Our town has five (5) firms that provide pool maintenance services. All firms provide the exact same service with no differences in quality, speed, or any other characteristic. The market demand is given by P = 150 - Q, where P is the price per pool and Q, is the number of pools. The marginal cost of maintenance is $15 per pool.

a. Assume that the firms compete through quantity. What will be the profit-maximizing quantities that each firm will produce? What will be the market price and firm profits? State the two conditions that are satisfied by the quantity decision that makes it profit-maximizing in this market structure.

b. i. Suppose that two of the pool maintenance firms merge. The new firm can now act as a leader in the market while the unmerged firms will act as followers. What will be the profit-maximizing quantities for the merged firm and unmerged firms? What will be the resulting market price and firm profits?

ii. Suppose that after the first merger, another two of the follower firms merge. What will be the profit-maximizing quantities for the new leaders and followers? What will be the resulting market price and firm profits?

c. With appropriate calculations, show that the first and second mergers were profitable for the firms involved. Briefly explain what happens to make the mergers profitable, and what outside factor(s) could potentially make the mergers unprofitable