There are two firms in a market with a market demand given as:

Q = 160 - 0.2P

Total cost for each firm is given below.

TC₁ = 200Q₁ + 5Q₁²

TC₂ = 100Q₂ + 2.5Q₂²

where Q = Q₁ + Q₂; Q₁ is the output for Firm 1 and Q₂ is the output for Firm 2.

a.Assuming the two firms behave as perfectly competitive firms, determine the market equilibrium price and quantity, and the profit maximizing level of output for each firm. What are each firm's profits?

b.If the two companies decide to collude, what are the equilibrium values of output for each firm and what is the prevailing price? What are each firm's profits?

c.Assuming each firm assumes the output of the other firm to be fixed and both firms decide simultaneously how much to produce. What are the equilibrium values of output for each firm and what is the prevailing price? What are each firm's profits?

d.Suppose Firm 1 enters the market first. What are the equilibrium values of output for each firm and what is the prevailing price? What are each firm's profits? Is there a first mover advantage in this market?

e.Now suppose the firms compete by simultaneously choosing a price instead of quantity. What are the equilibrium values of output for each firm and what is the prevailing price? What are each firm's profits?

Please explain.