As it is known, in simple economic growth models such as the Solow or the Ramsey model, all goods prices are set equal to 1 in each period.
Also, as we known from general equilibrium theory, homogeneity of degree zero of demand implies that only relative prices matter. Therefore, we can always set one price equal to 1 (or do other types of "normalization").
However, in economic growth models (which are general equilibrium models) we have an infinite number of good prices and all are set equal to 1. Why do we always do that? Doesn't it affect the analysis of the model?
I have search for an explanation, but I've been unable to find one. I have a hypothesis, though. Maybe we can normalize goods prices in each period because we assume the economy is in equilibrium at each instant. Then, by the same argument we use in static models, we can normalize goods price in each period. Is this explanation true? Or there is some other reason? And, if it is true, how do models that feature inflation are made?