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Why should time-subscript notation be avoided in Bellman equations?

Here is the general intuition: 1. Finite Horizon Case It is necessary to include the time subscript here because $V_t(k_t)$ and $V_{t+1}(k_{t+1})$ have different number of time periods ahead of them. ...
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2 votes
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A derivative with respect to Euclidean distance?

As Herr K. pointed out, if you write $\frac{du(g)}{dg}$, then $u$'s domain has to be $\mathbb{R}^+$ and $x,z$ have to be real numbers. You'd rather ask: When $u : \mathbb{R}^+ \to \mathbb{R}^+$ ...
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1 vote

Why are production functions linear in technology?

It is important to note that technology is an abstract concept and cannot be measured in concrete units, but simply with a positive scalar magnitude (the greater the technical development, the greater ...
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  • 150
3 votes

Convexity of preferences (dissimilar definitions)

For Q 1: Let me give you a preference relation on $\mathbb{R}^2_+$ $(x_1, y_1) \succsim (x_2, y_2)$ if and only if $(x_1^2 + y_1^2 > x_2^2 + y_2^2)$ or $(x_1^2 + y_1^2 = x_2^2 + y_2^2 \ \wedge x_1 \...
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2 votes
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Do practicing economists actually use complex mathematics, or is it just a thinking tool?

Do practicing economists actually use complex mathematics? I think by "practicing economists" you actually refer to those who work outside academia with "Economist" as part of ...
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4 votes
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Average Discounted Payoffs in Continuous Time

The $r$, or rather $\frac{1}{1/r}$, is the "average" part of the average discounted payoff. As you note, $\mathrm e^{-rs}$ is the discount factor. Observe that \begin{equation} \int_0^\infty ...
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4 votes

Euclidean spaces,vector spaces,metric spaces,commodity spaces,Cartesian spaces

Of all the types of structures or spaces you mention, vector space $\mathcal{V}$ is the simplest type of structure. Other structures are constructed from this: A real vector space with an inner ...
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  • 150
0 votes

Where to start studying the maths in economics?

I faced the same dilemma as you when I started my undergrad. Basic math courses are vital and necessary for grasping fairly complex economic topics. Personally, I believe that one should be acutely ...
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