Steady State in larger models

Hi Dear All
I have a problem computing and calibrating the steady state.Thank you in advance for your help. I can understand how to calibrate the RBC model. In these models, labor plays an important role. So that by calculating K/L (In firm demand for capital) and labor (in FOC wrt L in household sector) we can proceed well.

But in my model, FOC wrt K (in the firm sector) is as follows:

For ease of work, I divided all the variables of model (in all equations) on Y.So we have for the above equations:

And I did that for all the equations. But I have a problem only at one point in the model: FOC wrt H (or L (labor)) in the household sector:


The problem is that labor can no longer be divided into Y(On the left side of the equation) . That is, we do not have H/Y, but we have H(0.33). But in other equations we have H/Y. For example, in the production function and any equation that has H
My production function is as follows

Do I have to change my calibration method or is there a better solution?

It seem this is a model where you cannot analytically solve for the labor to output ratio. You may need a different approach, e…g fixing labor and then computing the parameters to make that work or numerically solve for the ratio.

Thank you very much for your answer, Professor.
Is it wrong if I do the following?
Y_ss=1 (It is almost equal to 1 )
H_ss/Y_ss = H_ss=0.33

Generally, this will be wrong, unless you set TFP to get an output of 1. But why can’t you set H_ss=0.33and work from there?