Question

A Monopolist selling a cell phone in two separate markets. They must decide how much to sell in each market in order to maximize their total profits.

The demand in the Brazilian Market is :  QBrazil = 120 – 10PBrazil

The demand in the United States Market is:  QUSA = 60 – 20PUSA

If Total Cost is: TC = 90 + 2(QUSA +QBrazil)

Calculate the Price and Quantity if the Monopolist Maximized their profit and sells in both markets? (8 Points)

Calculate the Profit if he Monopolist Maximized their profit and sells in both markets? (6 Points)

In the absence of 3rd Degree Price Discrimination and the firm must sell at the same price in both markets, what is the price, quantity and total profit? (6 Points)

Answer 1

Q_Brazil = 120 - 10 p = > P_Brazil = 12 - 1/10 Q_Brazil Q_USA = 60 - 20 p = > P_USA = 3 - 1/20 Q_USA TC = 90 + 2 (Q_Brazil + Q_USA) pi_Brazil = TR - TC = 12 Q_Brazil - 1/10 Q_Brazil^2 - 90 - 2 (Q_Brazil + Q_USA) partial differential pi/partial differential Q_Brazil = 12 - 1/5 Q_Brazil - 2 = 0 1/5 Q_Brazil = 10 Q_Brazil = 50 P_Brazil = 12 - 1/10 times 150 P_Brazil = 7 pi_USA = 3 Q_USA - 1/20 Q_USA^2 - 90 - 2 (Q_Brazil + Q_USA) partial differential pi_USA /partial differential Q_USA = 3 - 1/10 Q_USA - 2 = 0 1/10 Q_USA = 1 Q_USA = 10 P = 3 - 1/20 times 10 P_USA = 2.5 \r\n pi_Brazil = 12 Q_Brazil - 1/10 Q_Brazil^2 - 90 - 2 (Q_Brazil + Q_USA) = 12 (50) - 1/10 (50) ^2 - 90 - 2(50 + 10)