Consider a policy maker who uses and instrument kt, to control the path followed by some target variable Y, The policy maker has the following Objective function The environment imposes the following constraint on this policy maker Y t 2k t 6Y t 1 The initial Y 0 is known to be 60 (a) What is the best choice of k t for period t 4 (b) What is the best choice of k t for period t 3 (c) From these, can you iterate and find the best choice of k t for t 1 (d) Determine the value function V t that gives the optimal payoff for t 1, 2, 3, 4 (e) Plot the value function V t and interpret it U E12(k, k 1) 100(Y,

Question: Consider a policy maker who uses and instrument kt, to control the path followed by some target variable Y,. The policy maker has the following

Consider a policy maker who uses and instrument kt, to control the path followed by some target variable Y,. The policy maker has the following Objective function

The environment imposes the following constraint on this policy maker:

Y_t = .2k_t + .6Y_t-1.

The initial Y₀ is known to be 60.

(a) What is the best choice of k_t for period t = 4?

(b) What is the best choice of k_t for period t ? 3?

(d) Determine the value function V_t that gives the optimal payoff for t = 1, 2, 3, 4.

(e) Plot the value function V_t and interpret it.

U = E12(k, - k-1) + 100(Y,].

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