The Optimal Mark-Up and Price Discrimination Outline The optimal mark-up over cost What is price...
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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 demand
The Optimal Mark-Up and Price Discrimination Outline The optimal mark-up over cost What is price discrimination? Examples of price discrimination When
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 demand
Slide 3
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.
Slide 4
The trade-off between price and profit The firms 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)?
Slide 5
It depends on elasticity (E P ) We can show that the optimal
mark-up over MC is inversely proportional to elasticity of demand
(E P )
Slide 6
The markup rule The size of the firms 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]
Students at Sherwood High in Sandy Springs, Maryland talk about
things that bother them
Slide 9
Slide 10
What is price discrimination? Price discrimination is the
practice of selling the same product to different buyers (or groups
of buyers) at different prices.
Slide 11
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 buyerse.g., magazine
subscriptions. Theater ticket pricing
Slide 12
When is price discrimination feasible? 1.The seller must be
capable of identifying market segments that differ based on
willingness to pay, or elasticity of demand. 2.The seller must be
capable of enforcing the different prices charged to different
market segmentsthat is, the seller must be able to prevent
arbitrage.
Slide 13
1 st 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.
Slide 14
Auctions Auctions are designed to force buyers nearer to their
reservations prices.
Slide 15
3 rd degree price discrimination This is the practice of
charging different prices in different market segments
Slide 16
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 buyers
Slide 17
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 segment
Slide 18
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:
Slide 19
30,000 60 0 Quantity Price 25,000 Home Foreign 35.7 The demand
for cars
Slide 20
30,000 60 0 Quantity (000s) Price DHDH 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 H
Slide 21
18,000 60 0 Quantity (000s) Price 25,000 DFDF 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 F
Slide 22
Summary Notice that the price is higher in the Home market
where the manufacturer faces a less elastic demand curve
Slide 23
Interdependent demand Consider a microbrewery that brews lager
and pilsner. The price of the lager will likely affect the demand
for pilsner.
Slide 24
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
Slide 25
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:
Slide 26
Numerical example Let MC A = $80; MC B = $40 P A = 280 2Q A P B
= 180 Q B 2Q A Notice that increased sales of A adversely affect
sales of B, but not vice versa.
Slide 27
TR = R A + R B = (280Q A 2Q A 2 ) + (180Q B Q B 2 -2Q A Q B )
Thus we have: Therefore: MTR A = 280 4Q A 2Q B And: MTR B = 180 2Q
B 2Q A So set MTR A = MC A and MTR B = MC B and solve for Q A and Q
B 280 4Q A 2Q B = 80 180 2Q B 2Q A = 40 The result is a linear
equation system with two equations and two unknowns
Slide 28
The solutions Solving the equation system yields: Q A = 30 and
Q B = 40 Substituting into the price (or inverse demand) equations
yields: P A = $220 and P B = $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.
Slide 29
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.
Slide 30
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.
Slide 31
Phones and fax machines have zero autarchy value; whereas
computers do have some.
Slide 32
The development of bandwidth has greatly increased the
synchronization value of PCs.
Slide 33
Path Dependence and Lock-In Effects Network 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.
Slide 34
QWERTY: Example of an Unfortunate Lock-in effect RTY