Question

A monopolist faces two totally separated markets with inverse demand p=100 – qA and p=160−2qB respectively. The monopolist has no fixed costs and a marginal cost given by mc= 2 /3 q Find the profit maximizing total output and how much of it that is sold on market A and market B respectively if the monopoly uses third degree price discrimination.
a) What prices will our monopolist charge in the two separate markets?

Answer 1

a

For monopoly must be $MC=p$

For firm A

$$\frac{2}{3}Q=100-Q_A$$

$$\frac {4}{3}Q_A=100$$

$$Q_A=75$$

$$p=25$$

For firm B

$$\frac{2}{3}Q_B=160-2Q_B$$

$$\frac {8}{3}Q_B=160$$

$$Q_B=60$$

$$p=100$$

b

$$Q_A=100-p$$

$$Q_A^/=-1$$

$$E_A=Q_A^/\frac{p_A}{Q_A}$$

$$E_A=-\frac {25}{75}=-\frac{1}{3}$$

$$Q_B=80-0.5p$$

$$Q_B^/=-0.5$$

$$E_B=-0.5 \frac{60}{100}=-0.3$$

The absolute values ​​of elasticity at the points characteristic for equilibrium in these markets are mutually inverse to each other.