Question

A firm sells in two markets and has constant marginal costs of production equal to $2 per

unit. The demand and marginal revenue equations for two markets are as follows:

MARKET I MARKET II

P1 = 14 – 2Q1 PII = 10 – QII

MRI = 14 – 4QI MRII = 10 – 2QII

Using third-degree price discrimination, what are the profit maximizing prices and

quantities in each marker? Show that greater profits results from price discrimination than

would be obtained if a uniform price were used.

Answer 1

$$TR_1=14Q_1-2Q_!^2$$

$$\pi_1=TR_1-TC_1=14Q_1-2Q_1^2-2Q_1=12Q_1-2Q_1^2$$

$$\frac {\delta {\pi_1}}{\delta Q_1}=12-4Q_1$$

$$Q_1=3$$

$$p_1=8$$

$$TR_2=10Q_2-Q_2^2$$

$$\pi_2=8Q_2-Q_2^2$$

$$\frac{\delta \pi_2}{\delta Q_2}=8-2Q_2$$

$$Q_2=4$$

$$p_2=6$$