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Friday, January 28, 2011

More on the Solow Model...

In working through the material on the version of the Solow model from Chapter 6 of Economic Dynamics (if you want details of the model see previous posts) I began to wonder how an agent living in this world would go about choosing an optimal policy.  Here is the answer using U(c) = 1 - exp(-θc):

Iterations of the Value Function:

Note the jump up in the optimal savings policy.  

The Optimal Policy:
The plot of output above assumes that the shock takes its average value.  You can clearly see the two steady-state levels of output (they occur where the blue line cuts the 45 degree line from above). 

I am not quite sure what to make of this...I wasn't expecting the output and the optimal policy lines to cross...maybe a bug in my code.  Thoughts and interpretations are welcome!  The code has been posted to my Google Code repository.  Try it with a different (bounded and continuous) utility function and let me know your results...

2 comments:

  1. I think the lines cross because you aren't restricting consumption to be positive. You could do this by adding a penalty function to the utility function, e.g.
    def U(c): return 1 - exp(- theta * c) - 1e6*(c<=0)

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  2. Thanks, I'll give it a try and see. I thought I had restricted consumption to be greater than zero. I didn't have any problems with other implementations that I tried, but the graphic clearly doesn't make sense.

    I also think I worked out the code for simulating the marginal distributions. I will see if I can get both bugs fixed this evening and post the new code.

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