<p>See Thesis By Dr Abdul Rahim Wong, PhD</p>
<p><a href="https://ideas.repec.org/p/pra/mprapa/116595.html" rel="nofollow noreferrer">https://ideas.repec.org/p/pra/mprapa/116595.html</a></p>

CC BY-SA 4.0
2023-08-26T04:37:50.123Z
I think it got a -1 because the link just shows the first four pages.
mark leeds
CC BY-SA 4.0
2023-08-28T12:56:49.237Z
Hi, welcome to Economics SE. I think a policy of the site is that link only answers should be posted as comments.
Nicolas Torres
CC BY-SA 4.0
2023-08-28T12:57:15.017Z
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference.  Link-only answers can become invalid if the linked page changes. - [From Review](/review/late-answers/36507)
Nicolas Torres
CC BY-SA 4.0
2023-08-23T11:19:19.737Z
2023-08-23T11:19:19.737Z
Dr Abdul Rahim Wong
<p>An example: Vector calculus, in particular the gradient theorem, is used in the characterization of Bayesian incentive compatible social choice functions in mechanism design with multi-dimensional types. See the respectively first result in either of:</p>
<p>Jehiel, Philippe, Benny Moldovanu, and Ennio Stacchetti. &quot;Multidimensional mechanism design for auctions with externalities.&quot; Journal of economic theory 85.2 (1999): 258-293.</p>
<p>Jehiel, Philippe, and Benny Moldovanu. &quot;Efficient design with interdependent valuations.&quot; Econometrica 69.5 (2001): 1237-1259.</p>
<p>EDIT: In the same field, e.g. Armstrong uses the divergence theorem:</p>
<p>Armstrong, Mark. &quot;Multiproduct nonlinear pricing.&quot; Econometrica: Journal of the Econometric Society (1996): 51-75.</p>

CC BY-SA 4.0
2021-11-03T18:15:29.467Z
2021-11-03T18:31:25.670Z
2021-11-03T18:31:25.670Z
axelniemeyer
<p>What are some relevant examples of the application of vector calculus in economics, apart from using gradients and Hessian matrices for optimization? I'm mostly referring to the topics and concepts such as curl, divergence, gradient theorem, divergence theorem and Stokes' theorem.</p>

<mathematical-economics>
Application of vector calculus in economics
cc88
# Application of vector calculus in economics

(Asked by: username_0 on 2021-11-02)

What are some relevant examples of the application of vector calculus in economics, apart from using gradients and Hessian matrices for optimization? I'm mostly referring to the topics and concepts such as curl, divergence, gradient theorem, divergence theorem and Stokes' theorem.

**Tags:** mathematical-economics

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## 2 answers

### Answer by username_4 on 2021-11-03. Score: 6 | Accepted answer

An example: Vector calculus, in particular the gradient theorem, is used in the characterization of Bayesian incentive compatible social choice functions in mechanism design with multi-dimensional types. See the respectively first result in either of:

Jehiel, Philippe, Benny Moldovanu, and Ennio Stacchetti. "Multidimensional mechanism design for auctions with externalities." Journal of economic theory 85.2 (1999): 258-293.

Jehiel, Philippe, and Benny Moldovanu. "Efficient design with interdependent valuations." Econometrica 69.5 (2001): 1237-1259.

EDIT: In the same field, e.g. Armstrong uses the divergence theorem:

Armstrong, Mark. "Multiproduct nonlinear pricing." Econometrica: Journal of the Econometric Society (1996): 51-75.


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### Answer by username_1 on 2023-08-23. Score: -1

See Thesis By Dr Abdul Rahim Wong, PhD

<https://ideas.repec.org/p/pra/mprapa/116595.html>

> **Comments:**
> **username_2**: I think it got a -1 because the link just shows the first four pages.  
> **username_3**: Hi, welcome to Economics SE. I think a policy of the site is that link only answers should be posted as comments.  
> **username_3**: While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference.  Link-only answers can become invalid if the linked page changes. - [From Review](/review/late-answers/36507)  

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