Question

Problems and Exercises 1. Calculate the price elasticity for each of the following. State whether price elasticity of demand is elastic, unit elastic, or inelastic. Will revenue rise, decline, or stay the same with the given change in price? The price of pens rises 5%; the quantity demanded falls 10%. , a. The price of a Boston Red Sox baseball game rises from S10 to S12 a game. The quantity of tickets sold falls from 160,000 tickets to 144,000 b. The price of an economics textbook declines from $50 to $47.50. Quantity demanded rises from 1000 to 1075. c. The price of water beds rises from $500 to $600. Quantity demanded falls from 100,000 to 80,000. d.

Answer 1

Working notes:

(i) Using Point Estimate, Elasticity = % Change in Quantity / % Change in Price

(ii) Using Midpoint Method, Elasticity = (Change in Quantity / Average Quantity) / (Change in Price / Average Price)

(iii) Demand is elastic (inelastic) if absolute value of elasticity is higher (lower) than 1. Demand is unit elastic if absolute value of elastic is 1.

(iv) With elastic demand, a rise (fall) in price will lower (raise) revenue. With inelastic demand, a rise (fall) in price will raise (lower) revenue. With unit elastic demand, a change in price will not change revenue.

(a)

Elasticity = % Change in Quantity / % Change in Price = -10% / 5% = -2

Therefore, demand is elastic and a rise in price will decrease revenue.

(b)

Elasticity = (Change in Quantity / Average Quantity) / (Change in Price / Average Price)

= [(144,000 - 160,000) / (144,000 + 160,000)] / [(12 - 10) / (12 + 10)]

= (-16,000 / 304,000) / (2 / 22)

= -0.58

Therefore, demand is inelastic and a rise in price will increase revenue.

(c)

Elasticity = (Change in Quantity / Average Quantity) / (Change in Price / Average Price)

= [(1075 - 1000) / (1075 + 1000)] / [(47.5 - 50) / (47.5 + 50)]

= (75 / 2075) / (-2.5 / 97.5)

= -1.41

Therefore, demand is elastic and a fall in price will increase revenue.

(d)

Elasticity = (Change in Quantity / Average Quantity) / (Change in Price / Average Price)

= [(80,000 - 100,000) / (80,000 + 100,000)] / [(600 - 500) / (600 + 500)]

= (-20,000 / 180,000) / (100 / 1100)

= -1.22

Therefore, demand is elastic and a rise in price will decrease revenue.