The quantity theory of money states the price level is proportional to the amount of money in circulation. That is, if the quantity of money increases by some factor $k$, the price level will increase by the same factor $k$. My question is simple: in which economic models should one expect such a claim to hold true?
To be clear, I am asking about 'microfounded' models which contain full descriptions of the preferences and constraints of the underlying agents (including but not restricted to general equilibrium models). I am not interested in equations like $MV = PY$ unless you can show that they arise from such a model.