Please help with the following homework problem from a game theory in economics class. It is a differentiated-product Bertrand competition problem.

Assume there are only two Thai restaurants in Brighton, Mass. Bamboo and Thai Place. The two restaurants have already set their menus and now only compete by simultaneously and independently choosing their prices, PB and FTP, every month. The two menus are slightly different, so the two restaurants compete in the market for a differentiated good and face the following individual demand curves QB=442PB+PTP QTP=442PTP+PB Suppose that the cost of serving each customer is $8 and is the same for both restaurants. (a) Find the best response functions of Bamboo and Thai Place by maximizing their respective prots. (b) Graph the two best responses in the PBPTp coordinate plane. What is the pure strategy Nash equilibrium of this game? What are the equilibrium quantities and prots? (0) If the two restaurants are owned by the same owner, do you expect that they will charge higher or lower prices compared to those in part (b)? Calculate the prices that the two restaurants will choose in this case. [Hint: The owner will maximize the joint prots of the two restaurants H = 7TB + 7'er \"7113 PB and PTP-] (d) Now suppose instead that Bamboo is able to reduce its costs percustomer to 932 by being a takeoutonly restaurant. The Thai Place keeps its costs at $8. The demand stays the same as before. Recalculate the two best responses and the Nash equilibrium prices, given the change in the cost conditions. What are the equilibrium quantities and prots