McRonald's is a new fast food franchise. It can produce burgers at a cost of 2 each. It plans to charge a franchise fee F to whoever wants to open a fast food store with its brand name and then supplies the burgers to its franchisee at a price of w each. The Fast Food Company of Philadelphia is planning to open the first store of McRonald's. It did a market study and found out that the demand for this good is given by D(p) = 100 p.

1. (a)If McRonald's charges the Fast Food Company of Philadelphia w per burger what is the optimal price that the Fast Food Company of Philadelphia should set to sell the burgers to the final consumer? (It is a function of w).
2. (b)What fee F and price per burger w should McRonald's charge to the Fast Food Company of Philadelphia in order to maximize its profits?
3. (c)In light of what you learned on double marginalization, discuss how the optimal w found in b) compares to the marginal cost of McRonald's.