Question

The Hotel Madrileà ±a, a small Spanish hotel, is considering lowering its room rates to increase occupancy during the low season. At the present time, the price of its rooms in U.S. currency is $100 per night, and it rents an average of 25 rooms each night.

a. Find the new quantity of rooms rented per night if the Hotel Madrileà ±a low ers its price to $80 and its price elasticity of demand is -1.5.

b. After the Hotel Madrileà ±a lowers its price, a little pensià ³n across the street lowers its room rate from $35 to $30 per night. Find the new quantity of rooms rented per night for the Hotel Madrileà ±a after the pensià ³n lowers its price if the cross price elasticity between the price of the pensià ³n's rooms and the quantity demanded of the Madrileà ±a's rooms is 1.0. (Hint: Use the num ber you found in part (a) as Q, in this problem.)

c. What will be the final effect of the price decreases in parts (a) and (b) on Hotel Madrileà ±a's total revenue?

Answer 1

(a)

Percentage change in price:

$=\frac{80-100}{100}\times100=-20$%

Percentage change in quantity:

$=\frac{Q_2-25}{25}\times100=4Q_2-100$

PED= Percentage change in quantity divided by percentage change in price.

$-1.5=\frac{4Q_2-100}{-20}$

$\implies Q_2=32.5=33$

(b)

Cross price elasticity of demand is given by percentage change in quantity of X divided by percentage change in price of Y.

Percentage change in quantity of X:

=$\frac{Q_2-33}{33}\times100=3.03Q_2-100$

Percentage change in price of Y:

$=\frac{35-30}{35}\times100=14.3$

$\implies 1=\frac{3.03Q_2-100}{14.3}$

$Q_2=37.72=38.$

(c)

The total revenue of hotel madrilena will increase.