# 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?

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