Consider the savings functionwhere e is a random variable with E(e) = 0 and Var(e) = a2g....

Consider the savings function

where e is a random variable with E(e) = 0 and Var(e) = a2g. Assume that e is independent of inc.

(i) Show that E(u/inc) = 0, so that the key zero conditional mean assumption (Assumption SLR.4) is satisfied. [Hint: If e is independent of inc, then E(e/inc) = E(e).]

(ii) Show that Var(u|inc) = a2Jnc, so that the homoskedasticity Assumption SLR.5 is violated. In particular, the variance of sav increases with inc. [Hint: Var(e/inc) = Var(e), if e and inc are independent.]

(iii) Provide a discussion that supports the assumption that the variance of savings increases with family income.