New answers tagged dynamic-programming
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Has mathematical economics contributed to the mathematics of space exploration?
In the history of dynamic programming some economic works are considered pioneering contributions to the theory of dynamic programming (and in this sense it can be said that they contributed to ...
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How can I show that the policy function is non-decreasing?
Suppose $x'>x$. We'll show that $g(x')\geq g(x)$. Suppose that is not the case and we have $x'>x$ but $g(x')<g(x)$. Since $0\leq g(x') < g(x) \leq f(x)< f(x')$, $g(x')$ is feasible in ...
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How can I show that the policy function is non-decreasing?
I'm going to assume that everything is smooth and that the optimal solution $g(x)$ is interior (in $]0, f(x)[$)
First you can show that the function $V$ is concave as the Bellman operator maps concave ...
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Does this contraction mapping map strictly concave functions into strictly concave functions?
No. The maximum of two concave functions is usually not concave, so this is pretty hopeless.
Here is an explicit counterexample: Let $\bar{k}=1$, $W(k)=\sqrt{k}$, $f(k)=k$, $\beta=0.999$. Let $V(k)=k+...
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Understanding Duality between Individual and Collective Maximization in Macroeconomic Models
The proof of the first welfare theorem is almost the same as the one you are familiar with from MWG. The main difference is that if you have recursive budget constraints, you have to show that you can ...
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