Transcript Slide 1

Non-trivial pricing strategies
for firms with market power
So far, we’ve been discussing cases when every unit of
firm’s output was priced the same.
Now, it’s time to look at more interesting cases.
Welfare measures
Every consumer has some subjective valuation for
each unit of the good, called marginal value, or
marginal “utility”.
Think of it as the highest price she would pay, or
what the good is “worth” to her.
Consumer surplus (CS) – equals the value (“utility”)
a consumer gets from a good but doesn’t have to
pay for.
CS from an individual purchase:
(price)
CS = MV – P
(marginal value)
P
CS
Market price
Demand, derived
from a schedule of
marginal values
Q
Total market CS is represented by the area under the
demand curve and above the price.
By analogy, producer surplus (PS) is the difference
between the actual price and the minimum price at
which the producer would agree to sell the good (the
latter usually equals the marginal cost, MC).
PS = P – MC
Note the concept of PS is somewhat similar to but not
the same as profit!
P
Supply, derived
from a marginal
cost schedule
Market price
PS
Q
Total producer surplus in the market is represented
by the area below the market price level and above
the supply curve.
In a free market…
$
… the sum of consumer
and producer surpluses is
maximized
S
CS
PS
D
Q
Every opportunity to make someone better off
through exchange of goods is taken advantage of.
For a monopoly…
P
60
CS
35
Profit
DWL
MC
10
D
10
MR
Q
20
All pricing strategies to be discussed below are designed to
increase the chunk of the market surplus that goes to the
producer, thus further increasing its profit.
1. Price discrimination (3rd degree)
Price discrimination is a general name for the practice
of charging different consumers or groups of
consumers different prices for the same product.
Consider a town with 2000 college students and 1000
retirees.
Students want to see a movie as long as the price
doesn’t exceed $8. Elderly people are interested only if
the price is $5 or below.
If you set the ticket price at $8, the revenue is
TR = P * Q = 8 * 2000 = $16,000
If you lower the price to $5, the revenue is
TR = P * Q = 5 * (2000 +1000 ) = $15,000
If you frame it as a discount for seniors, your revenue is
TR = 8 * 2000 + 5 * 1000 = $21,000
An important condition is that students are ineligible for the
discount.
Such practice of splitting the market into two or more
groups and charging each a separate price – is called
third-degree price discrimination.
Conditions necessary for its success:
• Presence of at least two groups with known demand
differences;
• The ability of the firm to distinguish among groups;
The size of a group does not matter!
All that matters is elasticity of demand by each group.
The group with the more elastic demand
gets charged a lower price, and vice versa
•Certain degree of market power to the firm;
•The possibility of product resale has to be eliminated.
Other examples of 3rd degree price discrimination:
• Bus fare
• Museum admissions
• Airfare contingent on Saturday night stay
• Store coupons
2. Perfect (first-degree) price discrimination
The hypothetical case when each consumer is charged
the maximum price she is willing to pay (her subjective
value, that is).
It is rarely observed in real-world situations due to the
difficulty of determining each consumer’s Marginal
Value.
Still, we can think of examples when a seller tries to
achieve this.
The chances for success of such practice are higher
when the seller has only a few customers. Also,
consider person-to-person sales.
First-degree price
discrimination
$
- For every customer,
(individual) price gets
pushed all the way up
to his/her MU;
MC
Individual
prices
P
Q
First-degree price
discrimination
$
- For every customer,
(individual) price gets
pushed all the way up
to his/her MU;
MC - Producer gets the
ENTIRE market welfare
P
Q
3. Volume discounts (a.k.a. 2nd degree PD)
Also a form of price discrimination, since the buyers
self-select themselves into high-volume and lowvolume buyers, and each group pays a different perunit price.
Suppose you are a seller who has certain stock of
shirts you need to sell. For simplicity, let’s say your
goal is to maximize revenue.
Every day, a hundred customers visit your store.
Let’s start with the unrealistic case when
• All customers are identical;
• You know everyone’s valuation for successive shirts:
Shirt #
1
2
3
4
Marginal
Value, $
15
10
6
2
You need to decide what price tag to put on the shirt rack.
If charging a flat rate for each shirt:
P = $15,
P = $10,
P = $6,
P = $2,
TR = 15*100 = $1,500
TR = 10*200 = $2,000
TR = 6*300 = $1,800
TR = 2*400 = $800
A better idea:
Recognize the fact that each successive shirt is valued
less than the previous one and price them accordingly.
