2 Consider an agent characterized by a log - utility log ct , discounting the future ( so that 3 < 1 ) , living for three periods ( i.e. , 0 , 1 , and 2 , so that T = 2 ) and endowed with the technology Yt Akt , a ( 0 , 1 ) . Assume that capital fully depreciates within one period ( i.e. , 8 = 0 ) . The agent maximizes her lifetime . discounted utility subject to the dynamic constraint kt + 1 = yt - Ct . 1. Assume a = 0.3 , B = 0.97 , A = 3.44 , and ko = 0.5 and complete the following table : period kt Ct 0 1 2 3 2. Assume now that the agent lives for T + 1 periods . With the production and utility functions proposed above , show that the consumption function for an agent living T + 1 periods is ( i.e. , her optimal plan from the perspective of period 0 ) : Ct = 1 ( a ) Akt , i = 0 , 1 , ... , T