Chapter 12: more on monopoly
pricing
1
Motivation for price discrimination:
2
Types of price discrimination
„
„
„
First-degree: the firm is aware of each
individual buyer’s demand curve
==> relate to consumer’s surplus!
Second-degree: the firm charges a different
price, depending on the quantity each buyer
purchases
Third-degree: the firm breaks buyers into
groups based upon their price elasticity of
demand (what we discussed before)
3
First degree price discrimination
4
Price Discrimination:
second degree
• Demand for an
individual customer (all
customers are alike)
• What condition must
be fulfilled to make this
price discrimination?
5
Can you set different prices for
different groups of customers?
„
„
„
„
Ability to identify and segregate the groups
Demand elasticity is different
No possibility for arbitrage (resell the good to
1
the other group)
1+
η2
p1
Optimal price is:
=
p2
„
Because
MR1 = P1 (1 +
1
η1
1+
1
η1
) = P2 (1 +
1
η2
) = MR 2
6
Examples of third-degree price
discrimination
„
„
„
„
Students, senior citizens for travel, ...
„ (railway half-price identity card is also an
example of two-part tarifs – see below)
Airlines for business and tourists
Seasonal price discrimination
Prices for drugs, books, re-import not possible
because of regulation
7
Third Degree Price
Discrimination
8
Coupons as an example
of price discrimination
„
„
„
Esp. in U.S. firms distribute coupons (by mail or in
newspapers) which give a rebate for the product
Austria: Pizzamann, (Treuemarken),...
Why is it better to give out coupons as compared to a
general price cut??
„
„
„
Coupon users are more price-sensitive
Only a small proportion of coupon receivers actually use them
to claim the rebate
Coupon reminds the customer each time that she gets lower
price
9
Table 10.14 Repeat Buyers
All purchasers
Coupon users
Purchasers not using coupons
Chock Full
o’ Nuts
Maxwell
House
Folgers
Hills
Brothers
62
49
63
62
55
70
63
56
65
42
14
44
10
How to set an optimal coupon?
„
„
„
Price elasticities of rich (R) and poor (P)
clients: ηR = −2 and ηP = −5
P regular price, P-X price with coupon
MC=2
P[1 +
„
„
1
ηR
] = (P − X )[1 +
1
ηP
] = MC
P=4, X=1.5
Suppose, you get the coupon by mail, how
come, that not everybody is redeeming it?
11
Problem 5
Ann McCutcheon is hired as a consultant to a firm producing ball
bearings. The firm sells in two distinct markets, one of which is
completely sealed off from the other. The demand curve for the
firm’s output in the one market is P1=160 – 8Q1, where P1 is the
price of the product, and Q1 is the amount sold in the first
market. The demand curve for the firm’s product in the second
market is P2=80 – 2Q2, where P2 and Q2 are price and quantity
sold in the second market. The firm’s marginal cost curve is
5 + Q, where Q is the firm’s entire output. The firm asks Ann
McCutcheon to suggest what its pricing policy should be.
a) How many units of output should the firm sell in the second
market?
b) How many units of output should it sell in the first market?
c) What price should it establish in each market?
12
Solution Problem 5
P1 = 160 − 8Q1 , P2 = 80 − 2Q 2 , MC = 5 + Q = 5 + (Q1 + Q 2 )
MR1 = 160 − 16Q1 , MR 2 = 80 − 4Q 2
Setting marginal revenue in each market equal to marginal cost:
1 6 0 − 1 6 Q 1 = 5 + (Q 1 + Q 2 ) an d
8 0 − 4 Q 2 = 5 + (Q 1 + Q 2 )
155 − 17 Q 1 = Q 2 and 75 − Q 1 = 5Q 2
⇒ Q 1 = 8 .3 3 a n d Q 2 = 1 3 .3 3
P1 = 1 6 0 − 8 (8 .3 3) = 9 3 .3 3
P
2
= 8 0 − 2 (1 3 .3 3 ) = 5 3 .3 3
13
Tying
„
„
„
Occurs when a firm sells a product, the use of which
requires the consumption of a complementary product
The consumer is required to buy the complementary
product from the firm selling the product itself
Examples: Toner for computer printer, spare parts for
cars,
„
„
„
„
„
Price differently for consumer who use the good more/less
intensively (in sum those using more often pay more)
Brand name is protected
Insurance that product works properly
First item bought is more visible (price)
Build network effects, consumers have switching costs
14
Tying in the printer market
„
E.g. HP made half of its revenues with
cartridges in 2002
„
„
„
Possiblity to refill old cartridges
New chip in cartridges made it impossible
to refill
New EU law prohibiting this
15
Two-part tariffs
„
„
Monopoly is inefficient, sum of consumer and
producer surplus could be increased by producing
more
Optimal output should be where p=MC, but then
consumers get the surplus
„
„
„
So what should a “good” monopolist do ???
