Q. Classical model and the long-term Phillips curve?
In classical model, L and real wage are determined from equilibrium conditions in the labor market. L and W/P, hence, are only affected by marginal product of labor (that determines the demand for labor) and by utility function of the employees (that determines the supply of labor). All unemployment is voluntary and L, U or W / P are all affected by exogenous variables only.
In classical model, inflation is determined solely by the growth in money supply pM. From the quantity theory of money, M·V = P·Y and if growth rate of M is pM, then P should increase by the same rate as V and Y are constant. From quantity theory we can determine that p = pM must hold.
Relationship M·V = P·Y is therefore sometimes known as quantity theory in levels whereas p = pM is called the quantity theory in rates.
In classical model, inflation is balanced and pW = p (real wage is constant). Because p = pM, we have p = pM = pW. As U isn't affected by any endogenous variables, there is no relationship between pWoch U in classical model and vertical LPC applies even in the short run. The position on LPC determined by pM.
Unlike neo-classical synthesis, where economy temporarily may depart from LPC, economy should always be on the LPC in the classical model.