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 50g of sugar. The marginal cost of producing soft drinks is $1. There are 1000 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 50g. So, preferences for sugar are between 0g and 50g. Consumers get a disutility (in monetary value) of $0.10 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 $10. The two firms compete for consumers by setting prices. Firm A sets the price PA first and then firm B sets the price PB after observing PA. Consumers buy the soft drink that provides the highest consumer surplus.
(a) What prices will firms set in equilibrium? To get it right, normalize everything to be between 0 and 1.
(b) What are the profits of each firm in equilibrium?
(c) Suppose firm A invests in a new technology that reduces its marginal cost to $0.80. The marginal cost of firm B is still $1. What prices will firms set in equilibrium in this case?