(Before solving this exercise, it pays to return to the solution of Exercise 4.3.)

Anindividual can allocate his saving between a safe asset (m) paying a return r and a risky one (α) with return ˜ x(E(˜ x)>r).

In order to avoid heavy computations assume that y0 = y1 = y and that

δ =0.

If this individual has a quadratic utility in

c, compute the optimal values of s and its allocation between the two assets. (Hint: write Eu as a function of α

andm.Youwillhavetwofirst-orderconditions, one with respect to m andone with respect to α. Of course s = α + m. Notice also that to find the optimal values of α and m you will have to solve a system of two linear equations in two unknowns.)