A firm sells a product in a market where there are two types of consumers, high and low-valuation consumers. There are equally many of the two types of consumers, and the total number of consumers is normalized to 1. The product has value 3 to the high-valuation consumers and value 1 to the low-valuation consumers. All consumers have unit demand, i.e., they buy either one unit or do not participate. The product is produced at constant marginal cost equal to 0.

1. Find the profit maximizing price and calculate the firm’s profit. The firm considers introducing a damaged version of the product. The damaged version is produced at constant marginal cost equal to 1/10. It results in a utility of 5/10 to the low-valuation consumers and of 6/10 to the high valuation consumers.

2. Find the optimal price of the normal and of the damaged version of the product. Should the firm introduce the damaged version? What are the welfare consequences of the introduction of the damaged version?