Consider a market where the price of the production is determined by p=60-Q. Initially there are Three Firms which all produce the same product. All three firms have zero marginal cost and zero fixed cost. In Nash equilibrium, all firms produce the same quantity q*.
a. Given that firms 2 and 3 both produce q*, find Firm 1's best response q1 as a function of q*.
b. In equilibrium, Firm 1's choice q1 equals q* as well. Use this condition, together with the Firm 1's best response function found in the above to solve for q*. How much profit would each firm earn in Nash equilibrium?
c. If the three firms could form a single monopoly with the same zero production cost, how much would this monopolist firm produce? Verify if this monopolistic firm would earn more profit than what the three firms earned in total under oligopoly.