Ray's Diner offers traditional deli foods to lunch customers in the local market. On its lunch menu, Flo's Eatery offers more variety. The two establishments compete in a Bertrand market structure with differentiated products. Ray's Diner is confronted with the demand curve for its daily special given by qR = 100 - 10pR + 5pF , where pR is the price for the daily special at Ray's Diner and pF is the price for the daily special at Flo's Eatery. Flo's faces the demand curve for the daily special given by qF = 200 - 10pF + 2pR. The cost of providing the special at Ray's Diner is CR = qR, while the cost of providing the special at Flo's Eatery is CF = 3qF.
a. Identify for Ray's Diner the profit function from providing the special.
b. Identify for Ray's Diner the reaction function to the Eatery's price for the special.
c. Identify for Flo's Eatery the reaction function to the Diner's price for the special.
d. Identify the equilibrium price charged for a special at Ray's Diner and Flo's Eatery.