Patxiko, a producer of the famous liquor Patxaran, is the only producer in the whole Basque country. He identifies the following demand for his liquor:

Q = 12, 000 1250P

where P is the price per liter and Q is the quantity expressed in liters. Patxiko's total cost of production is c(Q) = 3.2Q.

(a) (3 points) What is the price P^m and quantity Q^m that maximize Patxiko's profits? Compute the maximized profits ^m . and the consumer surplus CS^m

(b) (3 points) The Basque country is divided between the French side and the Spanish side. Patxiko manages to identify two distinct aggregate demands:

and

Qs = 10, 000 1, 000P

QF = 2000 250P

where Qs and QF are the respective Spanish and French demands as a function of P. Being in the middle of the covid-19 pandemic, the border between France and Spain is closed.

Patxiko is thinking about applying 3^rd degree price discrimination. If so, what price should he charge in each country (call them P_*s and P_*F), and what quantities will he sell (call them Q*s and Q*_F)? Compute the corresponding profit _*SF and the consumer surpluses CS*s and CS*_F.