You are the manager of a firm that produces two products X and Y. The marginal cost of producing each product is constant and equal to $40.00. You know that different types of consumers value your two products differently, but you are unable to identify these consumers individually at the time of the sale. In particular, you know there are four types of consumers (100 of each type) with the following valuations (reservation prices) for the two products as follows:

Consumer type Product X Product Y
1 $25 $100
2 $40 $80
3 $80 $40
4 $100 $25

(a) What are the optimal prices for each product if you sell these products separately? What are your firm's profits? Explain.

(b) What is the optimal price if you sell the two products as a pure bundle containing one unit of product X and one unit of product Y? What are your firm's profits? Explain.

(c) Now suppose that you want to use mixed bundling strategy i.e., sell the two products as a bundle for a price of $125 and also sell the two products separately. What should you charge for product X and for product Y, such that your overall profits from mixed bundling would be maximized? What are your firm's profits?

(d) Which of the three pricing strategies above, i.e., (i) separate pricing, (ii) pure bundling, or (iii) mixed bundling is the most profitable strategy.