An entrepreneur is considering how many limousines to purchase when he starts up a limousine service. Below are his estimates of the number of limousine rentals the service will make during a year, depending on the number of limousines available. After paying all non-interest expenses, the owner expects to net $10 per rental. Each limousine costs $50,000. How many limousines should he purchase if the real interest rate is 4.5%?

Question

An entrepreneur is considering how many limousines to purchase when he starts up a limousine service. Below are his estimates of the number of limousine rentals the service will make during a year, depending on the number of limousines available.  After paying all non-interest expenses, the owner expects to net $10 per rental. Each limousine costs $50,000. How many limousines should he purchase if the real interest rate is 4.5%?

Quizplus · Accepted Answer

Since the additional number of rentals (marginal product), is diminishing when more limousines are purchased, the value of the marginal product is also diminishing. While the first limousine adds 350 rentals per year (350 - 0), the second limousine adds only 300 rentals per year (650 - 350) and so forth. The marginal value of marginal product is therefore: $3,500 for the first limousine (350 × $10), $3,000 for the second limousine (300 × $10), $2,500 for the third limousine (250 × $10), $2,000 for the fourth limousine (200 × $10), and $1,500 for the fifth and final limousine (150 × $10). Since the annual interest cost of each limousine is $2,250 (4.5% × $50,000), the value of marginal product exceeds $2,250 for the first three limousines but not for the fourth, so 3 limousines should be purchased.

An Entrepreneur Is Considering How Many Limousines to Purchase When