4. [8 points] Alan and Bella are two ice cream sellers. They each need to set the price for a scoop of ice cream. Alan's price is denoted Pa and number of scoops sold at that price Qa. Bella's price is denoted Pb and number scoops sold at that price Qb. It costs each Alan and Bella $1 to make a scoop of ice cream, assume they can always make ice cream if a customer requests it.

a) An initial market survey shows that the relationship between prices and quantities are Qa = 16 2Pa + 2Pb and Qb = 24 2Pb + 4Pa. What is the Nash equilibrium? [4 points]

b) Alan decides that he will only sell double scoops of ice cream and chooses his price rst. Pa2 is the price of a double scoop ice cream and Qa2 is the quantinty of double scoops sold at that price. The relationship between prices and quantities is now Qa2 = 8 Pa2 + 2Pb and Qb = 24 2Pb + 2Pa2.

What is the new Nash equilibrium? Does this decision earn Alan more prot? [4 points]