Set p=MC, then try to extract consumer surplus by
other means, say, a one time fee (only correct, if all
consumers are alike – otherwise you lose some)
Examples: telephone, golf clubs, Disneyland
16
17
Example: Telephone pricing
„
„
„
Telephone company is monopolist
Demand: P = 100-0.5Q
Marginal cost: MC = 10 (cents/minute)
„
„
„
„
Optimal price for monopolist? Profit?
Make also a graph
Optimal price for a two-part tariff: charge a fee
(Grundgebühr) and a price per minute
Profit?
18
Solution: Telephone Pricing
„
„
„
P = 100 – 0.5 Q
MC should equal MR:
TR = 100Q – 0.5 Q2
MR = 100 – Q
MR = MC =>
100 – Q = 10 => Q=90
P = 100 – 0.5 Q =>
P = 55
Π = 90* (55-10)= 4050
TWO PART TARIFF:
Q = 180
Price/Minute = 10
Fee= 90*180/2 = 8100
Profit = 8100
Price
100
55
10
MC = 10
90 100
200
Quantity
19
20
XXXXXXXXXX Strong demand
XXXXXXXXXX Weak demand
21
Two demand types:
„
Set use fee at MC and entry fee equal to
consumer surplus of strong type (A-F)
„
„
„
If (A+B+C+D+E+F) > (2A+2C+D+E)
Only the strong buys the good
Set use fee at P*>MC and entry fee equal to
consumer surplus of weak (A)
„
„
If (A+B+C+D+E+F) < (2A+2C+D+E)
All customers buy
22
Assume one strong and one weak demander
(otherwise weighting necessary)
„
4 Options
„
„
„
„
Charge high entry fee, such that only
strong demander buys
Charge low entry and MC price, such that
both buy
Charge low entry and price above MC
Charge different entry fee for strong and
weak demand
„
Example clubs or credit cards
23
Pricing strategies for monopoly:
Bundling
„
„
„
„
„
„
„
Consumer valuation of the product not directly observed (see price discrimination) but the firm would like to know willingness to pay of each person
Two (several) segments of the market exist
Valuation of the product differs and
Valuation by the two segments negatively correlated
Marginal cost of producing is low
Goods are on sale as a bundle
Examples:
„
„
„
„
„
restaurant menus,
TV channels,
quantity discount
CD as compared to Single
Sports tickets
24
Pure vs. mixed bundling
„
„
Consumers have a reservation price r; i.e. their willingness to pay for
the product
Firm chooses prices p to set
________________
„
Pure bundling: only bundle is on sale
„
„
Price can be calculated by looking at reservation price of costumers for the
bundle
Mixed bundling: both pure bundle as well as separate goods are on
sale
„
Prices difficult to obtain, either by experimentation (trial and error) or using
a computer program (checking all possible price-combinations)
25
26
27
Example
28
29
30
31
32
33
Mixed or pure or no bundling?
„
Above example: pure bundling best
„
Pricing goals for bundling:
„
„
„
Extraction: extract rent from consumers
Exclusion: do not sell a good to a consumer who values it
less than production cost (in case of bundle)
Inclusion: Sell to all those, who have a reservation price
higher than marginal cost
In general not all goals can be reached
34
When is bundling useful ?
„
If the segments of the market differ markedly in their evaluation of the products
„
If the benefits of the products are negatively correlated among the segments of
the market
„
„
(but there are cases, where it is possible even in case of positive correlation).
If marginal cost of producing is low
„
(see example in book: high marginal costs for producing makes pure bundle less
profitable as separate pricing, Tables 12.11, 12.10)
„
Mixed bundling weakly dominates pure bundling)
„
For pure bundling price strategy simple: take sum of reservation prices of
customers
„
For mixed bundling difficult
35
Some rules
„
If goods‘ reservation prices positively correlated,
maybe mixed bundling
„
If goods perfectly negatively correlated, then pure
bundling is best
„
If marginal cost of producing is high (exceeding its
reservation price), then no production best
„
If reservation prices negatively correlated
„
„
The higher marginal cost, the better is mixed bundling,
If MC increase further, separate pricing best.
