1. Chapter 14: Advanced Pricing Techniques
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

2. Advanced Pricing Techniques
Price discrimination
Multiple products
Cost-plus pricing

3. Capturing Consumer Surplus
Uniform pricing
Charging the same price for every unit of the product
Price discrimination
More profitable alternative to uniform pricing
Market conditions must allow this practice to be profitably executed
Technique of charging different prices for the same product
Used to capture consumer surplus (turning consumer surplus into profit)

4. The Trouble with Uniform Pricing (Figure 14.1)

5. Price Discrimination
Exists when the price-to-marginal cost ratio differs between two markets

6. Price Discrimination
Three conditions necessary to practice price discrimination profitably:
Firm must possess some degree of market power
A cost-effective means of preventing resale between lower- and higher-price buyers (consumer arbitrage) must be implemented
Price elasticities must differ between individual buyers or groups of buyers

7. First-Degree (Perfect) Price Discrimination
Every unit is sold for the maximum price each consumer is willing to pay
Allows the firm to capture entire consumer surplus
Difficulties
Requires precise knowledge about every buyer’s demand for the good
Seller must negotiate a different price for every unit sold to every buyer

8. First-Degree (Perfect) Price Discrimination (Figure 14.2)

9. Second-Degree Price Discrimination
Lower prices are offered for larger quantities and buyers can self-select the price by choosing how much to buy
When the same consumer buys more than one unit of a good or service at a time, the marginal value placed on additional units declines as more units are consumed

10. Examples of Second Degree Price Discrimination
Two-part pricing
Block pricing

11. Second-Degree Price Discrimination
Two-part pricing
Charges buyers a fixed access charge (A) to purchase as many units as they wish for a constant fee (f) per unit
Total expenditure (TE) for q units is:
Average price declines as more is purchased

12. Second-Degree Price Discrimination
When consumers have identical demands, entire consumer surplus can be captured by:
Setting f *= MC
Setting A* = consumer surplus (CS)
Optimal usage fee when two groups of buyers have identical demands is the level for which MRf = MCf

13. Inverse Demand Curve for Each of 100 Identical Senior Golfers (Figure 14.3)

14. Summary of Two Part Pricing
Consumers will purchase product until marginal benefit = unit price
Unit price will at least cover marginal cost
With consumers with different preferences unit price will be above marginal cost
Consumers will choose to purchase as long as consumer surplus given unit price is greater than lump-sum fee (right to purchase)
With identical preferences monopolist will capture the entire consumer surplus
With different preferences some consumers will retain part of their consumer surplus

15. Demand at Northvale Golf Club (Figure 14.4)

16. Second-Degree Price Discrimination
Declining block pricing
Offers quantity discounts over successive discrete blocks of quantities purchased

17. Block Pricing with Five Blocks (Figure 14.5)
Compare unit price of an additional block to MC

18. Third-Degree Price Discrimination
If a firm sells in two markets, 1 & 2
Allocate output (sales) so MR1 = MR2
Optimal total output is that for which MRT = MC
For profit-maximization, allocate sales of total output so that
MRT = MC = MR1 = MR2

19. Third-Degree Price Discrimination
Equal-marginal-revenue principle
Allocating output (sales) so MR1 = MR2 which will maximize total revenue for the firm (TR1 + TR2)
More elastic market gets lower price
Less elastic market gets higher price
IF MR1 ≠ MR2 then shifting a unit of sales from the lower marginal revenue market to the higher marginal revenue market will increase revenue and leave total cost unchanged.

20. Allocating Sales Between Markets (Figure 14.6)

21. Constructing the Marginal Revenue Curve (Figure 14.7)
Horizontally sum MR curves

22. Profit-Maximization Under Third-Degree Price Discrimination (Figure 14

23. Third degree price discrimination

24. Example of third degree price discrimination
Bigsoft sells software to students and commercial users
It prices the software at $100 for commercial users and $50 to students.
Commercial users have a price elasticity of demand of -1.5 and students have a price elasticity of demand of -4 at the current prices.
Is the firm practicing optimal third degree price discrimination?

