competitive analysis question

3. Population growth and market structure. (18 points) Consider the market for widgets in a country with a population of 200 million. Total demand is given by D = 200(60 - p). Production technology is given by a cost function C = F + cq, where F = 1000 and c = 30. Suppose the Cournot model provides a good description of the way firms compete. Finally, suppose there is a large number of potential competitors. (a) Determine the free-entry equilibrium number of firms. (6 points) (b) Suppose that the country's population increases by 50%. How will this impact the number the number of firms in equilibrium? Compute the equilibrium number of firms and explain carefully the intuition behind your calculation (if it changes by 50% or not and why). (6 points) (c) Suppose that, due to the larger market, each firm incurs in additional advertisement expenses, leading to an increase of 25% in its fixed costs. How do you expect this to impact the number of firms in equilibrium? Compare with your answers in (a) and (b) and explain the intuition behind your result. (6 points)