XL Corp has estimated its demand and cost functions to be as follows:

P = 60 - 0.2Q

TC = 200 + 4Q + 1.2Q²

where Q is in units, P is in $ and C is in $.

1. Calculate the profit-maximizing price and output for the firm
2. Calculate the size of the profit.
3. Illustrate your answer using the appropriate graph
4. Does the firm operate in the short run or in the long run? Why?
5. Describe the factors that drive profits to zero in perfectly competitive markets in the long run. Critically explain the incentives that drive the market to a long run equilibrium
6. When do firms decide to shut down production in the short run? Illustrate your answer using graphs
7. When do firms decide to shut down production in the short run? Illustrate your answer using graph.