This problem asks you to show that with some natural variants on the approach to modeling agency risk in Problem 10.7, consumption is not linear in the shocks, which renders the model intractable.

(a) Consider the model in Problem 10.7.

Suppose, however, that the representative hedge-fund manager, rather than receiving a payment or incurring a cost in period 1, is forced to sell quantity b(E0[P1] − P1)H, b > 0, of the risky asset in period 1. Show that in this case, the manager’s consumption is not linear in F1.

(b) Consider the model in Problem 10.7.

Suppose, however, that A1 is not exogenous but depends on the success of the period-0 sophisticated investors:

A1 = A+ b (P1 − E0[P1])Xa 0, b > 0. Show that in this case, the consumption of the sophisticated investors born in period 0 is not linear in F1.