4
votes
Accepted
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 ...
- 14.4k
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 ...
- 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 \...
- 5,112
2
votes
Accepted
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 $u : \mathbb{R}^+ \to \mathbb{R}^+$ ...
- 76
2
votes
Accepted
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 ...
- 14.4k
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 ...
- 150
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