Answer to Question #52824 in Microeconomics for Yana

Question

1.) There are only two travel agencies, A and B, offering Brazil World Cup 2014 Vacation Packages (flight, hotel acommodation, game tickets and group excursion). The demand function for Brazil World Cup 2014 Vacation Packages is given by P = 10 000-Q. The marginal cost is constant and it can be expressed by MC ( = ATC ) = $ 2 000.
a) The travel agencies try to coordinate their actions and set the price and quantity like a single monopolist. Once they set this profit maximizing price and quantity, they plan to split the resulting profit equally. What is the profit for each travel agency if they both adhere to the plan?
b) Now, suppose that both travel agencies set price equal to $ 4 000, and then split profit equally. What us the profit for each travel agency?
c)Now the travel agencies have two options: to charge a joint monopoly price as found in part a) or to see their price equal to $ 4 000. Fill in the pay-off matrix that represent these choices (use the template).

Answer 1

1) P = 10 000-Q, MC = ATC = $ 2 000. 
a) If the travel agencies try to coordinate their actions and set the price and quantity like a single monopolist, their profit maximizing quantity will be in the point, where MR = MC, so:
MR = TR' = (P*Q)' = 10000 - 2Q
MC = 2000
10000 - 2Q = 2000
Q = 4000 units.
Profit maximizing price P = 10000 - 4000 = $6000.
The profit for each travel agency if they both adhere to the plan will be:
TP = (P - ATC)*Q/2 = (6000 - 2000)*4000/2 = $8,000,000.
b) If both travel agencies set price equal to $ 4 000 (Q = 10000 - 4000 = 6000 units) and then split profit equally, the profit for each travel agency will be:
TP = (P - ATC)*Q/2 = (4000 - 2000)*6000/2 = $6,000,000.
c) If the travel agencies have two options: to charge a joint monopoly price as found in part a) or to see their price equal to $ 4 000, the pay-off matrix that represent these choices will be:
                    option A       option B
Firm A      $8 million     $6 million
Firm B     $8 million     $6 million