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BA 445 Lesson A.10 Monopoly Pricing

Overview

Markup Rules for a monopolized good determine price equal marginal cost times a decreasing function of own price elasticity of demand. — So, Apple has high markup since Apple demand has low elasticity.

BA 445 Lesson A.10 Monopoly Pricing

A Linear Example of Uniform Pricing

- As a benchmark for this lesson, consider a firm with linear demand and cost
- P = 10 - 2Q
- C(Q) = 2Q
- If the firm must charge the same price per unit to all consumers, find the profit-maximizing quantity by setting MR(Q) = MC(Q)
- 10 - 4Q = 2, so Q* = 2
- Then, find price from demand, P* = 10 - 2(2) = 6
- Profits = (6)(2) - 2(2) = $8.

BA 445 Lesson A.10 Monopoly Pricing

Graphing Uniform Pricing

Price

Profits from uniform pricing = $8

10

8

6

4

MC

2

P = 10 - 2Q

1 2 3 4 5

Quantity

MR = 10 - 4Q

BA 445 Lesson A.10 Monopoly Pricing

Potential Non-Standard Profits

Price

Consumer surplus that might be captured = $4

10

Profits from uniform pricing = $8

8

6

Deadweight loss that might be captured = $4

4

MC

2

P = 10 - 2Q

1 2 3 4 5

Quantity

MR = 10 - 4Q

BA 445 Lesson A.10 Monopoly Pricing

The Standard Markup Rule for Non-Linear Demand

- Let E denote the own price elasticity of demand for a firm’s product.
- Since MR = P[1 + E]/ E, setting MR = MC and simplifying yields the standard markup rule:

P = [E/(1+ E)] MC.

- The optimal price is a proportional markup over marginal cost.

BA 445 Lesson A.10 Monopoly Pricing

An Example

- Elasticity of demand for Kodak film is -2.
- P = [E/(1+ E)] MC
- P = [-2/(1 - 2)] MC
- P = 2 MC
- Price is twice marginal cost.
- Fifty percent of Kodak’s price is margin above manufacturing costs (marginal cost).

BA 445 Lesson A.10 Monopoly Pricing

Markup Rule and Market Power

- Market Power for any firm is inversely related to the magnitude of own-price elasticity. So, according to the markup rule, higher market power means higher price.
- For Apple computers elasticity is lower, say E= -2, so P = [E/(1+E)]MC = 2MC
- For HP computers elasticity is higher, say E= -4, so P = [E/(1+E)]MC = (4/3)MC
- For a perfectly competition, the own-price elasticity E= -∞, so the rule

P = [E/(1+ E)] MC = [1-(1/(1+ E))] MC

is

P = [1-(1/(1-∞))] MC = 1 MC

or

P = MC.

BA 445 Lesson A.10 Monopoly Pricing

Overview

Perfect Price Discrimination yields maximum possible profit (capturing all consumer surplus and recovering and capturing all deadweight loss) by charging higher prices equal to willingness to pay for initial units rather than a uniform price equal to willingness to pay for the marginal unit. Perfect price discrimination requires perfect knowledge of willingness to pay for each unit and for each consumer. --- Peter may be charged $4 for his first unit and $2 for his second unit, and Paul may be charged $6 for his first unit and $1 for his second unit.

BA 445 Lesson A.10 Monopoly Pricing

Example from CNN.com:

- According to a recent study, many consumers are unaware that price discrimination occurs over the Internet.
- The Internet allows shoppers to easily compare prices across thousands of stores. But it also enables businesses to collect detailed information about a customer's purchasing history, preferences, and financial resources -- and to set prices accordingly.
- So when you buy an airplane ticket or a DVD online, you may pay a higher -- or lower -- price than another customer buying the very same item from the very same site.
- Why? Because the information the site has compiled on you suggests that you may be willing to pay more -- or less -- than others for that item.
- (Another reason for price discrimination is to measure demand. The company my be conducting random price tests to figure out what is the ideal price point for its product.)

BA 445 Lesson A.10 Monopoly Pricing

- Until now, all models involved a single optimum price.
- But there is more profit in charging different prices.
- Price discrimination is the practice of charging different prices to consumers for the same good.
- Price discrimination can be perfect or imperfect.
- Perfect price discrimination achieves maximum profits, leaving no surplus for consumers.
- Imperfect price discrimination achieves less than maximum profits, and leaves some surplus for consumers.

