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Hi Suppose that I have a model in which TFP is increasing, call the TFP: At,
and Consumption Ct is increasing at the same order with TFP, thus Ct/At is stationary

How do I stationarize an endogenous discount factor
v(Ct,Lt)=ln(1+psi*[Ct^alpha*(1-Lt)^(1-alpha)])

Some literature uses this kind of endogenous discount factor in their utilities, but I never found any way to stationarize v(Ct,Lt).

The easiest way is to assume that this functional form for the endogenous discount factor applies to the stationarized model, i.e. the C_t is the detrended one. Otherwise, the functional form you provide is inconsistent with a balanced growth path.