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Chapter 11: Q14. (page 450)

You are selling two goods, 1 and 2, to a market consisting of three consumers with reservation prices as follows:

RESERVATION PRICE (\()

CONSUMER FOR 1 FOR 2

A 20 100

B 60 60

C 100 20

The unit cost of each product is \)30.

a. Compute the optimal prices and profits for (i) selling the goods separately, (ii) pure bundling, and (iii) mixed bundling.

b. Which strategy would be most profitable? Why?

Short Answer

Expert verified

  1. i) Optimal price for Good 1 and Good 2 will be $100. The profit of the firm will be $140.

ii) Optimal price for the bundle will be $120. The profit of the firm will be $180.

iii) Optimal price for Good 1 and Good 2 will be $100 for each of them and a bundle price (package of both goods) at $120. The profit of the firm would be $200.

  1. Mixed bundling. It provides the maximum profit.

Step by step solution

01

Step 1. Calculate the optimal prices and profits under different pricing policies.

  • Selling goods separately: The producer sets the price for each good according to the maximum reservation prices of the customer for that good. For the given information, the producer will set the price of Good 1 and Good 2 at $100 each.

At this price level, only Consumer C will buy Good 1, and Consumer A will buy Good 2. Consumer B will not be able to buy any of the goods. The firm's total profit would be (100-30)+(100-30) = $140.

  • Pure bundling: The producer will combine both the goods into a single unit or package. The producer will set the optimal price for the package at a level where it can cover the maximum of reservation prices set by consumers for both the goods.

Since the sum of reservation prices for both the goods is $120 for each consumer, the producer will set the optimal bundle price for the package at $120. The profit of the firm would be ($120-60)3 = $180.

  • Mixed bundling: The producer will charge individual prices for the goods from some consumers and bundle prices from others. The producer will charge separate prices for Good 1 and Good 2 from Consumers C and A for the given information and a bundle price for both the goods from Consumer B.

Thus, it will set the optimal price for Good 1 and Good 2 at $100 and bundle price at $120 for the package. Now sell Good 1 to Consumer C and Good 2 to Consumer A under separate pricing policy and sell the package to Consumer C. The total profit of the firm would be (100-30)+(100-30)+(120-60)= $200.

02

Step 2. Select the most profitable pricing policy for the producer

If the producer decides to sell the goods under a “separate pricing policy,” it will earn a profit of $140. If he sells under a “pure bundling” pricing policy, it will earn a profit of $180. And if he decides to sell them under “mixed pricing policy,” the producer will receive a profit $200. On comparing all the three pricing policies, the mixed pricing policy provides maximum profit to the producer.

Thus, the producer should apply a mixed bundling pricing strategy. This policy will provide maximum profit from the sale of goods.

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Most popular questions from this chapter

Your firm produces two products, the demands for which are independent. Both products are produced at zero marginal cost. You face four consumers (or groups of consumers) with the following reservation prices:

CONSUMER GOOD 1(\() GOOD 2(\))

A 25 100

B 40 80

C 80 40

D 100 25

a. Consider three alternative pricing strategies: (i) selling the goods separately; (ii) pure bundling; (iii) mixed bundling. For each strategy, determine the optimal prices to be charged and the resulting profits. Which strategy would be best?

b. Now suppose that the production of each good entails a marginal cost of $30. How does this information change your answers to (a)? Why is the optimal strategy now different?

Many retail video stores offer two alternative plans for renting films:

• A two-part tariff: Pay an annual membership fee (e.g., \(40) and then pay a small fee for the daily rental of each film (e.g., \)2 per film per day).

• A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., $4 per film per day).

What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff?

You are an executive for Super Computer, Inc. (SC), which rents out supercomputers. SC receives a fixed rental payment per time period in exchange for the right to unlimited computing at a rate of P cents per second. SC has two types of potential customers of equal number—10 businesses and 10 academic institutions. Each business customer has the demand function Q = 10 - P, where Q is in millions of seconds per month; each academic institution has the demand Q = 8 - P. The marginal cost to SC of additional computing is 2 cents per second, regardless of volume.

  1. Suppose that you could separate business and academic customers. What rental fee and usage fee would you charge each group? What would be your profits?
  2. Suppose you were unable to keep the two types of customers separate and charged a zero rental fee. What usage fee would maximize your profits? What would be your profits?
  3. Suppose you set up one two-part tariff—that is, you set one rental and one usage fee that both business and academic customers pay. What usage and rental fees would you set? What would be your profits? Explain why the price would not be equal to marginal cost.

Price discrimination requires the ability to sort customers and the ability to prevent arbitrage. Explain how the following can function as price discrimination schemes and discuss both sorting and arbitrage:

  1. Requiring airline travelers to spend at least one Saturday night away from home to qualify for a low fare.

  2. Insisting on delivering cement to buyers and basing prices on buyers’ locations.

  3. Selling food processors along with coupons that can be sent to the manufacturer for a $10 rebate.

  4. Offering temporary price cuts on bathroom tissue.

  5. Charging high-income patients more than low-income patients for plastic surgery

A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest). Demand and marginal revenue for the two markets are

P1 = 15 – Q1 MR1 = 15 - 2Q1

P2 = 25 - 2Q2 MR2 = 25 - 4Q2

The monopolist’s total cost is C = 5 + 3(Q1 + Q2). What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?
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