The demand curve and supply curve for carpet cleaning in the local market are currently as follows: Demand: Q = 1,000 - 10P

Supply: Q = 640 + 2P

The total cost function for the typical carpet cleaning company is: TC = 75 + 3q2and MC = 6q, where costs are measured in dollars and q is output per year. The market is perfectly competitive.

3.1 (20 points) Find the market price (P), the market quantity (Q), number of firms in the market (n), and the optimal quantity (q) that each firm produces in the short-run.

3.2 (15 points) Compute operating profits and total profits for the typical firm in the short run. Based on your results so far, would you say that this market is at the long-run equilibrium?

3.3 (25 points total) Now suppose that the local government increases the annual licensing fee that all carpet cleaning companies must pay by $33. All firms must pay licensing fee if they wish to operate in the market. Assume everything stays the same in this market except for the increase in license fee.

3.31 (5 points) How does the increased licensing fee affect the typical firm's fixed cost? And it's marginal

3.32 (20 points) What will be the long-run market equilibrium price after the licensing fee is increased? How much output will each firm produce in the new long-run equilibrium? How many firms will operate in the market after the licensing fee is increased?