BA 445 Lesson A.10 Monopoly Pricing

Perfect Price Discrimination

- Practice of charging each consumer the maximum amount he or she will pay for each incremental unit (the height of the demand curve).
- Permits a firm to extract all surplus from consumers and to recover all deadweight loss.

BA 445 Lesson A.10 Monopoly Pricing

Perfect Price Discrimination

Price

Profits*:

.5(4-0)(10 - 2)

= $16

10

8

6

Total Cost* =$8

4

2

MC

D

1 2 3 4 5

Quantity

* Assuming no fixed costs

BA 445 Lesson A.10 Monopoly Pricing

Example:

- A Pepperdine professor visiting Mexico paid $15 for a chess set (about equal to the maximum he was willing to pay).
- When he returned to the same store, he was offered a lower price on a second set. After refusing the offer, the price continued to lower as the manager read his posture and tried to figure out the maximum amount he would be willing to pay.
- Some say perfect price discrimination won’t work if consumers can resell the good. It does get harder, but it is still possible:
- Suppose a Pepperdine student is only willing to pay $10 for a chess set for himself, but that student could resell the set to the professor for $15.
- How much would the student be charged for the first set?
- For the second set? (the one he keeps for himself)

BA 445 Lesson A.10 Monopoly Pricing

Caveat:

- Information constraints make perfect price discrimination difficult (it is difficult to know how much someone is willing to pay).
- The information constraints are especially difficult if consumers can resell the good.
- The manager cannot just appraise the maximum price the customer before him would pay for the good if he were buying it for himself, but also how much that customer could get by reselling the good.

BA 445 Lesson A.10 Monopoly Pricing

Overview

Block Pricing packages goods into a block. Block pricing yields maximum possible profit from each consumer (just like Perfect Price Discrimination) when the block price results in an average price per unit equal to the average willingness to pay. Knowing the profit-maximizing block price for each consumer requires perfect knowledge of willingness to pay for each unit. --- Peter may be charged $6 for a bag of 6 cookies, and Paul may be charged $3 for a bag of 4 cookies.

BA 445 Lesson A.10 Monopoly Pricing

Block Pricing

- When consumers can not resell the good and when the firm has unlimited information, block pricing generates the same maximum profit as perfect price discrimination.
- The practice of packaging multiple units of an identical product together and selling them as one package.
- Examples
- Paper.
- Six-packs of soda.
- Different sized of cans of green beans.

BA 445 Lesson A.10 Monopoly Pricing

An Algebraic Example

- Typical consumer’s demand is P = 10 - 2Q
- C(Q) = 2Q
- Optimal number of units in a package?
- Optimal package price?

BA 445 Lesson A.10 Monopoly Pricing

Optimal Quantity To Package: 4 Units

Price

10

8

6

4

MC = AC

2

D

1 2 3 4 5

Quantity

BA 445 Lesson A.10 Monopoly Pricing

Optimal Price for the Package: $24

Price

Consumer’s valuation of 4

units = .5(8)(4) + (2)(4) = $24

Therefore, set P = $24.

10

8

6

4

MC = AC

2

D

1 2 3 4 5

Quantity

BA 445 Lesson A.10 Monopoly Pricing

Costs and Profits with Block Pricing

Price

10

Profits* = [.5(8)(4) + (2)(4)] – (2)(4)

= $16

8

6

4

Costs = (2)(4) = $8

2

MC = AC

D

1 2 3 4 5

Quantity

* Assuming no fixed costs

BA 445 Lesson A.10 Monopoly Pricing

Overview

Commodity Bundling packages non-identical goods into a block or bundle. Commodity bundling can yield more profit than uniform pricing (but not maximum possible profit) by charging an average price per unit equal to the average willingness to pay. Commodity bundling may yield more profit than block pricing when the seller does not know the profit-maximizing block price for each consumer.

BA 445 Lesson A.10 Monopoly Pricing

Commodity Bundling

- The practice of bundling two or more differentiated products together and charging one price for the bundle.
- Examples
- Vacation packages.
- Computers and software.
- Film and developing.
- Commodity bundling is always possible because there are no information constraints (unlike first-order price discrimination).
- Commodity bundling is sometimes profitable, sometimes not.
- Let’s see an example of each.
- Examples hint at a rule for when bundling is profitable.

