Suppose a parent and child play the following game, first analyzed by Becker (1974***). First, the child takes an action. A, that produces income for the child. l_C(A), and income for the parent. I_P(A). (Think of I_C(A) as the child's income net of any costs of the action A). Second, the patent observes the incomes l_C and I_P and then chooses a bequest. B, to leave to the child. The child's payoff is U(l_C+ B); the patent's is V(I_P-B) + kU(I_C+ B). where k > 0 reflects the parent's concern for the child's well-being. Assume that: the action is a non-negative number. A greaterthanorequalto 0; the income functions I_C(A) and I_P(A) are strictly concave and are maximized at A_C > 0 and A_P > 0. respectively; the bequest B can be positive or negative; and the utility functions U and V are increasing and strictly concave. Prove the Rotten Kid Theorem: in the backwards-induction outcome, the child chooses the action that maximizes the family's aggregate income. I_C(A)+ I_P(A). even though only the patent's payoff exhibits altruism