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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?

Short Answer

Expert verified

a.

i) The optimal price for Good 1 and Good 2 would be $80 each under the 'selling price separately' strategy. The firm will earn a profit of $320.

ii) The optimal price under pure bundling would be $120 for the bundle. The firm will earn a profit of $480.

iii) The producer will charge an optimal price of $100 for Good 1 from Consumer D and $100 for Good 2 from Consumer A. The producer will set a bundle price of $120 from Consumer B and Consumer C. The firm will earn a profit of $360.

The best strategy is pure bundling.

b. The best strategy will change. The new best strategy would be mixed bundling because the firm will earn more money by separating Consumer A from Good 1 and Consumer D from Good 2.

Step by step solution

01

Step 1. Calculate the optimal price of goods and select the best strategy

Selling goods separately: The producer will set separate prices for each good for consumers. Under this policy, the optimal price for Good 1 and Good 2 would be $80. At this price level, Consumers A and B will buy Good 2, and Consumers C and D will buy Good 1.

The firm will earn a profit of $320 (80×4).

Pure bundling:The producer will bundle both the goods into an individual package. It will price the bundle under a pure bundling pricing policy. Since each consumer has a reservation price of $120 for both the goods, the producer will set the bundle price at $120.

The firm will earn a profit of $480 (120×4).

Mixed bundling:The producer will charge; different prices for each good from consumers whose difference between the reservation prices is large; and bundle price from those consumers whose difference between the reservation prices is less. Thus, the producer will charge an optimal price of $100 for Good 1 from consumer D and Good 2 from consumer A. Also, a bundle price of $120 fr0m Consumers B and C.

The profit of the firm would be $360 (2×100+2×120 = 340)

The strategy of pure bundling is providing maximum profit to the producer. Thus, a pure bundling pricing strategy is best.

02

Step 2. Select the best strategy when there is marginal cost associated with goods

The profit under each pricing strategy will change if there is a marginal cost associated with the production of goods. The new profit level under each strategy is determined below:

Selling goods separately: The new profit will be $(80-30)×4= $200.

Pure bundling: The new profit will be (120-60)×4= $240.

Mixed bundling: The new profit will be (100-30)2+(120-60)2= $260.

The producer can gain maximum profit under a mixed bundling pricing strategy. Now, the best strategy for the producer is mixed bundling.

The best pricing policy changed when some marginal cost was associated with the goods.The marginal cost decreases the extent of profit under pure bundling.The best pricing strategy changed because the producer can benefit from consumers whose difference between the reservation price of goods and others is very large.

Therefore, the best pricing strategy changed for the producer.

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Most popular questions from this chapter

Look again at Figure 11.17 (p. 438). Suppose that the marginal costs c1 and c2 were zero. Show that in this case, pure bundling, not mixed bundling, is the most profitable pricing strategy. What price should be charged for the bundle? What will the firm’s profit be?

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?

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

Elizabeth Airlines (EA) flies only one route: Chicago–Honolulu. The demand for each flight is Q = 500 - P. EA’s cost of running each flight is \(30,000 plus \)100 per passenger.

  1. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA’s profit for each flight?
  2. EA learns that the fixed costs per flight are in fact \(41,000 instead of \)30,000. Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA’s average cost curve when fixed costs are \(30,000, and EA’s average cost curve when fixed costs are \)41,000.
  3. Wait! EA finds out that two different types of people fly to Honolulu. Type A consists of business people with a demand of QA = 260 - 0.4P. Type B consists of students whose total demand is QB = 240 - 0.6P. Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight?
  4. What would EA’s profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus?
  5. Before EA started price discriminating, how much consumer surplus was the Type A demand getting from air travel to Honolulu? Type B? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged?

Look again at Figure 11.12 (p. 434), which shows the reservation prices of three consumers for two goods.

Assuming that marginal production cost is zero for both goods, can the producer make the most money by selling the goods separately, by using pure bundling, or by using mixed bundling? What prices should be charged?

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