Reference no: EM131090270

You are in charge of managing a small group of rental car offices. Some customers are Costco and/or AAA members (“cardholders”), and these customers have been getting a discount on the weekly rate for the economy cars that you rent. At present, 100 customers per week rent cars and get the discount, and another 100 customers per week rent cars without getting a discount. These numbers are not expected to change for the time being. There has been a debate inside the company about whether there should be a charge for mileage driven during the week. The estimated wear and tear on the vehicles (depreciation) is $1.00 per mile driven, and the company has had a mileage charge of this amount (the marginal cost of driving) for all vehicles rented. Some people believe that there should not be any mileage charge at all. A few people believe the mileage charge should be $1.50 per mile. Based on past experience, the demand curves for the miles driven by a typical cardholder and the miles driven by a typical non-cardholder can each be approximated by a straight line. For the cardholders, the estimate is that, if there were no mileage charge, a cardholding renter would typically drive 800 miles during a one week rental. For non-cardholders the estimate is 450 miles. For cardholders, if the mileage charge reached $2.00 per mile, no cardholder would want to drive any miles. For non-cardholders, the mileage charge would have to reach $3.00 per mile for the quantity demanded to fall to zero. Draw a demand curve for a typical cardholder for miles to be driven during one week, and do the same for a typical non-cardholder. For the three different mileage charges under consideration--$0.00, $1.00, and $1.50—determine the maximum weekly rental charge that could be assessed without a typical cardholding customer dropping out of the market. Do the same for a typical non-cardholding customer. For the time being, which of the mileage charges, when combined with a weekly rental rate, would be best for the company? Would it still be wise to offer a discount for the cardholders? What would be the weekly rental rate for a cardholder, and what would be the weekly rental rate for a non-cardholder? Show all your work. Remember that the area of a triangle is ½ x the base x the height.