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.

(a) Determine the firm's profit maximizing quantity. Show your outcome on a graph. What is the firm's profit? Compute the point-elasticity of demand at the profit-maximizing output.

(b) Now suppose the firm's cost function is C(y) = 4y. Again determine the profit-maximizing quantity, profit and the elasticity at the profitmaximizing quantity. (No graph is required in this case.)

(c) Essentially, we have two types of monopolist. Which monopolist type operates at the higher level of elasticity? Why?

write all calculations with detail.