Hi dynare community, I am trying to learn dynare in Matlab (self taught) and would like to know how to calibrate a theoretical pension system (OLG framework) and the effects of an increase in longevity. I dont really know where to start, so I have uploaded a simple image of the equations I would like to use so solve for steady states. Keep in mind the endogenous variables are: R (all kinds of R^* in different scenarios), tau and consumption. I hope you can help me, and feel free to ask questions regarding the theoretical framework! 
What you posted looks like a stationary equilibrium without transition dynamics. Is that correct?
Correct. Is it possible to use around 50 shocks (increase in longevity for each generation) while still getting meaningful steady state dynamics? And should I use perfect_foresight?
I have tried to create two scenarios with a PAYG pension system. The first (nuvmundtlig.mod) statutory retirement age (R_bar) is indexed after longevity (danish data) and the second (fixedmundtlig.mod) has a fixed statutory retirement age. However, the fixed mod file cant seem to find steady state without using homotopy (which I have no idea what means) so I tried to enter (no_homotopy). Do you have any suggestions on how I can find a steady state? What is the standard approach.
nuvmundtlig.mod (1.7 KB)
fixedmundtlig.mod (1.7 KB)