"Purple Dream" has the monopoly on the production of purple light-emitting diodes (LEDs). It faces geographically separated markets, market 1 and 2. The demands are q_A = 1 - p_A and q_B = 1/2 - p_B, respectively. The transport and production costs are set to zero.

1. Assume that the firm chooses to set a uniform price across the two markets. What is the profit maximizing uniform price? What are the quantities sold on the two markets at this price?

2. Assume that the firm uses third-degree price discrimination. What are the profit maximizing prices and quantities on the two markets?

3. Calculate consumer surplus and profit under a uniform price and under third-degree price discrimination. Compare the two situations and comment on the result.

4. Does the result from question 3 hold generally? How would the results change if q_B = 1/3 - p_B?