In 1963 Paul Samuelson wrote about a colleague who said that he would turn down the prospect (0.5, −$100; 0.5, $200) but would accept 100 such prospects. Suppose that his utility function is u(x) = x

− w if x ≥ wand u(x) = −2.5(w − x) if w > x where w is his wealth.

Show why he turned down the prospect. Now, imagine two prospects will be done in turn and he will adjust his wealth level after each prospect. Show that he should turn down the two prospects. Finally, imagine that he only adjusts his wealth level after seeing the outcome of both prospects. Should he take on the two prospects? Should he take on 100 prospects?