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|

(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. 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 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: discriminates 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), p 1 /MC 1 ≠ p 2 /MC 2 (of course, MR 1 /MC 1 = MR 2 /MC 2 ).

Necessary conditions two consumer groups  At least two consumer groups exist with different elasticities, i.e., different demand curves. identify consumers  The organization can identify consumers in each group, and set prices differently for consumers in the two groups. no arbitrage 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