7. Damien Matthews is a busy actor. He allocates his free time to watching movies and working out at the gym. The accompanying table shows his utility from the number of times per week he watches a movie or goes to the gym.

Quantity of gym visits per week Utility from gym visits (utils) Quantity of movies per week Utility from movies (utils) 1 100 1 60 2 180 2 110 3 240 3 150 4 280 4 180 5 310 5 190 6 330 6 195 7 340 7 197 Damien has 14 hours per week to spend on watching movies and going to the gym. Each movie takes 2 hours and each gym visit takes 2 hours. (Hint: Damien’s free time is analogous to income he can spend. The hours needed for each activity are analogous to the price of that activity.)

a. Which bundles of gym visits and movies can Damien consume per week if he spends all his time either going to the gym or watching movies? Draw Damien’s budget line in a diagram with gym visits on the horizontal axis and movies on the vertical axis.

b. Calculate the marginal utility of each gym visit and the marginal utility of each movie. Then calculate the marginal utility per hour spent at the gym and the marginal utility per hour spent watching movies.

c. Draw a diagram like Figure 10-4 in which both the marginal utility per hour spent at the gym and the marginal utility per hour spent watching movies are illustrated. Use this diagram and the utility-maximizing principle of marginal analysis to decide how Damien should allocate his time.