Question

Consider a hotel which can supply an unlimited number of hotel rooms at the constant marginal cost c = 20 per room per night, so that the hotel’s total cost function is given by C(q) = 20q.1 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.

First suppose that the hotel acts as a price taker.

(a) What does it mean for the hotel to act as a price taker? What condition determines a price taker’s optimal supply decision?

(b) Assuming the hotel acts as a price taker, what will be the equilibrium price and quantity sold on game days? What about on non-game-days? (Remember, the hotel’s marginal cost is constant!)

(c) Briefly discuss, without solving, how your results in (b) would change if the hotel instead had increasing marginal costs (say for example MC(q) = qrather than MC = 20).

Answer 1

(a).Acting as a price taker means taking price as given.

Optimal decision occurs when:

P = MC

Since P is given, P is marginal revenue also.

(b).

For game days:

P = MC = 20

100 - q = 20

q = 80

For non- game days:

P = MC = 20

q = 60 - 2(20) = 20

(c).

With increasing marginal costs:

P = MC(q)

This implies q will be less than the case with constant MC.

Reason: MC is rising in q. More q will reduce profit margin by marginally more significant amount than before.