

for money– product design => functionality,

ergonomics– Packaging => attractiveness, shelf appeal– Promotion => perceptions, perhaps status;

“bandwagon” or “snob” effects

CROSS-PRICE ELASTICITY OF DEMAND

If EQX,PY > 0, then X and Y are substitutes.

If EQX,PY < 0, then X and Y are complements.

Y

dX

PQ P

QE

YX

%

%,

PREDICTING REVENUE CHANGES

FROM TWO PRODUCTSSuppose that a firm sells two related goods. If the price of X changes, then total revenue will change by:

XPQYPQX PERERRXYXX

%1 ,,

EXAMPLE: NORTHSTAR SELLS LIFT TICKETS AND RENTS SKI EQUIPMENT. IF LIFT TICKET PRICES ARE CUT BY 25%, AND THE ESTIMATED ELASTICITIES ARE -1.2 (OWN PRICE) AND -0.5 (CROSS PRICE), WHAT WILL HAPPEN TO TOTAL REVENUES?

INCOME ELASTICITY

If EQX,M > 0, then X is a normal good.

If EQX,M < 0, then X is a inferior good.

M

QE

dX

MQX

%

%,

If EQX,M > 1, then X is a luxury good.

USES OF ELASTICITIES

• Pricing strategies• Managing cash flows • Impact of changes in competitors’ prices• Impact of economic booms and recessions• Impact of advertising campaigns• Analyzing a combination of changes in the

marketplace

GAINS FROM TRADE• Consumer surplus - the difference

between what consumers are willing to pay and what they actually pay– measured as the area below the demand

curve and above the price

• Producer surplus - the difference between the price received and willingness to produce– measured as the area above the supply

curve and below the price

CONSUMER AND PRODUCER SURPLUS

Q

P

Supply

Demand

10

$10

$20

Incremental productionCosts (Triangle C)

Producer surplus(Triangle B)

Consumer surplus(Triangle A)

C

B

A

GOVERNMENT INTERVENTION

• Consumer and producer surplus can be used to examine the effects of government intervention on gains from trade

• Price caps limit the maximum price that can be charged

• Price floors are a legally set minimum price at which goods can be traded

GOVERNMENT PRICE CAP ON GASOLINE

$/Gallon

Lost gainsfrom trade

Supply

Excess demand(shortage) for gasoline

$3.00 price cap

Demand

$3.00

$4.00B

A

QQS QD

MINIMUM WAGE LAWS

$6.00

$7.25

Unemployment(excess supplyof labor)

Labor Supply

Minimum Wage

Lost gains fromtrade

Labor Demand

Quantity of labor

QS QDQ*

A

B

DECISION MAKING UNDER UNCERTAINTY

• Since nothing is guaranteed, we make decisions based on the expected value of the outcome:

• The amount of risk is measured by the standard deviation of the value of the outcomes:

• People choose a balance between expected value (return) and risk

iiVpVE )(

)( VVpSD iiV

RISK VERSUS RETURN

THE TELEVISION GAME: DEAL OR NO DEAL

• Rules of the game: 26 briefcases; dollar amounts from $1 to $1,000,000, all shown on a large Board

• Choose one, then eliminate all the others

• Offers are made along the way• Example: 3 briefcases remaining at

$10, $10,000; and $1 million. Offer: $300,000. Deal or No Deal?