Answer (e) and (f).

Firm A manufactures velvet hats and agrees to sell them through two Baltimore retail stores at a wholesale price of $10, making a profit of $6 on each hat. Demand for these hats is Q=30-p. Retailers compete in a Bertrand game.

(a) Is the $10 wholesale price the optimal wholesale price for the manufacturer? If not, what is the optimal wholesale price?

Each retailer (but not firm A itself) can pay $50 to endorse Firm A's hats. Demand for these hats is Q=40-p if endorsed. Note that demand is enhanced as long as one of the retailers pays the endorsement fee.

(b) Will either retailer pay the endorsement fee?

Now assume Firm A decides to sign a contract with one of the retailers, making it the exclusive retailer of its products in Baltimore. Continue to assume that Firm A charges a whole price of $10 per hat and makes a profit of $6 on each hat. (c) What is the retail price for the exclusive retailer?

(d) What is the optimal wholesale price under exclusive contract?

Now assume Firm A sign a franchise agreement with the exclusive retailer. Firm A will receive a franchise fee F from the exclusive retailer.

(e)What is the optimal wholesale price and retail price under Franchise agreement?

(f) What is the optimal franchise fee?