Problem: You are the manager of a firm that produces products X and Y at zero cost. 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 three types of consumers (1,000 of each type) with the following valuations for the two products
Consumer type Product X Product Y Bundle
1 $60 $50 $110
2 $40 $100 $140
3 $25 $120 $145
1) Find the prices that maximize profits if you sell the two products separately.
2) Find the price of the bundle that maximizes profits, if you can only offer the two products together as a bundle.
3) Find the optimal prices for the bundle and the two products separately, if you can offer a mixed bundle.
4) Which of the above three strategies yields the highest profits?