Hi Prof. Pfeifer
When the agents maximizes in the RBC and DSGE models the objective function of households, they take into account only the budget constraint. They have ignored the non-negativity constraint on consumption.
Why they do this?
I really appreciate any help you can provide.
Actually you should take these into account when deriving the first order conditions and use e.g. A Kuhn Tucker Lagrange approach. However, due to the functions we typically use in DSGE modeling, the constraints are usually not binding an we do not get these corner solutions. So for convenience we simply neglect this in the derivations. I guess a prominent exception to this is of course the Zero-Lower-Bound on interest rates. You will find much information in the literature and in this forum how to do this with Dynare.
Cheers!
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Dear Wmutschl,
Thanks for help!