<p><a href="http://www.tandfonline.com/doi/pdf/10.1080/1350486X.2010.531588?needAccess=true" rel="nofollow noreferrer">Here</a> and <a href="http://www.tandfonline.com/doi/abs/10.1080/135048698334673" rel="nofollow noreferrer">here</a> are two application of the theorem to finance.</p>

<p><a href="https://ideas.repec.org/p/fth/bereco/176.html" rel="nofollow noreferrer">Here</a> is an application to game theory. </p>

<p><a href="http://www.sciencedirect.com/science/article/pii/S0047259X0900089X" rel="nofollow noreferrer">This</a> is an application of the theorem to complex Bayesian stuff (potentially useful in econometrics).</p>

<p>Also, the Green's theorem is used in <a href="https://en.wikipedia.org/wiki/Bendixson%E2%80%93Dulac_theorem" rel="nofollow noreferrer">this proof</a>, which relates to dynamics system, and therefore could be related to economic models (source of this <a href="https://matheducators.stackexchange.com/questions/376/applications-of-vector-calculus-to-economics-finance#comment2379_376">here</a>)</p>

<p>Last but surely not least, <a href="http://www.springer.com/la/book/9783540073901" rel="nofollow noreferrer">this book</a> might have relevant stuff. At least <a href="https://books.google.co.uk/books?id=x5_wCAAAQBAJ&amp;pg=PA228&amp;lpg=PA228&amp;dq=green+theorem+use+in+economics&amp;source=bl&amp;ots=Iys4Nq7Qzv&amp;sig=ikQhNoygdMx1C2EwFGAVk2YUuiQ&amp;hl=es-419&amp;sa=X&amp;ved=0ahUKEwjS-q3Mvp7TAhWMCcAKHR8LA1sQ6AEIVTAI#v=onepage&amp;q=green%20theorem%20use%20in%20economics&amp;f=false" rel="nofollow noreferrer">Chapter 12</a> does use it.</p>

CC BY-SA 3.0
2017-11-08T16:41:34.863Z
Lucho, what about for the Stokes' theorem? ;)
An old man in the sea.
CC BY-SA 3.0
2017-04-12T08:28:15.303Z
2017-04-12T08:28:15.303Z
2017-04-13T12:50:24.493Z
luchonacho
<p>I was wondering about possible of application of integration to economics (other than welfare), more specifically, how might Green's theorem be useful for an economist?</p>

<hr>

<p>Let <em>C</em> be a positively oriented, piecewise smooth, simple closed curve in a plane, and let <em>D</em> be the region bounded by <em>C</em> . If <em>G</em> and <em>H</em> are functions of <em>(x,y)</em> defined on an open region containing <em>D</em> and have continuous partial derivatives there, then</p>

<p><span class="math-container">$$\oint_C{(G\ dx + H\ dy) = \int\!\!\!\int_D {\left({{\partial H} \over {\partial x}} - {{\partial G} \over {\partial y}}\right)\ dx\ dy} } $$</span></p>

<p>where the path integral is traversed counterclockwise.</p>

<p>The idea behind this theorem is that if you have a line integral in two dimensions, then Green's theorem can be used to compute the integral: 
 Green's theorem transforms the line integral around a simple closed curve <span class="math-container">$C$</span> into a double integral over the plane region <span class="math-container">$D$</span> bounded by <span class="math-container">$C$</span>.</p>

<mathematical-economics>
Applications to Green's Theorem in Economics?
Jaffar 
# Applications to Green's Theorem in Economics?

(Asked by: username_0 on 2017-04-12)

I was wondering about possible of application of integration to economics (other than welfare), more specifically, how might Green's theorem be useful for an economist?

---

Let *C* be a positively oriented, piecewise smooth, simple closed curve in a plane, and let *D* be the region bounded by *C* . If *G* and *H* are functions of *(x,y)* defined on an open region containing *D* and have continuous partial derivatives there, then

$$\oint\_C{(G\ dx + H\ dy) = \int\!\!\!\int\_D {\left({{\partial H} \over {\partial x}} - {{\partial G} \over {\partial y}}\right)\ dx\ dy} } $$

where the path integral is traversed counterclockwise.

The idea behind this theorem is that if you have a line integral in two dimensions, then Green's theorem can be used to compute the integral:
Green's theorem transforms the line integral around a simple closed curve $C$ into a double integral over the plane region $D$ bounded by $C$.

**Tags:** mathematical-economics

---

## 1 answers

### Answer by username_1 on 2017-04-12. Score: 5 | Accepted answer

[Here](http://www.tandfonline.com/doi/pdf/10.1080/1350486X.2010.531588?needAccess=true) and [here](http://www.tandfonline.com/doi/abs/10.1080/135048698334673) are two application of the theorem to finance.

[Here](https://ideas.repec.org/p/fth/bereco/176.html) is an application to game theory.

[This](http://www.sciencedirect.com/science/article/pii/S0047259X0900089X) is an application of the theorem to complex Bayesian stuff (potentially useful in econometrics).

Also, the Green's theorem is used in [this proof](https://en.wikipedia.org/wiki/Bendixson%E2%80%93Dulac_theorem), which relates to dynamics system, and therefore could be related to economic models (source of this [here](https://matheducators.stackexchange.com/questions/376/applications-of-vector-calculus-to-economics-finance#comment2379_376))

Last but surely not least, [this book](http://www.springer.com/la/book/9783540073901) might have relevant stuff. At least [Chapter 12](https://books.google.co.uk/books?id=x5_wCAAAQBAJ&pg=PA228&lpg=PA228&dq=green+theorem+use+in+economics&source=bl&ots=Iys4Nq7Qzv&sig=ikQhNoygdMx1C2EwFGAVk2YUuiQ&hl=es-419&sa=X&ved=0ahUKEwjS-q3Mvp7TAhWMCcAKHR8LA1sQ6AEIVTAI#v=onepage&q=green%20theorem%20use%20in%20economics&f=false) does use it.

> **Comments:**
> **username_2**: Lucho, what about for the Stokes' theorem? ;)  

---

