Please show all steps and workings: Horizontal Cournot Merger

Consider a homogenous good industry with five identical firms. Inverse demand in this market is given by p = 50 -1/2Q:

All n firms have the same constant marginal cost c = 10. Suppose firms compete in quantities.

(a) Calculate the Nash equilibrium in quantities. Give each firms profit.

(b) Suppose a merger between two firms in this industry decreases the marginal cost of the merged company to a level of c with 0 1. Derive the condition under which a two-firm merger is profitable. Briefly discuss this condition. .

(c) Show that the profit of the non-merging firms increases for = 1/2 and decreases for = 1/4 due to the merger. Explain the difference.

(d) The competition authority (CA) is confronted with the merger proposal of (b). The companies claim that the merger will reduce their marginal cost by 50 percent. Should the CA allow the merger if their aim is to:

(i) maximise total welfare

(ii) maximise consumer surplus

Explain the difference