I will be teaching a course focusing on multivariable integration soon, for the millionth time. The most difficult topic in such a course is certainly Vector Calculus, by which I mean line and surface integrals of vector fields. It is essential to present good applications of these so that students are motivated, but all examples I've ever used are standard physical ones. My course will have many economics/finance majors, and I would love to have some examples I could present along these lines. However my knowledge in these fields are lacking, so I ask: what are some common applications of vector calculus to economics and/or finance, ones which will keep students in these fields motivated? If possible, these applications should be understandable by someone who has (or will have) only an undergraduate background in economics.
I could probably come up with some ad-hoc example where I model the flow of resources from one sector of an economy to another using a vector field and then come up with some interpretation of a line or surface integral involving this, but I would really like some examples which actually come up in practice. Bonus if they use Stokes' or Gauss' Theorem.