Mike's utility function is U(c, d, h)= 4c + 14d

Question

Mike's utility function is U(c, d, h)= 4c + 14d - d ² - 6h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other citizens of his town, and c is the amount of money he has to spend on other things than gasoline and auto repairs.There are 1,001 identical citizens in Mike's home town.Mike's expenses for gasoline and auto repairs amount to $.50 per hour for the time he spends driving.If Mike believes that his amount of driving won't affect the amount that others drive, how many hours per day will he choose to drive? A)7 B)8 C)6 D)3 E)0.50

Quizplus · Accepted Answer

To maximize his utility, Mike will choose the number of hours driving (d) where the marginal utility of driving equals the marginal cost. The derivative of the utility function with respect to d is 14 - 2d. Setting this equal to the cost of driving, which is 0.50, gives 14 - 2d = 0.50. Solving for d gives d = 6.75. However, since the options are whole numbers, the closest choice is 6.