In certain town, the market for a particular product has a single dominant firm that behaves as a price setter a competitive fringe comprised of many firms that behave as price takers. The dominant firm sets the price and the competitive fringe follows. There is no shortage or surplus in the market, i.e the market always clears. The market demand and the competitive fringe supply are given as follows:

Q_M = 140 - 32P

Q_F = 60 + 8P

where Q_M = market quantity demanded, and Q_F = the supply of the competitive fringe.

The dominant firm has an estimated total cost to be:

TC = 5 + 0.025Q_D²

where Q_D = the demand of (quantity produced by) the dominant firm.

a.Determine the profit maximizing level of output for the dominant firm. (Hint: You have to determine the demand faced by the dominant firm)

b.What price does the dominant firm set?

c.Determine the dominant firm's profit.

d.How much output does the competitive fringe produce?

e.What is the total industry output?