The market demand curve in the nickel industry in Australia is given by Qd = 400 - 8P. The industry is dominated by a large firm with a constant marginal cost of $10 per unit. There also exists a competitive fringe of 100 firms, each of which has a marginal cost given by MC = 10 + 50q, where q is the output of a typical fringe firm.
a) What is the equation of the supply curve for the competitive fringe?
b) Restricting your attention to the range of prices that exceed the dominant firm's marginal cost, what is the equation of the residual demand curve?
c) What is the profit-maximizing quantity of the dominant firm? What is the resulting market price? At this price, how much does the competitive fringe produce, and what is the fringe's market share (i.e., the fringe quantity divided by total industry quantity)? What is the dominant firm's market share?
d) Let's consider a twist on the basic dominant firm model. Suppose the Australia government, concerned about the amount of dominance in the nickel industry decides to break the dominant firm into two identical firms, each with a constant marginal cost of $10 per unit. Suppose further that these two firms act as Cournot quantity setters, taking into account the supply curve of the competitive fringe. What is the Cournot equilibrium quantity produced by each dominant firm? What is the equilibrium market price? At this price, how much does the competitive fringe produce, and what is the fringe's market share?