Monopoly producer of this product. Assume that the inverse demand function for t
ID: 1199083 • Letter: M
Question
Monopoly producer of this product. Assume that the inverse demand function for this product is: P(Q) = 800 Q and your cost functions are TC(Q) = 50Q; MC(Q) = 50. What is the MR function? What is the profit-max quantity and price? What is the MR at that level of output? What is the Monopoloy pofit? What is the "efficient" level of production? What is the price at the ecient level? Graph the marginal revenue, marginal cost, and demand curves, and show the area that represents deadweight loss due to monopoly on the graph. Calculate the amount of deadweight loss.
Another firm has entered the market.
Assume this rm faces the same costs of production as you do, and that the market demand is the same except that now, Q = Q 1 + Q 2 . Suppose that you and this other rm play “Cournot”. Write the marginal revenue functions of each rm as functions of Q 1 and Q 2 What are the “best-response” functions for each rm? Cournot equilibrium: . What is the market price? What are the prots for each firm?
Hello, the second part of the question is what I need help with. Not sure I understand how to do the "Cournot" and best response once another firm enters the market and its no longer a monopoly
Explanation / Answer
Once the 2nd firm enters the market the profit function for Firm1 would be [800 - (Q1 + Q2)]* Q1 - 50Q1
= 800Q1 - Q12 - Q1Q2 - 50Q1
Firm1's total revenue 800Q1 - Q12 -Q1Q2.
Firm1's marginal revenue = 800 - 2Q1 - Q2 = 0
Maximising profits we get 800 - 2Q1 - Q2 - 50 = 0.
750 - 2Q1 - Q2 = 0
Q1 = (750 - Q2) / 2 (Reaction curve of firm1).
Firm 2's profit function = [800 - (Q1 + Q2)]Q2 - 50Q2
Firm 2 's total revenue = 800Q2 - Q1Q2 - Q22 = 0
Firm2's marginal revenue = 800 - Q1 - 2Q2 = 0.
800Q2 - Q1Q2 - Q22 - 50Q2
Maximising profits we get 800 - Q1 - 2Q2 - 50.
750 - Q1 - 2Q2 = 0.
(750 - Q1) / 2 = Q2.(Firm2's reaction function)
Substituting firm1's reaction function in firm2's reaction function we get
Q1 = [750 - (750 - Q1) / 2] / 2
Solving we get Q1 = Q2 = 250.
Price charged in the counot model = 800 - (250 + 250) = 800 - 500 = 300.
Profit for firm 1 = (300 - 50) * 250 = 250 * 250 = 62500.= profit for firm2
Total profit in the market = 62500 + 62500 = 1,25,000.