Alice and Bob have £100, 000 to bequeath to their two children, Carrie and Danny. Bob’s preferences are represented by

U(xc,xd)=xc +xd
where xc is the amount of money left to Carrie, and xd is the amount of money left to Danny.

Alice’s preferences are represented by

U(xc, xd) = min{xc, xd}
That is, Alice’s utility is equal to the minimum bequest left for either of her children: for

instance, if Danny received £50 and Carrie received £40, Alice would obtain a utility of 40. Whichever parent survives the longest decides how to arrange their will, and so, decides the

sums bequeathed to each child.

a) [9 marks] In what sense do Alice and Bob face a budget constraint? In separate graphs, one each for Alice and for Bob, draw the parent’s budget constraint. (Hint 1: Think of the two bequests as goods from which Alice and Bob derive utility. Hint 2: What are these goods’ prices? Hint 3: Remember to label all graphs, axes, and intercepts.)

b) [9 marks] On each of the parent’s graphs, draw 3 points representing “consumption bundles” giving different levels of utility, per the utility functions given. Include at least one point that lies on the budget constraint. Label each point with its coordinates and with the level of utility associated with it.

c) [7 marks] To what extent do you agree with the following claim?: “Even though the parents have different preferences, both parents love their children equally.” Explain.

d) [8 marks] Explain why Alice will always divide the bequests equally.