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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.

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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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See Thesis By Dr Abdul Rahim Wong, PhD

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

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  • $\begingroup$ I think it got a -1 because the link just shows the first four pages. $\endgroup$
    – mark leeds
    Commented Aug 26, 2023 at 4:37
  • $\begingroup$ Hi, welcome to Economics SE. I think a policy of the site is that link only answers should be posted as comments. $\endgroup$ Commented Aug 28, 2023 at 12:56
  • $\begingroup$ 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 $\endgroup$ Commented Aug 28, 2023 at 12:57

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