Suppose we are studying the long-run competitive market for robots, the market demand for robots is given by D(p) = 24p. All the firms are identical with the following cost curve C(y) = 2y2 + 8.

a) What is the long-run competitive market equilibrium?

Rick is a single consumer in the market; his consumption of robots is given by Di(p) = M - p, where M is his fixed income. Rick is also a government regulator for the robot market; he decides if the market is competitive or a monopoly.

Morty is a firm in the market (he faces the same cost curve as everyone else: C(y) = 2y2 + 8). Morty would like to operate as a monopolist (instead of a firm in a competitive market).

b) How much would Morty have to pay/compensate Rick in order for Rick to allow Morty to operate as a monopolist (The market demand curve is the same as part a))?

c) Suppose instead this was an oligopoly market with 2 firms engaged in Bertrand competition; both firms face the same cost curve and demand curve as part a). How much higher is Morty's profit under the Bertrand equilibrium versus the competitive market equilibrium? Make sure to justify your response.

d) Why does a firm at the Bertrand equilibrium have no incentive to increase its price (holding constant its opponent's strategy)?