BA 445 Lesson A.10 Monopoly Pricing

Example of unprofitable bundling

- Two products (combs and head wax), zero production cost.
- Two consumers (Fabio and Bruce Willis)
- Fabio would pay $1 for a comb and $0 for head wax.
- Bruce would pay $0 for a comb and $3 for head wax.
- If the goods are sold separately, compute the optimum non-discriminating prices?
- $1 per comb, $3 for head wax. Profit = $4.
- If the goods are bundled, compute the optimum price for the bundle of 1 comb and 1 jar of head wax?
- Fabio would pay $1 for the bundle (tossing the wax).
- Bruce would pay $3 for the bundle (tossing the comb).
- Optimum price is $3. Profit = $3.
- It was better to keep the products unbundled.

BA 445 Lesson A.10 Monopoly Pricing

Example of profitable bundling: The Kodak Moment

- Total market size for film and developing is 4 million consumers.
- Four types of consumers
- 25% will use only Kodak film (F).
- 25% will use only Kodak developing (D).
- 25% will use only Kodak film and use only Kodak developing (FD).
- 25% have no preference (N).
- Zero costs (for simplicity).
- Maximum price each type of consumer will pay is as follows:

BA 445 Lesson A.10 Monopoly Pricing

Reservation Prices (maximum consumers are willing to pay) for Kodak Film and Developing by Type of Consumer:

BA 445 Lesson A.10 Monopoly Pricing

- Optimal Film Price?
- Assume no production cost.
- Optimal Price is $8; only types F and FD buy, resulting in profit of $8 x 2 million = $16 Million.
- At a price of $4, only types F, FD, and D will buy, profits = $12 Million.
- At a price of $3, all will types will buy, profit = $12 Million.

BA 445 Lesson A.10 Monopoly Pricing

- Optimal Developing Price?
- Assume no production cost.
- At a price of $6, only “D” type buys, profit = $6 Million.
- At a price of $4, “D” and “FD” buy, profit = $8 Million.
- Optimal price $3, only types “F”, “FD”, and “D” buy, profits = $9 Million.
- At a price of $2, all will types will buy, profit = $8 Million.

BA 445 Lesson A.10 Monopoly Pricing

- Total Profits by Pricing Each Item Separately.
- Assume no production cost.
- Total Profit = Film Profits + Development Profits
- Total Profit = $16 Million + $9 Million = $25 Million.
- The firm can earn even greater profits by bundling.

BA 445 Lesson A.10 Monopoly Pricing

- Consumer valuation of a “Bundle” of Film and Developing
- Assume no production cost.
- Do not allow consumers to separately buy Film and Developing.

BA 445 Lesson A.10 Monopoly Pricing

- Optimal Bundle Price?
- Assume no production cost.
- At a price of $12, only “FD” type buys, profit = $12 Million.
- At a price of $11, “F” and “FD” buy, profit = $22 Million.
- Optimal price $10, only types “F”, “FD”, and “D” buy, profits = $30 Million.
- At a price of $5, all will types will buy, profit = $20 Million.

BA 445 Lesson A.10 Monopoly Pricing

Overview

Two Part Pricing charges both a customer fee and a uniform price per unit. Two-part pricing yields maximum possible profit from each consumer (just like Perfect Price Discrimination) when the uniform price equals marginal cost and the customer fee equals consumer surplus, and when customers cannot buy then resell to other customers. Knowing the profit-maximizing two-part price for each consumer requires perfect knowledge of consumer surplus. --- Peter may be charged $36 for admission to Disneyland and a price of $0 (= marginal cost) per ride, and Paul may be charged $13 and a price of $0 per ride.

BA 445 Lesson A.10 Monopoly Pricing

Two-Part Pricing

- When consumers can not resell the good and when the firm has unlimited information, two-part pricing generates the same maximum profit as perfect price discrimination.
- Two-part pricing consists of a fee and a per unit charge.
- Examples:
- Disneyland with admission fee and zero per ride.
- $2 cokes with free-refills ($2 fee and zero per refill).
- Athletic club memberships.
- Netflix with monthly fee and free movie streaming.
- Spotify with monthly fee and free music streaming.
- Other examples?

