10. Consider the Dynamic Problem of a Consumer/Investor:
s.t. at = ? ...
where ct is consumption at time t, at is assets at the beginning of period t; and the gross interest rate R > 1 are given.
(a) Write down the above sequence problem as a functional equation problem. Which variable is the state?
(b) Assuming the problem has a solution, solve the functional equation from (a) for the value function, v and policy function, g. Hint: use the "guess and verify method"!
(c) Do you need to assume anything about the relationship between R and B for the problem to have a solution?
(d) If RB = 1 what is the time path of consumption implied by the optimal policy function'? What is the intuition for this result?
A Dynamic Problem of a Consumer / Investor is investigated. The solution is detailed and well presented.