Gotcha, the only seller of stun guns, faces the inverse market demand curveP=40012Q, whereQmeasures the number of stun guns per day andPis the price per stun gun. The marginal cost is constant at$64.

a. What are Gotcha's profit-maximizing price and quantity?

b. Suppose a new firm, Ouchy, enters the stun gun market. Ouchy's marginal cost is also constant at$64. Gotcha and Ouchy decide to form a cartel and evenly split the market output. What is the market price? How much output does each firm produce?

c. Now suppose that Ouchy no longer abides by the cartel agreement; it decides to produce and sell five additional stun guns per day. What happens to the market price and market output?