4. Brown City Pet Food Company produces a complete line of dry pet foods. During the past year they have been test marketing Pet Life, a meat-based dog food that extends the life of the pet by one year. The demand for the dog food is: Q = 40,000 - 2000P where Q is cases of dog food demanded per month. The long run average (and marginal) cost of production, which is constant, is $8 per pound.

a. Suppose the company obtains a patent on Pet Life. Determine Brown City's price, quantity, and profit if they have a patent.

b. Once their patent expires, other firms can enter this industry. Calculate the social welfare gain to (long run) competition, as compared to monopoly. You may find it helpful to include a graph in your answer, but it is not required