JuMP indeed has annoying shadow price behavior. This issue, first raised by @chkwon also matters in the presence of non-linear models/constraints in JuMP.
The behavior is not there in GAMS. My model is an economic growth model. Took me a while to actually figure out what was going on—kind of annoying as I could have saved time, had I worked right away in GAMS. But I love JuMP/Julia and the flexibility it offers.
I had to re-program everything in GAMS and also derive the complementarity problem to be sure I was not making errors.
Moreover, “JuMP. shadow_price” does not work with “NLconstraint”. Non linear constraints are the bread and butter of economic modelling. So shadow_price wont work in this case.
I do not want to come off as ungrateful as I cannot do the great work that is being done and has been done with JuMP. But it would be great to address this issue once and for all. This is likely to affect new users.
I see three ways out. 1) make shadow_price work with nonlinear constraints, 2) have JuMP be consistent with GAMS/AMPL—may be by first checking if the problem is Max/Min and the multiplying duals/shadow_prices by -1 for Max. 3) Make it more explicit in the manual what is actually being done by JuMP.dual, in order for people like me to back out the proper shadow prices.