You are the manager of a gas station and your goal is to maximize profits.Based on your past experience,the elasticity of demand by Texans for a car wash is −4,while the elasticity of demand by non-Texans for a car wash is −6.If you charge Texans $20 for a car wash,how much should you charge a man with Oklahoma license plates for a car wash?
A) $1.50
B) $15.00
C) $18.00
D) $20.00

Question

Quizplus · Accepted Answer

Since the elasticity of demand for non-Texans is higher, their demand is more sensitive to changes in price. This means that if we increase the price of a car wash for non-Texans, their demand will decrease more than the decrease in demand by Texans if we increase the price for them.

Therefore, we can charge more for non-Texans without a significant decrease in demand. To find the optimal price for the man with the Oklahoma license plates, we can use the price elasticity formula:

Price elasticity of demand = (% change in quantity demanded) / (% change in price)

We know that the elasticity of demand for non-Texans is -6 and we need to find the price that would make the elasticity for the man with the Oklahoma license plate -6 as well. Let x be the price we charge for the man with Oklahoma license plates.

-6 = ((Qd_Oklahoma/Qd_Texans) - 1) / ((x/$20) - 1)

Simplifying this equation, we get:

Qd_Oklahoma / Qd_Texans = 3/2 * (x/20) - 5/2

We know that Qd_Texans will not change since we are only changing the price for the man with Oklahoma license plates. We can assume that Qd_Texans is 1 (for simplicity). So,

Qd_Oklahoma = 3/2 * (x/20) - 5/2

We want to find x when the price elasticity for the man with Oklahoma license plates is -6, so we can use the formula:

Price elasticity of demand = (% change in quantity demanded) / (% change in price)

-6 = ((Qd_Oklahoma/1) - 1) / ((x/$20) - 1)

Simplifying this equation, we get:

Qd_Oklahoma = 6x/5 - 6

Substituting this into our equation for Qd_Oklahoma, we get:

3/2 * (x/20) - 5/2 = 6x/5 - 6

Solving for x, we get:

x = $18

Therefore, we should charge the man with an Oklahoma license plate $18 for a car wash.

You Are the Manager of a Gas Station and Your