Homework

(^1) Solve the consumption optimization problem withu(c)=cα,α> 0.
Consider the casesα< 1 ,α= 1 ,α> 1.
(^2) Solve the following problem with constrained optimization and with
dynamic programming wherest>0 andc>0 are constants:
T

∑

t= 1

sta^2 t!max.

T

∑

t= 1

at=c,at 0.

(^3) Solve the following problems with constrained optimization and with
dynamic programming whereδt>0 andc>0 are constants:
T

∑

t= 1

atδt!max,

T

∑

t= 1

at=c,at 0.

(^4) Solve the following problems with constrained optimization and with
dynamic programming
T

∏

t= 1

at!max.

T

∑

t= 1

at=c,at 0.