Question

The demand plan for hotel rooms is as follows: Price (dollars per night) Quantity demanded (millions of rooms per night) 200 100 250 80 400 50 500 40 800 25 1000 20 a. What happens to the total income if the price drops from $400 to $250 per night? Calculate the price elasticity of demand for that price range and indicate what type of elasticity occurs.

Answer 1

To calculate the total income, we need to multiply the price by the quantity demanded.

Before the price drops from $400 to $250 per night:
Total income = price x quantity demanded
= $400 x 50 million rooms per night
= $20,000 million

After the price drops to $250 per night:
Total income = price x quantity demanded
= $250 x 80 million rooms per night
= $20,000 million

There is no change in the total income when the price drops from $400 to $250 per night.

To calculate the price elasticity of demand for that price range, we use the formula:
Elasticity = Percentage change in quantity demanded / Percentage change in price

Percentage change in quantity demanded:
= (New quantity demanded - Old quantity demanded) / Old quantity demanded
= (80 - 50) / 50
= 30 / 50
= 0.6

Percentage change in price:
= (New price - Old price) / Old price
= (250 - 400) / 400
= -150 / 400
= -0.375

Elasticity = 0.6 / -0.375
= -1.6

The price elasticity of demand for the price range from $400 to $250 per night is -1.6. This indicates that the demand is elastic, meaning that a decrease in price leads to a more than proportionate increase in quantity demanded, resulting in increased total income.