Suppose David's utility function depends not only on his consumption x1 but also on Lucy's consumption x2, and has a functional form of U1(x1, x2) x1 - a max(x1 - x2, 0)- max(x2-x1, 0), where > a > 0. We say David is altruistic if an increase in Lucy's consumption leads to an increase in David's utility. We say David is spiteful if an increase in Lucy's consumption leads to a decrease in David's 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 x such that David's consumption is 100- x and Lucy's consumption is 3x. If David's choice is x = 10, what is the range of a? What if David's choice is x = 0? What if David's choice is x = 100?