Question

2. 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.

(a) Suppose that the hotel price on game days is ph = 80. What quantity is demanded at this price?

(b) Find the inverse demand curve on non-game-days. Assuming that the price on game days is ph = 80 as above, what price would induce the same quantity demanded on non-game-days as on game days?

(c) Plot the demand curves on game days and on non-game-days. Pay careful attention to the price and quantity intercepts for both curves.

(d) Assuming the price on non-game-days is as you found in (ii), what is consumer surplus in this market on non-game-days? What is consumer surplus on game days?

(e) Suppose that you encounter the following claim: “Because the hotel price is higher on game days than on non-game-days, consumer surplus in the hotel market must be lower on game days.” What is wrong with this claim?

Answer 1

a) price of the hotel on the game day = 80

demand curve on the game day q = 100 - p

putting p = 80

(Quantity demanded on the game day ) q = 100 - 80 = 20

b) demand curve on non game day q = 60 - 2p

now , inverse demand curve

q - 60 = - 2p

60 - q / 2 = p ( INVERSE DEMAND CURVE ON THE NON GAME DAY )

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

if quantity demanded = 20 as per in the part (a) then , price should be ( by using inverse demand curve )

p = 60 - 20 / 2 = 40 / 2 = 20 rupees.

c) the graphs will not intercepts anywhere.

d) on the game day 100 - p = q

putting p = 0 and then putting q = 0

then q = 100 and p =100 respectively

consumer surplus 1/2 * 100 * 100 = 5000

similarly on non game days 1/2 * 60 * 30 = 900

e) the consumer surplus will not be lower in the case of game days as shown above or we can say because the prices of the hotel on game days are higher than non game days.