Question

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) On Game Days:

The hotel price ph = 80

Demand is described by the demand curve q = 100−p

The quantity that is demanded at this price is q = 100 - 80 = 20 units

The quantity demanded is found out by putting the value of price ph in the demand function.

(b) On Non Game Days:

Demand is described by the demand curve q = 60 − 2p.

So, the inverse demand curve on non-game-days is found out by solving for price

q = 60 − 2p,

2p = 60 - q

p = 30 - q/2

Assuming that the price on game days is ph = 80 as above, the price that would induce the same quantity demanded on non-game-days as on game days is:

When the price is ph 80 on game days, the quantity demanded is 20 units. So, for 20 units to be demanded on non-game days, we put this quantity in the demand function and solve for the price.

Demand curve for non game days q = 60 − 2p

20 = 60 - 2p

2p = 60 - 20

p = 40/2 = ph 20

(c) The demand curves on game days can be plotted from the demand function

The demand function is: q = 100−p

Price	Quantity
100	0
90	10
80	20
70	30
60	40
50	50
40	60
30	70
20	80
10	90
0	100

We find these quantities by substituting price in the demand function above. Plotting these points on a graph:

The demand curves on non game days can be plotted from the demand function

The demand function is: q = 60 − 2p

Price	Quantity
30	0
20	20
10	40
0	60

We find these quantities by substituting price in the demand function above. Plotting these points on a graph:

(d) The consumer surplus  in this market on non-game-days when the price is 20 is shown by the area of the red triangle in the graph:

Consumer Surplus = 1/2 * Base * Height

= 1/2 * 20 * (30-20)

=1/2 * 20 * 10

= 100

The consumer surplus  in this market on game-days when the price is 20 is shown by the area of the red triangle in the graph:

Consumer Surplus = 1/2 * Base * Height

= 1/2 * 80 * (100-20)

=1/2 * 80 * 80

= 3200

(e) 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.” is not correct because the demand function for both game and non-game days is different. The quantity demanded for hotel price on game days is higher than the quantity demanded for hotel-price on non-game days. For example, on non game days, atprice 30, the quantity demanded is 0 whereas on game days, at price 30, the quantity demanded is 70 so the consumer surplus would also be different.