Iacoviello 2005 Steady State problem

Hello everyone. In the technical appendix of Iacoviello 2005, (Technical Appendix, Iacoviello 2005) the authors write on page 5: “One can always normalize the technology parameter A so that Y = 1 in steady state, so the trick is to express all the variables as a ratio to Y”. I did exactly that and dynare has no problem finding the steady state with Y normalized to 1, but my problem is that I want to include two types of enterpreneurs in the model which have different values of steady state productivity (One firm has more SS productivity than the other) in their production functions, but I cannot assign these values myself, I must vary parameters s.t. one firm has higher SS productivity than the other.

My question is, does this model feature multiple steady states and is that the reason behind normalizing Y=1? Is there a way to assign a value to A and then calculate Y with some numerical methods?

Thank you in advance!

If the model features constant returns to scale, you can always normalize everything with TFP.

Thank you for your answer! Does that mean that I can set A=1 instead of choosing Y=1? If I set A=1 I cannot solve for the steady state analytically. Would it be possible to find such solution numerically?

Yes, you can set A=1, but this requires to solve for Y. Often, this requires numerical solution techniques, but is generally feasible.