Question

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

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

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.

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.