36
Peak-load pricing
„
Demand for goods and services may shift over time
„
During the day
„
„
During the week
„
„
Vacation, leisure activities, tourisme
During season
„
„
Electricity, gas, transport, telephone
Holidays for school kids, weather
Plant capacity does not change over time:
„
„
Number of beds in hotel
Energy production
37
Peaks and troughs
„
„
Marginal revenue curves differ over
time
Marginal cost curves differ over time
„
„
Working near capacity in high season
Different form 3rd degree price
discrimination
38
39
„
Price discrimination:
„
„
Marginal cost = f(Q1 + Q2)
Pricing solution:
„
„
MR1(Q1) = MR2(Q2) = MC(Q1+Q2)
Peak-load:
„
„
Marginal costs: demanders use same
capacity but at different times
Pricing:
„
„
MR1(Q1) = MC1(Q1) and
MR2(Q2) = MC2(Q2)
40
Transfer Pricing
„
„
„
„
Occurs in large firms when one division sells
product to another division
The transfer price is the price at which the
transfer of product takes place within a firm
If a market exists for the intermediate
product, transfer price should be market price
If no market exists --- transfer price should
be marginal cost of intermediate product
division
41
Transfer Pricing
(given no external market)
42
Transfer Pricing
(given a p. c. external market)
43
Problem 4
The Locust Corporation is composed of a marketing division and a
production division. The marginal cost of producing a unit of the
firm’s product is $10 per unit, and the marginal cost of marketing it
is $4 per unit. The demand curve for the product is
P = 100 – 0.01Q.
There is no external market for the good made by the production
division.
a) What is the firm’s optimal output?
b) What price should the firm charge?
c) How much should the production division charge the marketing
division for each unit of the product?
44
Solution Problem 4
Setting marginal revenue equal to marginal cost:
MR = 100 – 0.02Q = 10+4 = MC
=> 86 = 0.02Q => Q = 4,300.
P = 100 – 0.01(4,300) = $57
The transfer price should be set at the selling
division’s marginal cost, $10, in the case of the
producing division.
45
Problem 10
The Breen Company makes a scientific instrument used in chemical
laboratories. The price of the instrument is set at 180 percent of average
variable cost. The firm’s marketing manager receives a telephone call from a
large chemical company offering to buy six of the instruments at $5,000
each. To meet the terms of the offer, Breen would have to manufacture the
six instruments in the next three months, which would mean that Breen
would lose orders for four instruments because of its limited production
capacity. If fulfilled, these orders would be at the regular price of $7,200 per
instrument. (Because the chemical firm was ordering six of the instruments,
it wanted a reduced price of $5,000.)
a) Should the firm accept the offer from the chemical company? Why or why
not?
b) If not, what is the minimum price it should ask the chemical company to
pay?
c) If you were a consultant to Breen’s chief executive officer, would you
advise her to maintain or abandon the firm’s cost-plus pricing policy? Why?
46
Solution Problem 10
a)
b)
c)
The firm should not accept the special order since the
order will only contribute $6,000 toward fixed costs
and profit, while the order displaces regular business
which would contribute $12,800.
In order to contribute the same to profit as the
regular business, it would displace, the special order
would need to be priced at $6,133.33 per instrument.
We don’t have enough information to determine
whether the current mark-up is profit maximizing.
47
Problem 6
The Morrison Company produces tennis rackets, the marginal cost
of a racket being $20. Since there are many substitutes for the
firm’s rackets, the price elasticity of demand equals about 2. In the
relevant range of output, average variable cost is very close to
marginal cost.
a) The president of the Morrison Company feels that cost-plus
pricing is appropriate for his firm. He marks up average variable
cost by 100 percent to get price. Comment on this procedure.
b) Because of heightened competition, the price elasticity of
demand for the firm’s rackets increase to 3. The president
continues to use the same cost-plus pricing formula as before.
Comment on its adequacy.
48
Solution Problem 6
a) The profit-maximizing markup from marginal
cost is 1/(1+1/ŋ)*100, which if the elasticity is
(-)2 equals 100 percent. If marginal cost equals
average variable cost, then the 100 percent
markup from average variable cost is profit
maximizing.
b) If the elasticity changes to (-)3, then the
profit-maximizing markup is 50 percent.
49