Final answer:
The student's question involves using inverse demand curves to determine the Nash equilibrium and firm profits in a competitive setting. The steps include setting up an objective function, deriving best response functions, and finding the equilibrium under the assumption of symmetry.
Step-by-step explanation:
The question deals with finding the Nash equilibrium for competing firms that are price setters rather than price takers, which is a stark contrast from a perfectly competitive firm that faces a horizontal demand curve allowing it to sell at a single market price. The student is asked to perform an analysis using inverse demand curves to determine firm decision-making in the context of competition. Specifically, the steps required are setting up the objective function for profit-maximization, deriving the best response functions for each firm, and finally finding the Nash equilibrium and equilibrium profits, assuming symmetric firms.
These steps align with the process depicted in Figure 9.7 for a monopolist's profit maximization, where a firm chooses quantity where marginal revenue (MR) equals marginal cost (MC), and then identifies the corresponding price on the perceived demand curve. It differs from the case of a natural monopoly, which is left alone to maximize profits at the point where MR = MC without competition influencing its decisions. In a monopolistic competition setting, over time, positive economic profits attract new entrants which erode the original firm's monopoly power, leading to a long-run equilibrium of zero economic profits.