Price Discrimination Overheads

1. Price Discrimination Overheads

2. Price discrimination is the selling of two varieties of a product to two different buyers at different net prices, where the net price is the price paid by the buyer, adjusted for any cost of product differentiation Price discrimination occurs when a firm charges different prices to different customers for reasons other than differences in production costs

3. Requirements for Price Discrimination There must be a downwards sloping demand curve for the firm's output The firm must be able to raise price without losing all its customers

4. The firm must be able to identify consumers who are willing to pay more for the product The firm must know who will pay the higher price Auctions Airlines

5. The firm must be able to prevent low-price customers from reselling to high-price customers Arbitrage is the purchase of products at a low price in order sell them at a high price

6. Ways to identify customers long term relationships insurance agent jeweler doctor age sex type of job other commonly bought items place of residence

7. Prevention of Arbitrage Customer specific products haircuts house plans dental filling gall bladder operation

8. Use of product predicated on specific characteristics student discount card senior citizen discount air travel with weekend stay summer use of condominium at ski resort

9. Product is hard to resell because of distance or transactions costs purchase of corn silage purchase of feeder cattle purchase of custom made shoes

10. First-degree (perfect) price discrimination A firm practices first-degree or perfect price discrimination if it is able to charge the maximum price each consumer is willing to pay for each unit sold Specifically, perfect price discrimination involves the seller charging a different price for each unit of the good in such a way that the price charged for each unit is equal to the maximum willingness to pay for that unit

11. Example of Grandpa Jones 5 Spoker D tractors Marginal value of zero to Grandpa Jones 2 identical interested buyers

12. Value (demand) schedule for each buyer Tractors Price First $16,000 Second $12,000 Third $8,000 Fourth $6,000 Fifth $4,000

13. Price and Demand $ 16 14 12 10 8 6 4 2 1 2 3 4 5 6 7 8 9 10 Tractors

14. Uniform pricing Price (Demand) Total Revenue > $16,000 0 0 $16,000 1 16,000 $16,000 2 32,000 $12,000 3 36,000 $12,000 4 48,000 $8,000 5 40,000 $8,000 6 48,000 $6,000 7 42,000 $6,000 8 48,000 $4,000 9 36,000 $4,000 10 40,000

15. To sell all 5 tractors the uniform price must be $8,000 Total revenue = $40,000

16. Can Grandpa Jones do better? How about $12,000 a piece for 4 tractors? Total revenue = $48,000

17. Grandpa Jones ends up with a tractor of no value to him An individual willing to pay $8,000 for a tractor is shut out of the market But revenue is higher than when selling all 5 at a uniform price of $8,000

18. First Degree Price Discrimination Charge the maximum price each consumer is willing to pay for each unit sold

19. First Degree Price Discrimination Sell the first tractor for $16,000 Sell the second tractor for $16,000 Sell the third tractor for $12,000 Sell the fourth tractor for $12,000 Sell the fifth tractor for $8,000 Total Revenue = $64,000

20. How does Grandpa Jones do it? Offer a bundle of two tractors for $28,000 Each consumer will buy one bundle Total revenue is $56,000 $48,000 < $56,000 < $64,000

21. Even better Offer a bundle of two tractors for $28,000 With an option to bid on a third Or an option to buy a third for $8,000 Each consumer will buy one bundle The auction for the remaining tractor will yield $8,000 Total revenue = $64,000

22. Another way Offer a three unit bundle for $36,000 Either one guy buys or the other guy buys and Grandpa Jones is left with two tractors Offer a two unit bundle for $28,000 Either one guy buys or the other guy buys and Grandpa Jones is left with no tractors Total profit = $64,000

23. Why not offer all five units Offer a bundle of five tractors for $46,000 One buyer will purchase all five of them All the tractors are gone and Grandpa Jones’s profits are only $46,000

24. But first buyer can then sell two tractors for $28,000 to the other buyer First buyer has profits of $18,000 Total profits are $64,000 But poor Grandpa only gets $46,000 of them

