Question

Suppose N firms compete once by simultaneously choosing quantities. Inverse demand is P(Q) = a – bQ, where Q is total quantity and the known parameters a and b both are positive. Each firm’s marginal cost is c, with 0 ≤ c < a. Specify what limit the Nash equilibrium market price approaches as N → [infinity].

Answer 1

In a market with an infinite number of firms and an inverse demand function, as N approaches infinity, the Nash equilibrium market price will equate to the marginal cost c, due to the market becoming perfectly competitive with firms being price takers and earning zero economic profits in the long run.

Step-by-step explanation:

The student has posed a question about the Nash equilibrium market price in a scenario where an infinite number of firms compete in a market with an inverse demand function P(Q) = a – bQ and all firms have the same marginal cost c. As N approaches infinity, the market structure becomes one of perfect competition, where each firm perceives the demand curve it faces to be perfectly elastic or flat, and thus they are price takers.

In a perfectly competitive market, firms cannot influence the market price by their individual output decisions; the market price is determined by the intersection of the industry supply and demand. In the long run, the equilibrium price in a perfectly competitive market will be equal to the marginal cost (c) of producing the good, as firms enter or exit the market until economic profits are zero. Thus, as N approaches infinity, the Nash equilibrium market price in this model will approach the marginal cost, c.