Suppose an ocean-front hotel rents rooms. In the winter, demand is: P_1 = 80 - 2Q_1 with marginal revenue of: MR_1 = 80-4Q_1. However, in the summer, demand is: P_2 = 140 - 2Q_2 with marginal revenue of: MR_2 = 140-4Q_2. Furthermore, suppose the hotel's marginal cost of providing rooms is MC = 20 + 2Q, which is increasing in Q due to capacity constraints. Suppose the hotel engages in peak-load pricing. During the winter, the profit-maximizing price is S and the profit-maximizing quantity is rooms. (Enter numeric responses rounded to two decimal places.)

Question

Andrew Chen

Business

21 May, 05:32

Suppose an ocean-front hotel rents rooms. In the winter, demand is: P_1 = 80 - 2Q_1 with marginal revenue of: MR_1 = 80-4Q_1. However, in the summer, demand is: P_2 = 140 - 2Q_2 with marginal revenue of: MR_2 = 140-4Q_2. Furthermore, suppose the hotel's marginal cost of providing rooms is MC = 20 + 2Q, which is increasing in Q due to capacity constraints. Suppose the hotel engages in peak-load pricing. During the winter, the profit-maximizing price is S and the profit-maximizing quantity is rooms. (Enter numeric responses rounded to two decimal places.)

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Answers (1)

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Parker Costa · Answer 1

The ocean-front hotel maximize the rent at 10 rooms at a price of 60 each

Explanation:

We have to calculate to maximize the winter peak:

we maximize at marginal revenue = marginal cost

MR = 80 - 4q

MC = 20 + 2q

80 - 4q = 20 + 2q

60 = 6q

10 = q

Now we deteminate the cost of a room per night:

P = 80 - 2q = 80 - 2 (10) = 60