Two firms (A and B) are planning to produce a new soft drink for the summer. The soft drinks produced by the two firms can differ only in the level of sugar, aside from that they will be exactly equal. Suppose firm A chooses to produce a soft drink with 0g of sugar and firm B chooses to produce a soft drink with 125g of sugar. Firms have different marginal costs. The marginal cost for firm A of producing soft drinks is $0.50, whereas for firm B the marginal cost is $1.1. There are 500 consumers in this market. Consumers differ in their preference for sugar and are uniformly distributed according to their preference for sugar. Consumers with the lowest valuation for sugar prefer a soft drink with 0g of sugar, whereas consumers with the highest valuation for sugar prefer a soft drink with 125g. So, preferences for sugar are between 0g and 125g. Consumers get a disutility (in monetary value) of $0.02 for each gram of sugar different from their preferred level. Each consumer reservation value for the soft drink with the most preferred level of sugar is $12. The two firms compete for consumers by setting prices and prices are chosen simultaneously. Consumers buy the soft drink that provides the highest consumer surplus.

a. What prices will firms set in equilibrium?

b. What are the profits of each firm in equilibrium?