Transcript cross price elasticity

DEMAND
FOURTH LECTURE
February 14, 2012
William R. Eadington, Ph.D.
Professor of Economics, College of Business
Director, Institute for the Study of Gambling and Commercial Gaming
University of Nevada, Reno
www.unr.edu/gaming
PROBLEM OF THE WEEK
REQUEST: 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 FUNCTION
A 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 VALUES
Suppose the variables have the
following values:
P = $30
Ps = $50
Pr = $40
I = $50,000
How many tickets will the Theater
Company sell?
THE DEMAND CURVE
Substitute 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
$
$
Ticket price (in dollars)
Income = 51,000
61
60
60
Income = $50,000
D1
D
D0
Q
Q
400
Quantity of Theater tickets
406.0
Quantity of Theater tickets
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:
 %Q 
  

 %P 
CALCULATING ELASTICITY
ARC 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 ELASTICITY
ARC PRICE ELASTICITY
Note definition as a ratio of percentage changes, & causeeffect where price influences quantity demanded
 Q 
 (Q1  Q2 ) 
 Q 


 (Q  Q ) 
2
2
   1

  
 P 
 P 
 ( P1  P2 ) 
 ( P1  P2 ) 


2
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
$
$
Price (in dollars)
Price (in dollars)
D
η=0
D
η=∞
Q
Quantity
Perfectly Inelastic
Q
Quantity
Perfectly Elastic
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
Ticket price (in dollars)
$
60
Elastic demand (n > 1)
n=1
30
Inelastic demand (n < 1)
Q
Total revenue (in dollars)
$
6,000
200
Quantity of Theater tickets
Q
OTHER DEMAND INFLUENCES
• Complements versus substitutes
– Cross price elasticity of demand
Q x
Qx1  Qx 2
 xy 
Py
Py1  Py 2
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
Q x
Qx1  Qx 2
I 
I
I1  I 2
or ȠI = dQx/dI*I/Qx
• 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)
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
EQX , PY
%QX

%PY
d
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
PREDICTING REVENUE
CHANGES
FROM TWO PRODUCTS
Suppose that a firm sells two related
goods. If the price of X changes, then total
revenue will change by:
 


R  RX 1  EQX , PX  RY EQY , PX  %PX
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
EQX , M
%QX

%M
d
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is a inferior good.
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
P
$20
Consumer surplus
(Triangle A)
Supply
A
Producer surplus
(Triangle B)
$10
B
Incremental production
Costs (Triangle C)
C
Demand
10
Q
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
Supply
Lost gains
from trade
A
$4.00
B
Excess demand
(shortage) for gasoline
$3.00 price cap
$3.00
Demand
QS
QD
Q
MINIMUM WAGE LAWS
Unemployment
(excess supply
of labor)
Labor Supply
Minimum Wage
$7.25
A
$6.00
Lost gains from
trade
B
Labor Demand
QS
Q*
QD
Quantity of labor
DECISION MAKING UNDER
UNCERTAINTY
• Since nothing is guaranteed, we make
decisions based on the expected value of the
outcome:
E (V )   piVi
• The amount of risk is measured by the standard
deviation of the value of the outcomes:
SDV   pi (Vi V )
• People choose a balance between expected
value (return) and risk
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?