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Damian Matthews is busy. He allocates his free time between watching movies and

ID: 1191775 • Letter: D

Question

Damian Matthews is busy. He allocates his free time between watching movies and working out at the gym. The table below shows his utility from the number of times per week he watches a movie or goes to the gym. Damien has 14 hours a week to spend on movies or the gym (think of hours like $ of income here). Each takes 2 hours. Each gym trip takes 2 hours. What bundles of gym visits and movies can Damien consume if he spends 1) all his time in the gym or 2) all his time watching movies? Calculate the marginal utility of each gym visit and movie. Then calculate the Marginal Utility per hour of each activity. How should he allocate his time to maximize his utility?

Explanation / Answer

a. Damien may consume the below stated bundles if he spends all his time going to the

gym and watching movies:

0 gym visits, 7 movies

1 gym visit, 6 movies

2 gym visits, 5 movies

3 gym visits, 4 movies

4 gym visits, 3 movies

5 gym visits, 2 movies

6 gym visits, 1 movie

7 gym visits, 0 movies

b. The given table shows Damien’s marginal utility per gym visit, marginal

utility per movie, marginal utility per hour spent on gym visits, and marginal utility

per hour spent on movies.

Quantity of gym                utility from gym visits     marginal utility per gym visit                 marginal utility per hr.

visits per week  

1                                     100                                     

                                                   >                                 80                                                      40

2                                     180

                                                    >                                60                                                      30

3                                     240

                                                     >                               40                                                      20

4                                     280

                                                    >                                30                                                      15

5                                     310

                                                      >                             20                                                       10

6                                     330

                                                      >                             10                                                        5

7                                    340

c.Of all the bundles , the bundle containing 4 gym visits and 3 movies is

optimal: this is the bundle at which the marginal utility per hour spent in the gym

is equal to the marginal utility per hour spent watching movies.