Question

If the price elasticity of demand for tickets to a dance performance

of the Alvin Ailey American Dance Theatre is -1.2 for any quantity

of tickets sold, what would happen to the number of tickets sold if

the price were lowered from $100 to $90, if the quantity demanded at

$100 is 500 tickets? (HINT: Round your answer to the nearest whole

number.) Compute the total revenues for each of the two prices.

What is the (approximate) marginal revenue of the additional tickets

sold at the lower price? If Alvin Ailey is deciding between the two

ticket prices based on expected profits, which should they choose?

Repeat this exercise for a price elasticity of demand of -0.25. Does

the decision of Alvin Ailey change? Explain.

Answer 1

Price elasticity of demand = -1.2

Price elasticity = ∆Q/∆P x P/Q

P= 100 ,P1 = 90 ∆P = 90-100 = -10

Q = 500, Q1 = ? ∆Q = Q1 - Q

-1.2 = ∆Q / (-10) x 100/500

- 1.2 x (-10) x 500 = ∆Q x 100

6000/100 = ∆Q

∆Q = 60

Q1 - 500 = 60

Q1 = 560

Quantity Demanded at $90 is 560 units. This means that when price falls from $100 to $90 , Quantity Demanded rises from 500 to 560 units.

Price	units	Total revenue = price x Quantity	Marginal revenue = ∆TR/∆Q
100	500	50000	-
90	560	50400	(50400-50000)/(560-500) = 400/60 = 6.67

In order to increase its profit, firm must choose low price as the demand is elastic.

When price elasticity is - 0.25

Price elasticity = ∆Q/∆P x P/Q

P= 100 ,P1 = 90 ∆P = 90-100 = -10

Q = 500, Q1 = ? ∆Q = Q1 - Q

-0.25= ∆Q / (-10) x 100/500

- 0.25 x (-10) x 500 = ∆Q x 100

1250/100 = ∆Q

∆Q = 12.5

Q1 - 500 = 12.5

Q1 = 512.5

Quantity Demanded at $90 is 512.5 units. This means that when price falls from $100 to $90 , Quantity Demanded rises from 500 to 512.5 units.

Price	units	TR	MR
100	500	50000
90	512.5	46125	-310

Here demand for the product is inelastic, therefore in order to earn more profit, firm must keep price high. At low price marginal revenue is Negative.