Pricing

1
Pricing

• The fundamental pricing rule
• Price discrimination
• Dynamic limit pricing

2
The fundamental pricing rule

• Produce up to the point where MRMC, where MR
  P1-(1/e)
• For a price taker
• MR P1-(1/e) P, hence PMC
• For a price searcher MR MC implies
• P MC/1 - (1/e), hence (P- MC)/P 1/e
• And P/(P- MC) e

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The fundamental pricing rule
P/(P- MC) e
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(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.)

5
QUESTION

• True or false the optimal price will always be
  on the elastic portion of the residual demand
  curve?

6
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.

7
QUESTION

• When will the optimal price be set where the e
  of the residual demand curve is 1

8
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

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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?
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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).
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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).

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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).

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• 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.

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• 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.

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• 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

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Price discrimination via 2 part tariff
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Dynamic limit pricing