A monopolist has access to an industry with market demand P = 10 ? y where y is the firm’s quantity. Its cost function is C(y) = 2y
1. Decide the firm’s profit maximizing quantity. Show your outcome on a graph. What is the firm’s profit? Calculate the point-elasticity of demand at the profit-maximizing output.
2. Now presume the firm’s cost function is C(y) = 4y
Again determine the profit-maximizing quantity, profit and the elasticity at the profit-maximizing quantity. (No graph is required in this case.)
3. Essentially, we have two types of monopolist. Which monopolist kind operates at the higher level of elasticity? Why?
4. Prove that for any linear demand, p = a ? by, and constant marginal cost, c, that a monopolist would never ever operate at a point elasticity less than 1.