Suppose an ocean-front hotel rents rooms. In the winter, demand is: P1 110-20, M

Question

Suppose an ocean-front hotel rents rooms. In the winter, demand is: P1 110-20, MR1 110-401 P2 140-202 MR2 140-402 with marginal revenue of: However, in the summer, demand is: with marginal revenue of: 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-maxizing quantity isrooms. (Enter numeric responses rounded to two decimal places.)

Explanation / Answer

P1=110-2Q

TR=P*Q

TR=(110-2Q)*Q

TR=110Q-2Q^2

MR=d(TR)/dQ

MR=110-4Q

MC=20+2Q

Profit maximizing level:MR=MC

110-4Q=20+2Q

6Q=90

Q=90/6

Q=15

P=110-2(15)

P=80

Profit maximizing price=80

Profit maximizing quantity=15

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