An agent has a wealth of W, that he can invest in a riskless asset that pays off i and a risky pay-off Y = (g,p ; b,1 p), where g stands for good, and b stands for bad, and g > b.

a) Denote 0 W, the amount invested in the risky asset. Write the lottery that represents final wealth W()

b) Suppose that > 0. Graph the cumulative distribution function (CDF) F(t) = Prob(W() t).

c) Show graphically that if i < b < g, then for all values of , W() stochastically dominates W(0).

d) Explain this result in words.

e) Same question if b < g < i