PanCakes Creations is considering franchising its single brand of pancakes to stall-holders on the Zandvoort beach, which is 5 kilometers long. PanCakes Creations estimates that on an average day there are 1000 sunbathers evenly spread along the beach and that every sunbather will buy one pancake per day given that they cost no more than €5. The effort of getting up from the sand to get a pancake and return to the sunbed is estimated at 25 cents for each ¼ kilometer the sunbather is from a stall. Every pancake costs 50 cents to make and it costs €40 per day to operate a stall no matter how many pancakes it makes.
a. Assume that PanCakes Creations award a franchise to only one stall-holder. This beach holder locates its stall in the center of the beach. Write down the stall's demand function for pancakes as a function of price.
b. Assume that the franchise contract needs the stall-holder to cater to all consumers on the beach. What price will the stall-holder charge and what will be its profits?