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Pricing
The fundamental pricing rule
Price discrimination
Dynamic limit pricing
The fundamental pricing rule
Produce up to the point where MR=MC,
where MR = P[1-(1/|e|)]
For a price taker:
MR = P[1-(1/|e|)] = P, hence P=MC
For a price searcher MR = MC implies
P = MC/[1 - (1/|e|)], hence (P- MC)/P = 1/|e|
And P/(P- MC) = |e|
The fundamental pricing rule
P/(P- MC) = |e|
Elasticity
Marginal
Revenue
Price
|1.5|
|2|
|3|
|4|
1
1
1
1
3
2
1.5
1.33
(P-MC)/P = 1/|e|
The higher the elasticity, the lower the
markup of price over marginal cost.
The lower the elasticity, the higher
the markup.
(Elasticity tends to be higher when
there are many competitors and
substitutes.)
QUESTION
True or false: the
optimal price will
always be on the
elastic portion of
the residual
demand curve?
QUESTION
True or false: the
optimal price will
always be on the
elastic portion of
the residual
demand curve?
True.
If |e| is less than 1,
raising price will
both increase
revenue, and
decrease costs.
QUESTION
When will the
optimal price
be set where
the |e| of the
residual
demand curve
is = 1
QUESTION
When will the
optimal price
be set where
the |e| of the
residual
demand curve
is = 1
If |e| is 1, MC
must equal
zero.
P/[P-MC] = |e|
P/[P- 0] = 1
QUESTION: Given a linear demand curve that
intersects the Y axis at a price of $10, and a
marginal cost of $2 per unit, what is the
optimal price?
ANSWER: P = $6. 1/|e| = (Pmax - P)/P = ($10 - P)/P.
(P - MC)/P = (P-2)/P. Equating the right side of the
equation to the left, ($10-P)/P = (P - $2)/P or ($10 - P)
= (P - $2).
Price discrimination
Definition: A single organization price
discriminates when it charges different
prices to different consumers that are
not proportional to differences in
marginal cost, i.e., when for two
different consumers (1 & 2), p1/MC1 ≠
p2/MC2 (of course, MR1/MC1 =
MR2/MC2).
Necessary conditions
 At least two consumer groups exist with
different elasticities, i.e., different demand
curves.
 The organization can identify consumers in
each group, and set prices differently for
consumers in the two groups.
• The organization must be able to prevent
consumers in one group from selling to
consumers in the other (no arbitrage).
Price discrimination: Note
P1 is 3 times MC; P2 is
twice MC. Solving for
|e|: (3 - 1)/3 = 1/|e| =
1.5; (2 - 1)/2 = |e| = 2.
The more inelastic the
demand, the higher the
markup: inverse
elasticity pricing rule
or, where subject to a
revenue constraint,
Ramsey optimal
pricing.
Examples of price discrimination
 Senior citizen and children's' discounts offer
lower prices to those with more elastic
demands for movies.
 Universities offer lower prices in the form of
financial aid ("need" based aid) to those with
higher elasticities of demand (note: it is easier
to discriminate where services are concerned
than where goods are concerned and where
consumables are concerned than durables).
 Tying supplies to use of a durable piece of
equipment, sometimes called Barbie Doll
Marketing: give away the dolls but charge a
lot for the dresses.
One of the most effective price-discrimination
mechanisms is the multi-part tariff.
Multi-part tariffs decompose product/services to
their fundamental attributes and charge users
for their actual consumption of each.
The best example of a multi-part tariff is your
phone bill.
Multi-part Ramsey-optimal tariffs are also
commonly used in internal transfer pricing,
initially for IT services, now more widely in
intra-net based organizations
Price discrimination via 2
part tariff
Dynamic limit pricing