Question

1. There are only two firms producing identical goods. Each firm has the cost structure TCi = 2qi2 + 40qi + 11552 which makes the firm’s MCi = 4qi + 40 for i = 1,2 for the two firms. These are the only two firms in the market where the MARKET demand for the good = P = -3Q+ 800.

a) Explain why each firm producing q1 = q2 = 47.5 generates the monopoly outcome. Find the market price and firm profit of each firm for this situation. (2 points)
b) Show that if firm 1 sticks to the monopoly quantity, but firm 2 produces q2 = 59.5, then firm 2 makes more profit that at their monopoly quantity. (2 points)
c) Write the matrix for a game where the strategies for each firm are “produce 47.5” and “produce 59.5”. The numbers from (a) and (b) will help you fill in some of the payoffs but others will take some more calculation. Explain why the numbers in your game are consistent with each firm producing q = 47.5 being the monopoly outcome. (2 point)

d) Explain why the game is a prisoner’s dilemma. (1 point)

Answer 1