Consider a homogeneous product industry with inverse demand given by P = 100 - 2Q. Variable cost is given by C = 10Q. There is currently one incumbent firm and one potential competitor. Entry into the industry implies a sunk cost of F.

i) Determine the Incumbents optimal in the absence of potential competition.

ii) Suppose the entrant takes the incumbent output choice as a given. Show that the entrants equilibrium profit is decreasing in the incumbent output.

iii) What output should the incumbent firm set in order to deter entry?