Question

Let’s return to Tallahassee 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 room 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.

1. 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) = q rather than MC = 20).

Answer 1

1. Marginal Cost (MC) = 20

Total Cost (TC) = 20q

Demand curve on game days - q = 100 - p

Demand curve on non-game days - q = 60 - 2p

a. Hotel acting as a price taker means that the hotel cannot decide prices on its own i.e. prices are determined by the market forces of demand and supply since the hotel is in perfectly competitive market. A price taker's optimal supply decisions are at the point where the profits are maximized which takes place at the point where price equals the marginal cost.

b. Marginal Cost can be calculated by differentiating the total cost with respect to q which becomes 20. Equilibrium price and quantity can be determined at the point where price equals marginal cost.

On game days:

P = MC

100 - q = 20

q = 80

Putting q = 80 in the demand function:

p = 100 - 80 = 20

On non-game days:

P = MC

(60 - q)/2 = 20

60 - q = 40

q = 20

Putting q = 20 in the demand function:

p = (60 - 20)/2

p = 40/2

p = 20

So, equilibrium price and quantity on game days are 20 and 80 respectively whereas the equilibrium price and quantity on non-game days are 20 and 20 respectively.

c. If marginal cost is not constant then prices will fluctuate along with the marginal costs in order to produce optimally. Prices may initially fall in the short run but may increase with time which will affect the quantity demanded because of its inverse relationship with price.