25. Bigsoft example MR = P(1+1/E) Commercial users
Student users
MR = $50 (1-1/4) = $37.5
How much can Bigsoft increase revenues by shifting one sale?
$ = 4.5

26. Bigsoft example
Suppose we have constant price elasticities of demand and constant marginal cost
Ec = -1.5
Es = -4
MC = $40
What are optimal prices?

27. Bigsoft example MRc = MRs = MC MRc = $40, MRs = $40
Given that MR = P(1+1/E) then P = MR/(1+1/E)
Pc = $120 and Ps = $53.33

28. Multiple Products Related in consumption MRX = MCX and MRY = MCY
For two products, X & Y, produce & sell levels of output for which
MRX = MCX and MRY = MCY
MRX is a function not only of QX but also of QY (as is MRY) – conditions must be satisfied simultaneously
Example: Disney sells DVD and complementary toys

29. Disney studios
Disney is considering lowering the price of its latest DVD from $20 to $15. This will increase unit sales but lower profits from the sale of the DVD’s by $10 million.
Increased sales of the DVDs will produce more sales of action figures. If the profit margin on an action figure is $5, how many more action figures must Disney sell to offset the decline in profits on the DVDs?
Answer ($10 million/$5) = 2 million

30. Multiple Products Related in production as substitutes MRPX = MRPY
For two products, X & Y, allocate production facility so that
MRPX = MRPY
Optimal level of facility usage in the long run is where MRPT = MC
For profit-maximization:
MRPT = MC = MRPX = MRPY

31. JBL Plastics
JBL has a vacuum press that can produce plastic cars or tanks.
The marginal cost of producing two cars or one tank is $5.
The marginal revenue from the sale of a toy car is $3 and the price is $6.
The marginal revenue from the sale of a toy tank is $7 and the price is $14.
MRPc from toy cars is $3x2= $6
MRPt from toy tanks is $7x1=$7
Should JBL readjust the ratio of cars to tanks it is producing so that
MRPt= MRPc= MC

32. Profit-Maximizing Allocation of Production Facilities (Figure 14.9)
Horizontally sum MRP curves

33. Multiple Products Related in production as complements MRJ = MC
To maximize profit, set joint marginal revenue equal to marginal cost:
MRJ = MC
If profit-maximizing level of joint production exceeds output where MRJ kinks, units beyond zero MR are disposed of rather than sold
Profit-maximizing prices are found using demand functions for the two goods

34. Profit-Maximization with Joint Products (Figure 14.11)
Vertically sum MR curves

35. Farmer Jones
The marginal revenue from another cow brought to market includes marginal revenue of $300 from the sale of beef at a price of $500 and a price of $50 and marginal revenue $25 from the sale of the hide.
If the marginal cost of bringing another cow to market is $350, should he slaughter another cow?

36. Farmer Jones Product Marginal Revenue Beef $300 Hide 25 Total MR $325
Marginal Cost
$350

37. Bundling Multiple Products
When price discrimination is not possible, bundling multiple goods and charging a single price can be more profitable than charging individual prices for multiple goods
Two conditions for profitable bundling
Consumers must have different demand prices for each good in the bundle
Demand prices must be negatively correlated across consumer types

38. Bundling of Tickets to Football Game
Max TR =$3,300 = 2 x $1,400 + $500
Max TR = $4,000 = 2 x $2,000

39. Cost-Plus Pricing
Common technique for pricing when firms do not wish to estimate demand & cost conditions to apply the MR = MC rule for profit-maximization
Price charged represents a markup (margin) over average cost:
P = (1 + m) ATC
Where m is the markup on unit cost

40. Cost-Plus Pricing Does not generally produce profit-maximizing price
Fails to incorporate information on demand & marginal revenue
Uses average, not marginal, cost

41. Practical Problems with Cost-Plus Pricing (Figure 14.13)
Manager assumes the firm can produce 5,000 units and sell at a 50 percent mark-up

42. Consider Optimal Markup Over MC Relative to Price