please write clearly

Bertrand Duopoly

Consider the market for smart phones. Suppose that Apple and Samsung companies are the only players in this market and that the marginal cost of producing a smartphones is the same and equal to $150 for both companies. You can assume that in this question Apple and Samsung compete in their prices.

a.Assuming that Apple and Samsung produce identical products (ie: no product differentiation), find the Nash equilibrium of the smart phone market. You can further assume that both companies begin competing with each other at an initial price of $1,000 per smart phone. Illustrate the best response functions of both companies and the Nash equilibrium of the market.(10 pts)

b.Now suppose that through successful advertising campaigns Apple and Samsung have able to create the impression in the minds of their customers that their products or different (or it might actually be the case that their products are different.). Suppose that the demand for Apple smartphones is given by the equation Qa = 1,000,000 - 0.4 Pa + 0.5 Ps and the demand function for Samsung smartphones is symmetrical, ie: Qs = 1,000,000 - 0.4 Ps + 0.5 Pa where Qa is the amount of Apple smartphones demanded, Qs is the amount of Samsung smartphones demanded, Pa is the price of an Apple smartphone, and Ps is the price of a Samsung smartphone. You can again assume that the marginal cost of production is the same for both companies and is equal to $150 per smartphone.

Given the information above, find the Nash equilibrium in the market for smartphone. Illusrate the best response functions of both companies and the Nash equilibrium of the market.(10 pts)