代做program、代写Java/c++编程设计

日期：2025-03-27 08:41

Homework 1

Due on March 31st 5:00pm, 2025

Be sure to include all the material that shows your work and to present your results in a

way that it is easy to understand. List your computer code and output in the appendix. Donít

just give me computer code and output. Remember: ignorance and inability to communicate

are observationally equivalent.

I recommend you write your homework using La Tex, since you need to learn it to write

your dissertation anyway. However, La Tex is not required.

All the exercises will be based on the following neoclassical growth model:

where the technology level zt follows a Markov Chain that takes values in:

zt 2 f 0:0673;   0:0336; 0; 0:0336; 0:0673g

with transition matrix

1 Steady State (20 points)

Compute the deterministic steady state of the model. What is the deterministic steady state

level of capital, kss; consumption, css; and labor lss?

2 Value Function Iteration with a Fixed Grid (40 points)

Fix a grid of 500 points of capital, centered around kss with a coverage of 25% of kss and

equally spaced. Iterate on the Value function implied by the Social Plannerís Problem using

linear interpolation until the change in the sup norm between to iterations is less than 10  6

.

Compute the policy function and the euler equation error function. Plot the policy functions

and the euler equation error (in log10).

3 Policy Iteration (20 points)

Recompute your solution to 2) using an accelerator, i.e., skipping the max operator in the

Bellman equation 9 out of each 10 times. Compare accuracy and computing time between the

simple grid scheme implemented in 2) and the results from the accelerator scheme. Present

evidence to support your claims.

4 Multigrid (20 points)

Implement a multigrid scheme (Chow and Tsitsiklis, 1991) for a Value function iteration,

with the grid centered around kss with a coverage of 25% of kss and equally spaced.

You will have 100 capital grid points in the Örst grid, 500 capital grid points in the second,

and 5000 capital grid points in the third.

Compare accuracy and computing time between the simple grid scheme implemented in

2) and the results from the multigrid scheme. Present evidence to support your claims.

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5 Bouns Points (20 points)

Except for the methods that we discussed in the class. Do you have any other idea that can

improve the performance of Value Function Iteration?

1. Please describe your algorithm.

2. Please implement your algorithm and compare it with the results in Section 2.

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