Exercise 3: Merging Firms Consider a perfectly competitive market with demand given by Qa = 500 - 2P. Let there be 3 firms (indexed by i = 1,2,3), each with a cost function given by C(q;) = 6q: + 497- a) (5 points) Suppose that firms interact in a competitive market. What is the equilibrium price and quantity? b) (10 points) Suppose firms 1 and 2 merge and become a more efficient firm with reduced cost function given by C(qi) = =q;, while firm 3 remains exactly the same. The market is still perfectly competitive. What is the merged firm's output. What is the equilibrium market price and quantity now? c) (5 points) In the scenario of b), what are the market shares of each firm? Comment briefly on the distribu- tion of output between them