Review • Own price elasticity • Empirical estimation of demand curve • Linear and log-log model • Interpretation of coefficient and computation of price elasticity.
Introduction • Price dispersion – different prices for the same product - is prevalent in the marketplace • The “law of one price” is dead • Example: Microsoft software version and upgrade prices • Example: Prices of 1/3 liter Coca-Cola cans in Germany
Example: Student rates • Why do software manufacturers have lower rates for students? • One explanation is that they have lower willingness to pay & higher elasticity than business users. • Charging two prices is more profitable
Example: Airline pricing • Why do airlines have “first class” rates often 2-3 times higher than cabin? • There is a small group of “elite” customers who are less price elastic than “regular” customers • It is more profitable to charge two prices • The “elites” must be “fenced in” from buying cabin seats by making cabin seats uncomfortable
Illustration of benefits of price customization Price ($) 100 Demand curve Gross Margins (p-c)*q p c=10 0 1000 q
Remember the meaning of the demand curve The demand curve is an aggregation of the demands of individual or segment, who have different reservation prices (max. willingness to pay) Price ($) q 0 Ideally, charge each customer their reservation price (as long as it is above c) – (i) no profitable customer is excluded from buying and (ii) no money left on table.
A single price is inefficient Money left on the table Price ($) 100 Profit (p*-c)q* No trade – deadweight loss p* c=10 0 q 1000
Calculation • The demand function is p = 100 – 0.1q • The profit-maximizing price is • The demand at the profit maximizing price is • The profit (gross margins) is
Demonstration of benefits using 2 price points Price ($) Rule of 1/3 for linear demand functions 100 p1* p2* c 0 1000 q1* q2*
Calculation p = a – bq q = A – Bp • Assume that we can put a “fence” that prevents higher price customers from paying the lower price, also, c=$10 • The demand function is q= D(p) = 1000 – 10p • Profit at prices p1 and p2 are • The profit-maximizing prices are • The maximized profit is (p1-c)D(p1)+(p2-c)(D(p2)-D(p1)) p2* =$40, p1*=$70 (70-10)*300+(40-10)(600-300)=$27000
Calculation p = a – bq q = A – Bp • In general, in the case of the linear demand, constant variable cost and two prices, the profit-maximizing prices are • p2* = (2c + a)/3, or p2* = (2cB + A)/3B • p1* = (2a + c)/3, or p1* = (2A + cB)/3B
This is price discrimination • Charging different prices to different people for the same (or similar) product. • Since “discrimination” has a negative connotation, call it “price customization” • A useful result - Most of the benefit of price customization may be realized with relatively few price points
Implementation • Key problem: How do we prevent higher willingness-to-pay customers from paying the price meant for lower willingness-to-pay customers? • Place “fences” that corral customers
Next Lecture • Price Discrimination 2 - Implementation