Question

2. Sunny Time Snow Lodge is a resort hotel that has an inverse demand of P = 150 ? Q during the peak season and an inverse demand of P = 74 ? 0.5 × Q in the off season as it is the only resort the stays open during the off season. The marginal cost and average cost for the resort is $50 per night.

(a) Suppose the resort can act as a monopolist, what price would they charge in the peak season and off season? What is the dead weight loss in each situation? What sort of profits can be expected here?

(b) Suppose the resort only has 40 room, does your answer change? How does it change? Does it affect the dead weight loss? Does it affect profits?

(c) What happens when another hotel starts to stay open during the off season? Explain in words.

(d) The hotel estimates their new inverse demand as P = 74 ? Q. How does your answer differ from part (b) (hint: Think dead weight loss and profits)?

Answer 1

in mathematical terms, if the demand function is f(P), then the inverse demand function is f?1(Q), whose value is the highest price that could be charged and still generate the quantity demanded Q.[This is to say that the inverse demand function is the demand function with the axes switched. This is useful because economists typically place price (P) on the vertical axis and quantity (Q) on the horizontal axis.

The inverse demand function is the same as the average revenue function, since P = AR.

To compute the inverse demand function, simply solve for P from the demand function. For example, if the demand function has the form Q = 240 - 2P then the inverse demand function would be P = 120 - 0.5Q.