Question

6.    Fred is a teenager who likes to listen to music and to play games on his computer. Suppose that he has an annual entertainment budget of $144 and that each music CD costs $12 and each computer game costs $24.

Quantity Consumed                   Total Utility                    Total Utility

     (per year)                             of Music CDs                of Computer Games

            0                                           0                                     0

            1                                       200                                 160

            2                                       236                                 232

            3                                       268                                 296

            4                                       296                                 352

            5                                       320                                 400

            6                                      340                                 440

            7                                       344                                 472

1. Calculate the marginal utility of each unit of music CDs and computer games.
2. Using the prices mentioned above, calculate the marginal utility per dollar of music CDs and computer games. Round to two decimal places.
3. What much of each good will Fred purchase to maximize satisfaction? (Find the utility-maximizing combination of music CDs and computer games.)
4. What is the total amount of utility that Fred will receive when he consumes the combination computed in Part C, i.e. the total utility from the music CDs plus the total utility from the computer games?
5. Given your answer in C, explain why buying two more music CDs and 1 less computer game makes Fred worse off.

Answer 1

a). The marginal utility is the addition made to the total utility when an additional unit of the commodity is consumed. The marginal utility is calculated by the following formula.

Mu .

Change.

b). The marginal utility per dollar is calculated by dividing the marginal utility of the product of by the respective price.

Marginal utility per dollar

c). With the given budget the profit maximizing unit is where the marginal utility per dollar is equal for both the music Cd's and computer games, that is where he purchases 4 units of the Cd and 4 computer games.

.

d). Total utility is .

e). At this point the marginal utility per dollar would not be equal , so it is not profit maximizing.