Assume a consumer has the utility function below and makes best choices

as described in Chapter 4.

U(c1, c2, ..., c50) = ?1 log(c1) + ?2 log(c2) + + ?50 log(c50)

Also assume that (i) ?1 = ?2 = = ?50 = 1/50, (ii) the real interest rate

is r = 0 and (iii) the agent starts out with no financial wealth in model period

1.

(a) Calculate the best consumption choices (c1, c2, ..., c50) when the agent's

earnings profile is w1 = w2 = = w40 = 1 and w41 = w42 = = w50 = 0.

Discuss the logic that underlies these best choices.

(b) Calculate the best consumption choices (c1, c2, ..., c50) when the agent's

earnings profile is w1 = w3 = = w39 = 2 and w2 = w4 = = w40 = 0 and

w41 = w42 = = w50 = 0. Discuss the logic that underlies these best choices.

U(C1, C2, ..., (50) = 1 log(c1) + @2 log(C2) + . . . + @50 log(C50) Also assume that (i) a1 = 02 = . . . = 050 = 1/50, (ii) the real interest rate is r = 0 and (iii) the agent starts out with no financial wealth in model period 1. (a) Calculate the best consumption choices (C1, C2, ..., C50) when the agent's earnings profile is w1 = W2 = . . . = W40 = 1 and w41 = W42 = . . . = W50 = 0. Discuss the logic that underlies these best choices. (b) Calculate the best consumption choices (c1, C2, ..., C50) when the agent's earnings profile is w1 = W3 = . . . = W39 = 2 and w2 = W4 = . . . = W40 = 0 and W41 = W42 = . . . = W50 = 0. Discuss the logic that underlies these best choices