2. Aaron and his friends Britney, Carlos, Diana, Emily, Frank, Gwen, Hugo, Isabela, and Juliana have two choices for weekend activities. They can either go to the neighborhood park or get together in Aaron's hot tub. The park isn't much fun, which means that the benefits from being there are low on the friends' common utility scale. In fact, each of the friends receives a benefit equal to 6 "utils" from being at the park. This benefit doesn't depend on how many of the friends go to the park. Aaron's hot tub, on the other hand, can be fun, but the benefits of using it depend on how many of the friends are present. When the tub isn't too crowded, it's quite enjoyable. When lots of people show up, however, the tub is decidedly less pleasant. The relationship between benefit per person (measured in utils) and the number of people in the hot tub (denoted by T) is AB = 3+ 7 . T - T2, where AB denotes "average benefit." a) Using the above formula, compute AB for T = 1, 2, 3,...,10. Next compute total benefit from use of the hot tub for the above T values as well as T = 0. Total benefit is just T times AB. Finally, compute marginal benefit (MB), which equals the change in total benefit from adding a person to the hot tub. To do so, adopt the following convention: define MB at T = T' to be the change in total benefit when T is increased from T' - 1 to T (in other words, MB gives the change in total benefits from entry of the "last" person). Deviation from this convention will lead to inappropriate answers. For example, computation of MB using calculus will lead you astray, since we are dealing with a discrete problem rather than a continuous one. T AB TB MB O N W UT Co 10