Instructions: Answer all parts of the following exercise. Question: Let's return to Tullahassee hotel market we considered in Problem Set 1, but now from the perspective of a hotel manager. Consider a hotel which can supply an unlimited number of hotel rooms at the constant marginal cost c=20 per foom per night, so that the hotel's total cost function is given by C(q)=20q. Assume that demand for hotel rooms in Tallahassee takes two possible values: on game days, demand is described by the demand curve q=100−p, while on non-game-days demand is described by the demand curve q=60−2p. Next suppose that the hotel also acts as a monopolist on non-game-days. We want to determine the hotel's optimal quantity and price on non-game-days. (h) Using the MR = MC optimality condition for a price-setting firm, find the hotel's optimal quantity on non-game-days. (i) What will be the hotel's price on non-game-days? And how much profit will the hotel earn? (j) Show that these quantity and price choices satisfy the margin-elasticity rule. That is, using the hotel's optimal non-game-day prices and quantities, verify that P−MC/P = 1/|ϵ|
Where ϵ is calculated using the hotel's non-game-day demand curve. Bonus: Suppose I tell you that another hotel (a profit-maximizing local monopolist in Thomasville, Georgia) sets a game-day price of p=40, at which the price elasticity of demand is ϵ = -4/3. What is this hotel's marginal cost?