25. A simple example of discriminating monopolist p = 20 - 2Q Q = 10 - 1/2p Cost = MC = $4.00

26. Uniform pricing first

27. TR MR MC Profit Q Price UNF UNF Cost Exact 0 20 0 --- 0 4 0.00 1 18 18 18 4 4 14.00 2 16 32 14 8 4 24.00 3 14 42 10 12 4 30.00 4 12 48 6 16 4 32.00 5 10 50 2 20 4 30.00 6 8 48 -2 24 4 24.00 7 6 42 -6 28 4 14.00 8 4 32 -1 32 4 0.00 9 2 18 -1 36 4 -18.00 10 0 0 -1 40 4 -40.00

28. 22 $ 20 18 Price Profit 16 MR 14 12 MC 10 PU Revenue 8 QU 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Profit Max for Uniform Price Monopolist Cost

29. Results Uniform Price Monopolist Q = 4 TR = 48 TC = 16 Profit = 32

30. Now consider a price discriminating monopolist Each unit receives a different price

31. MC TR MR Profit Q Price Cost Exact DSC DSC DSC 0 20 0 4 0.00 0 1 18 4 4 18.00 18 14.00 2 16 8 4 34.00 16 26.00 3 14 12 4 48.00 14 36.00 4 12 16 4 60.00 12 44.00 5 10 20 4 70.00 10 50.00 6 8 24 4 78.00 8 54.00 7 6 28 4 84.00 6 56.00 8 4 32 4 88.00 4 56.00 9 2 36 4 90.00 2 54.00 10 0 40 4 90.00 0 50.00

32. 22 $ 20 18 Price 16 MR 14 12 MC 10 PU 8 QU 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Profit Max for Discriminating Monopolist

33. 22 $ 20 18 Price 16 14 12 MC 10 PU 8 QU 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Profit Max for Discriminating Monopolist

34. Discriminating Monopolist Uniform Price Monopolist Results Q = 8 Q = 4 TR = 88 TR = 48 TC = 32 TC = 16 Profit = 56 Profit = 32

35. Monopoly and Competition The perfectly discriminating monopolist will produce the same amount as a competitive industry with the same cost structure

36. Consumers much prefer competition They pay much less for the same quantity

37. 22 $ 20 18 Price 16 14 12 MC 10 8 6 4 Cost/ Revenue 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Competitive Equilibrium

38. Non-integer quantities (sales) If the monopolist can charge for and sell partial quantities, then the maximum that can be charged is the total area under the demand curve to the left of a given quantity

39. 22 $ 20 18 Price 16 14 12 MC 10 8 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Output Profit Max for Discriminating Monopolist Profit Cost

40. Results Perfectly Discriminating Monopolist Discriminating Monopolist Q = 8 Q = 8 TR = 96 TR = 88 TC = 32 TC = 32 Profit = 64 Profit = 56

41. Segregating Markets Identify Consumers Prevent Arbitrage Airline Example

42. Profit MC E Demand H MR Uniform Price Monopoly Total Profit = $1200 $ 160 120 Revenue 100 80 Cost 0 0 10 30 40 Number of Round-trip Tickets

43. Gain Profit MC E Demand H AC MR Charge $160 for No Restriction Ticket Total Profit = $1600 $ 160 120 100 Revenue 80 Cost 0 0 10 30 40 Number of Round-trip Tickets

44. MC P > MC Demand H MR Charge $100 for Student Tickets $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

45. MC P > MC Demand Charge $100 for Student Tickets $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

46. MC P > MC Demand Charge $100 for Student Tickets $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

47. MC Additional Revenue Demand Additional Cost Charge $100 for Student Tickets $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

48. MC Additional Profit Demand H Additional Cost Charge $100 for Student Tickets $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

49. Gain MC Demand H Overall Gain from Price Discrimination $ 160 120 100 80 0 0 10 30 40 Number of Round-trip Tickets

50. The End