Suppose the demand for widgets is p(Q) = 100 - Q.Initially, there are two firms producing widgets, each with cost function C(q) = 40q, and these firms engage in Cournot quantity competition.Now suppose these two firms propose to merge so as to reduce their marginal costs to 0

C_M(q) = cq.

a)What is the equilibrium price and profit of each firm before the merger?

b)In terms of c, what is the price and profit of the merged firm after the merger?

c)For what values of c is the merger profitable?

d)For what values of c does the merger increase consumer surplus?

e)Are there values of c for which the merger decreases consumer surplus, but it increases social welfare (which is the sum of firm profits and consumer surplus)? Explain.