For example:
P = $15, buy one, get second for 40% off
TR = (15 + 9)*100 = $2,400 – better than any of the above cases
Of course
• People have different tastes, therefore different utility
schedules.
• You never know what those schedules are.
But stores do know that the willingness to pay falls with
every successive shirt.
Therefore, the above example explains how some stores
in some cases may benefit from running sales of the
“Buy one, get second at X% off” type.
Other examples of volume discounts:
• declining rates in parking garages,
• pricing by (some) electric companies,
• frequent flyer programs.
4. Bundling, or tie-in sales
The table below shows how Bill and Linda value two
rides at an amusement park.
Ride
Mamba
Timberwolf
$5
$3
$1
$2
Person
Bill
Linda
Suppose you, the manager of the amusement park, first
decide to charge a separate price for each ride.
What is the best price to charge?
For Mamba:
P = $5, TR = 5*1 = $5
P = $3, TR = 3*2 = $6
For Timberwolf:
P = $2, TR = 2*1 = $2
P = $1, TR = 1*2 = $2
Total revenue from Linda and Bill = 6 + 2 = $8
A better idea: sell the two rides together, as a “bundle”.
Ride
Mamba
Timberwolf
M+T
$5
$3
$1
$2
$6
$5
Person
Bill
Linda
Best price for the bundle:
P = $5, TR = 5 * 2 = $10 - better than under “regular” pricing
This strategy works best when the valuations of different
consumers for different goods or services are negatively
correlated.
Other examples – Newspapers, Cable TV.
5. Block pricing
P
Demand of an
individual consumer
2
1.5
1.25
1
0.5
MC
D
3
MR
6
If selling individually:
The best price is $1.25
Q
5. Block pricing
Demand of an
individual consumer
2
1.5
1.25
1
0.5
MC
D
3
If selling individually:
Profit =
MR
6
Q
5. Block pricing
Demand of an
individual consumer
2
1.5
1.25
1
0.5
MC
D
3
MR
6
If selling individually:
Profit = (1.25 – 0.50)*3 = $2.25
Q
5. Block pricing
Demand of an
individual consumer
2
1.5
1.25
1
0.5
MC
D
3
MR
6
Each consumer values units up to #6 above MC
Q
5. Block pricing
Demand of an
individual consumer
2
1.5
1.25
1
0.5
MC
D
3
MR
6
What if we sell this product ONLY as a six-pack?
Q
Pricing the 6-pack:
A customer would pay:
Up to $1.75 for the first unit;
Up to $1.50 for the second;
Up to $1.25 for the third;
Up to $1.00 for the fourth;
Up to $0.75 for the fifth;
Up to $0.50 for the sixth.
(units after #6 are not worth producing)
Total value consumer places on a six-pack is $6.75.
That is the price we should charge.
5. Block pricing
2
1.5
1.25
1
0.5
MC
D
3
MR
Q
6
Profit under block pricing and under regular pricing
6. Two-part pricing
P
Demand of an
individual consumer
60
35
MC
10
D
10
MR
Q
20
Same
The
profit-maximizing
price + one-timepoint
fee equal
is P =to
$35,
consumer’s
Q = 10, ΠCS
= $250
from
purchase
6. Two-part pricing
P
Demand of an
individual consumer
60
35
MC
10
D
10
MR
Q
20
Same price + one-time fee equal to consumer’s CS from
purchase
6. Two-part pricing
P
Demand of an
individual consumer
60
35
MC
10
D
10
MR
Q
20
An even better idea: lower the per-unit price and keep
charging the fee (which will now be larger)
6. Two-part pricing
P
Demand of an
individual consumer
60
35
MC
10
D
10
MR
Q
20
An even better idea: lower the per-unit price (P=MC=$10)
and keep charging the fee (which will now be larger)
The i-Phone case
Prices are falling over time – WHY?
Possible explanations:
- Obsolescence – Better products developed – demand drops
- More firms enter – stronger competition – profit margin drops
- More efficient production technologies developed – production
costs drop – price drops
- “Intertemporal price discrimination”, or separating customers
across time, based on their patience factor
$
Demand from all the consumers
who will ever want your product
MC
Q
You could satisfy them all at once…
$
Demand from all the consumers
who will ever want your product
MC
Q
$
July
June
May
April
Demand from all the consumers
who will ever want your product
MC
Q
… or, you could serve them one group at a time,
starting with those who value the good the most
$
Demand from all the consumers
who will ever want your product
MC
Q