A car wash company charges $8 per car. The car wash company rents the space from a gas station, and pays $5 for each car to the gas station. The car wash company washes 300 cars per week on average. If the company increase the price to $9, it will serve 270 cars. Determine the price elasticity of demand when the price is $8? What is the change in revenue when prices change from $8 to $9? What happens to the revenues of the gas station after the price change? If the gas station owned the car wash company, would it set the price to $8 or $9 per car? Why?

A car wash company charges $8 per car. The car wash company rents the space from a gas station, and pays $5 for each car to the gas station. The car wash company washes 300 cars per week on average. If the company increase the price to $9, it will serve 270 cars. Determine the price elasticity of demand when the price is $8? What is the change in revenue when prices change from $8 to $9? What happens to the revenues of the gas station after the price change? If the gas station owned the car wash company, would it set the price to $8 or $9 per car? Why?

 

 

Answer:

i) Price Elasticity of Demand = Percentage Change in Quantity Demanded / Percentage change in Price

Given : Original Quantity (Q1) = 300 cars

New Quantity (Q2) = 270 cars

Original Price (P1) = $8

New Price (P2) = $9\Delta Q/ Q_{1} * P_{1}/ \Delta P

Price Elasticity = \Delta Q/ Q_{1} * P_{1}/ \Delta P

= 270 – 300 / 300 * 8 / 9 – 8

= -30 /300 * 8/ 1

= -0.8

ii) Revenue = No. of units * Selling Price per unit

Revenue when the price was $8 =300 * $8 = $2400

Revenue when the price is $9 = 270 * $9 = $2430

Change in Revenue = $2430 – $2400 = $30

iii) Revenue = No of units * Amount per unit ($5 being paid by the carwash company)

Revenue earned by gas station when the price was $8 = 300 * $5 =$1500

Revenue earned by gas station when the price is $9 = 270 * $5 = $1350

Change in Revenue = $1350 – $1500 = – $150.

Loss of $150 for the gas station after the price change.

iv) If the gas station owned the car wash company, it would set the price to $9 as the revenue generation is more in the case of $9 ($2430) than $8 ($2400).

Asked on February 13, 2018 in economics.
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