A consumer has two basic choices: rent a DVD movie for $4.00 and spend 2 hours watching it, or spend $13 for a miniature golf game that takes 1 hour. If the marginal utilities of the movie and the miniature golf game are equal, and the consumer values time at $12 an hour, the rational consumer will most likely
A) rent the movie instead of playing miniature golf.
B) play miniature golf instead of renting the movie.
C) be indifferent between the movie and the miniature golf game.
D) not have enough basis for making a utility-maximizing decision.

Question

Quizplus · Accepted Answer

To determine the best choice, we need to calculate the total utility per dollar spent for each option. 
For the DVD movie, the total utility is:
TU = 2 hours * MU(movie) = 2 hours * x 
where x is the marginal utility of the movie. 
For the miniature golf game, the total utility is: 
TU = MU(miniature golf) * (13/12) = x * (13/12)
where (13/12) represents the total time spent (including the 1 hour of golf and the 1/12 of an hour spent earning the $1 extra to spend on golf).

Since the marginal utilities of the movie and the miniature golf are equal, we can set these two equations equal to each other:

2x = (13/12) x 
x = 0.65

Now we can calculate the total utilities per dollar spent:

TU/Dollar for DVD movie = (2 hours * 0.65) / $4 = 0.1625 
TU/Dollar for miniature golf = (0.65 * 13/12) / $13 = 0.05

The TU/Dollar for the DVD movie is greater, so the rational consumer would choose to rent the movie instead of playing miniature golf. Option B is incorrect. Option C is also incorrect because we have found that the consumer does not have equal utility from both choices. Option D is incorrect because we have made a utility-maximizing decision based on the information provided.

A Consumer Has Two Basic Choices: Rent a DVD Movie