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(Solved): 2. Consider the following consumption-savings problem: {ct,xt+1}t=0maxt=0 ...




2. Consider the following consumption-savings problem:
\[
\max _{\left\{c_{t}, x_{t+1}\right\}_{t=0}^{\infty}} \sum_{t=0}^{\i
2. Consider the following consumption-savings problem: subject to , with given. Assume that and . (i) Set up the problem recursively, and find the policy functions explicitly. (ii) Parameter values are given by and . Numerically approximate the value function and policy functions using the following procedure: a. Discretize the state space using the grid , where and takes on values from 1 to 41 . This defines the state variable on a grid of equally spaced points. b. Define the value function as an vector, and set your initial guess, , as an vector of zeros. Find the new value function by solving for . c. Iterate on until . d. Compute the policy functions and using the approximate fixed point . Do not hand in your code or any numerical answers. Please just submit two figures: one that plots the optimal policy for consumption, , and another that plots the optimal policy for savings, .


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(i) To set up the problem recursively, we can star
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