Outline The optimal markup over cost What is price discrimination Examples of price discrimination When is price discrimination feasible First second and third degree price discrimination Multinational pricing of autos ID: 660215
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Slide1
The Optimal Mark-Up
and Price Discrimination
Outline
The optimal mark-up over cost
What is price discrimination?
Examples of price discrimination
When is price discrimination feasible?
First, second, and third degree price discrimination
Multinational pricing of autos
Interdependent demandSlide2
Price as the decision variable
Thus far we have assumed that quantity was the relevant decision-variable.
In reality, most firms establish a price for their product and then try to satisfy demand for their product at that price.
The price established by management is generally based on costs plus a mark-up.Slide3
The trade-off between price and profit
The firm’s contribution can be written as:
Contribution = (P – MC)Q
We assume that marginal cost (MC) is constant.
Issue: How far above MC should the firm raise P to maximize its contribution (and hence profits)?Slide4
It depends on elasticity (EP)
We can show that the optimal mark-up over MC is inversely proportional to elasticity of demand (E
P
)Slide5
The markup rule
The size of the firm’s mark-up (above marginal cost expressed as a percentage of price) depends inversely on the price elasticity of demand for a good or service.
That is, the optimal markup is given by:
[3.12]
Rearranging [3.1] we obtain:
[3.13]Slide6
Elasticities and optimal prices
Elasticity
MC
Price
-1.5
3.0
100
300
-2.0
2.0
100
200
-3.0
1.5
100
150
-5.0
1.25
100
125
-11.0
1.1
100
110-1.0100100Slide7
Students at Sherwood High in Sandy Springs, Maryland talk about things that bother themSlide8Slide9
What is price discrimination?
Price discrimination is the practice of selling the same product to different buyers (or groups of buyers) at different prices.Slide10
Examples of price discrimination
Airlines charge full fares to business travelers, whereas they offer discount fares to vacationers.
“Sizing up their income” pricing by dentists, plumbers, and auto mechanics.
Publishers of academic journals charge higher prices for library as compared to individual subscriptions.
Senior citizen discounts.
Discounts for new buyers—e.g., magazine subscriptions.
Theater ticket pricingSlide11
When is price discrimination feasible?
The seller must be capable of identifying market segments that differ based on willingness to pay, or elasticity of demand.
The seller must be capable of “enforcing” the different prices charged to different market segments—that is, the seller must be able to prevent “arbitrage.”Slide12
1st degree price discrimination
Sometimes called “perfect” price discrimination, the seller charges each buyer their “reservation price” for every unit purchased.
Reservation price
is the maximum price a buyer is willing to pay rather than go without the last unit of the good. Slide13
Auctions
Auctions are designed to force buyers nearer to their reservations prices.Slide14
3rd degree price discrimination
This is the practice of charging different prices in different market segmentsSlide15
Examples of market “segments”
Business travelers versus tourists.
Kids versus adults
Those covered by health insurance and those not covered.
Senior citizens versus everyone else.
Mercedes Benz owners versus Chevrolet owners.
Domestic versus foreign buyersSlide16
Multinational pricing of autos
The problem for a car manufacturer is to establish profit-maximizing prices on cars sold domestically and in the foreign market segmentSlide17
The Demand Functions
The inverse demand equation for the home (H) market is given by:
Where P
H
is the price charge in the home market and H is the quantity sold in the home market
The inverse demand equation for the foreign (F) market is given by:Slide18
30,000
60
0
Quantity
Price
25,000
Home
Foreign
35.7
The demand for carsSlide19
30,000
60
0
Quantity (000s)
Price
D
H
30
Profit maximization in
the Home segment
MR
H
MC
H
10,000
20,000
20
To maximize profits in the Home segment, set MR
H
= MC
HSlide20
18,000
60
0
Quantity (000s)
Price
25,000
D
F
35.7
Profit-maximization in
the foreign market segment
MR
F
MC
F
11,000
10
To maximize profits in the Foreign segment, set MR
F
= MC
FSlide21
Summary
Notice that the price is higher in the Home market where the manufacturer faces a less elastic demand curveSlide22
Interdependent demand
Consider a microbrewery that brews lager and pilsner. The price of the lager will likely affect the demand for pilsner.Slide23
Example
Let A denote lager and B is pilsner. Let the profit function be given by:
Note:
We assume that there are no interdependencies or complementarities in production Slide24
Determining the optimal quantity
Produce up to the point in which the extra total revenue (MTR) from the sale of product A is equal to the marginal cost of A, and similarly for B.
That is:
And:Slide25
Numerical example
Let MC
A
= $80; MC
B
= $40
P
A = 280 – 2QAPB = 180 – QB – 2QA
Notice that increased sales of A adversely affect sales of B, but not vice versa.Slide26
TR = R
A
+ R
B
= (280Q
A
– 2Q
A2) + (180QB – QB2-2QAQB)
Thus we have:
Therefore:
MTR
A
= 280 – 4Q
A
– 2Q
B
And:
MTR
B
= 180 – 2Q
B
– 2Q
A
So set MTRA = MCA and MTRB = MCB and solve for QA and QB280 – 4QA – 2QB = 80180 – 2QB – 2QA = 40The result is a linear equation system with two equations and two unknownsSlide27
The solutions
Solving the equation system yields:
Q
A
= 30 and Q
B
= 40
Substituting into the price (or inverse demand) equations yields:PA = $220 and PB = $80
Contrast this outcome to the case where the brewery ignored the cross effect of A and B and simply tried to maximize profits from A.Slide28
Information Goods
Examples: Databases, video games, word processing applications, sheet music, news articles.
Properties of information goods:
High fixed costs
Zero or negligible marginal cost.
Network externalities.
Information is costly to produce but cheap (often costless) to reproduce.Slide29
Network Effects
Network externality
is defined as a change in the benefit, or surplus, that an agent derives from a good when the number of other agents consuming the same kind of good changes.
Autarky value:
Value generated by the product even if there are no other users.
Synchronization value: additional value derived from being able to interact with other users of the product, and it is this latter value that is the essence of network effects.Slide30
Phones and fax machines have zero autarchy value; whereas computers do have some.Slide31
The development of bandwidth has greatly increased the synchronization value of PCs.Slide32
Path Dependence and Lock-In EffectsNetwork industries may exhibit path dependence, so that the behavior of early adopters may have a disproportionate influence on the equilibrium outcome.
Lock-in may occur on the “wrong” technology because if, for whatever reason, the wrong technology is chosen, it may be difficult to achieve the coordinated
movement of large numbers of users required for the “right” technology to become the standard. Slide33
QWERTY: Example of an Unfortunate Lock-in effect
R
T
Y