BA 445 Lesson A.10 Monopoly Pricing

How Two-Part Pricing Works

Price

1. Set price at marginal cost (to maximize total surplus).

2. Compute consumer surplus.

3. Charge a fixed-fee equal to consumer surplus (to capture all surplus as profit).

10

8

6

Fixed Fee = Profits* = $16

Per Unit

Charge

4

MC

2

D

* Assuming no fixed costs

1 2 3 4 5

Quantity

Overview

Group Pricing applies markup rules for groups like seniors, students, and kids. Group pricing yields more profit than uniform pricing but less than maximum profits. Group pricing does not require perfect knowledge of each consumer. — So, Knott’s Berry Farm discounts to seniors because seniors cannot survive Knott’s distinctive thrill rides.

BA 445 Lesson A.10 Monopoly Pricing

Imperfect Price Discrimination

- Third-degree price discrimination: The practice of charging different groups of consumers different prices for the same product.
- Group must have observable characteristics for third-degree price discrimination to work.
- Examples:
- Student discounts
- Child discounts
- Poverty discounts (like when poor people clip coupons)
- Senior citizen’s discounts
- Regional and international pricing.

BA 445 Lesson A.10 Monopoly Pricing

Implementing Third-Degree Price Discrimination

- Suppose the total demand for a product is comprised of two groups with different elasticities, E1 < E2 < - 1
- Notice that group 1 is more price sensitive than group 2.
- Profit-maximizing prices?
- P1 = [E1/(1+ E1)] MC < [E2/(1+ E2)] MC = P2

Qualitative Examples

- Why are seniors charged less than others at Disneyland and at restaurants? Higher elasticity (more substitutes).
- They shop at Disneyland, like they shop at the mall.
- They eat plain food at restaurants, like they eat at home.

BA 445 Lesson A.10 Monopoly Pricing

A Numerical Example

- Suppose the elasticity of demand for Kodak film in the US is EU = -1.5, and the elasticity of demand in Japan is EJ = -2.5.
- Marginal cost of manufacturing film is $3.
- PU = [EU/(1+ EU)] MC = [-1.5/(1 - 1.5)] $3 = $9
- PJ = [EJ/(1+ EJ)] MC = [-2.5/(1 - 2.5)] $3 = $5
- Kodak’s optimal third-degree pricing strategy is to charge a higher price in the US, where demand is less elastic.

BA 445 Lesson A.10 Monopoly Pricing

Summary

- Consider a monopolist with demand Q = 100 – 0.1P and constant unit cost of 500.
- The Lesson covered three levels (orders) of price discrimination:
- Perfect discrimination, including two-part pricing and block pricing.
- Commodity bundling and imperfect discrimination.
- No price discrimination.

BA 445 Lesson A.10 Monopoly Pricing

- No price discrimination
- Q = 100 – 0.1P implies P = 1,000 – 10Q
- MR = 1,000 – 20Q
- MC = 500
- MR = MC implies 1,000 – 20Q = 500, or Q = 25.
- P = 1,000 – 10(25) = 750
- P = (P-MC)Q - FC = (750-500)(25) – 10,000 = -3,750

BA 445 Lesson A.10 Monopoly Pricing

- Perfect price discrimination: Two-part price.
- P(Q) = 1,000 – 10Q
- P(Q) = MC implies 1,000 – 10Q = 500, and Q = 50.
- Firm breaks even on P = MC per unit profit.
- Consumer surplus triangle = .5(1,000-500)(25) = 12,500.
- Fee = Consumer surplus = 12,500.
- Profit = 12,500 – 10,000 = 2,500.

BA 445 Lesson A.10 Monopoly Pricing

Conclusion

- First-degree price discrimination, two part pricing, and block pricing and permit a firm to maximize profit and extract all consumer surplus.
- Commodity bundling and imperfect price discrimination permit a firm to extract some (but not all) consumer surplus.
- Markup rules are the simplest to implement, but leave consumers with surplus.
- Different pricing strategies require different information.

BA 445 Lesson A.10 Monopoly Pricing

- Review Questions
- You should try to answer some of the review questions (see the online syllabus) before the next class.
- You will not turn in your answers, but students may request to discuss their answers to begin the next class.
- Your upcoming Exam 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.

BA 445 Lesson A.10 Monopoly Pricing

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