Suppose Davids utility function depends not only on his consumption 1 but also on Lucys consumption 2, and has a functional form of

1(1, 2) = 1 ( 1 2, 0) ( 2 1, 0), where > > 0.

We say David is altruistic if an increase in Lucys consumption leads to an increase in Davids utility. We say David is spiteful if an increase in Lucys consumption leads to a decrease in Davids utility.

a. Under what condition is David altruistic and under what condition is David spiteful?

b. Is it possible for David to only care about efficiency (in terms of maximizing the sum of the consumption of the two)? Is it possible for David to only care about the fairness (in terms of minimizing the difference of the consumption of the two)?

c. Suppose David can choose such that Davids consumption is 100 and Lucys consumption is 3. If Davids choice is = 10, what is the range of ? What if Davids choice is = 0? What if Davids choice is = 100?