Infinite steady state value


I am trying to simulate a Ramsey equilibrium model. I first characterise the optimal policy of the government in a neoclassical model by hand. Then I determine the steady state by hand as well in order to study the dynamics around it using Dynare. The problem is that, in the steady state, I have two equations that yield w = infinity (the labor wage). Does this mean that the model is non-stationary? If yes, can this problem be solved under Dynare?

Thank you for your help in advance.

Usually, that would mean you have an unbounded solution. Why is that the case?

Could you tell me what does this mean exactly? thanks !
Why is that the case. I don’t know. It is a fiscal policy model with a collateral constraint and two types of non contingent debt (short and long term debt). The collateral friction constraints the firm’s wage bill (liquidity).

If a wage is infinite, you need infinite resources to pay for it. Thus, there is no scarcity and utility will be infinite as well. You need to understand why that happens in steady state.