PROBLEM (5) In a dominant firm market with demand Q = 30 - p, the dominant firm has MC(Q) = 2Q (that is, with TC(Q) = Q²) and the fringe is composed of 5 identical firms, each with MC(Q) = 10Q (that is, with TC(Q)=5Q²). (a) Calculate the market price in the dominant firm model. Calculate the quantity produced by the fringe. (b) Now assume that the 5 fringe firms form a "union", and act as 5 "plants" of the union firm and this union firm competes as one single firm against the dominant firm in quantities, as in Cournot competition. What is the Cournot-Nash equilibrium price and quantity in this market organization? (c) Now, the dominant firm convinces the "union" not to compete with it but instead collude (to maximize the sum of profits) to form a cartel. What is the market price and quantity? (d) Back to the problem description. If all the firms (the dominant firm and the 5 fringe firms) acted as price takers, as in the perfect competition, what would be the market equilibrium price and quantity?

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