Basket A contains 1 unit of x1 and 5 units of x2. Basket B contains 5 units of x1 and 1 unit of x2.
Basket C contains 3 units of x1 and 3 units of x2. Assume throughout that tastes are monotonic.
A: On Monday you are offered a choice between basket A and C, and you choose A. On Tuesday you are offered a choice between basket B and C, and you choose B.
(a) Graph these baskets on a graph with x1 on the horizontal and x2 on the vertical axis.
(b) If I know your tastes on any given day satisfy a strict convexity assumption—bywhich I mean that averages are strictly better than extremes, can I conclude that your tastes have changed from Monday to Tuesday?
(c) Suppose I only know that your tastes satisfy a weak convexity assumption—by which I mean that averages are at least as good as extremes. Suppose also that I know your tastes have not changed from Monday to Tuesday. Can I conclude anything about the precise shape of one of your indifference curves?
B: Continue to assume that tastes satisfy the monotonicity assumption.
(a) State formally the assumption of “strict convexity” as defined in part A(b).
(b) Suppose your tastes over x1 and x2 were strictly non-convex—averages are strictly worse than extremes. State this assumption formally. Under this condition, would your answer to part A(b) change?
c) Consider the utility function u(x1,x2) = x1 + x2. Demonstrate that this captures tastes that give rise to your conclusion about the shape of one of the indifference curves in part A(c).