I am a PhD student in economics. I'm currently dealing with a computable general equilibrium model with many constrained optimisation problems.
https://i.stack.imgur.com/36mbU.png
As you can see in the picture, that's the kind of optimisation problems I have to deal with. Nothing exceptional, but I have more than 14 production sectors, many economic agents, many variables and parameters, therefore, I have to deal with a large number of problems to solve.
My question is:
Is there was a software that can help me derive analytical solutions (as opposed to numerical solutions) to the many optimisation problems at hand, like in the example shown in the picture. It doesn't necessarily have to be through the lagrange tool. The goal is to have analytical solutions, like the one shown in equation (2.1), in the picture.
Thank you!
Assuming that your equations allow analytic solutions, then you'll need a computer algebra system, i.e. software that can perform symbolic manipulation as opposed to numeric.
There are a number of such systems, although some of the more popular general-purpose options are Mathematica, Maple, and SageMath.