Cost-pushing and demand-pulling as monetary phenomena

So called cost-push inflation and demand-pull inflation don't have to be viewed as explanations contrary to the idea that inflation is a strictly monetary phenomenon. Increasing prices through cost-pushing and demand-pulling are indeed present in inflationary episodes and can validly be recognized from a monetary viewpoint. They have, however, to be viewed not only as manifestations or symptoms but as causes of inflation, via either money supply or money demand.

This is true even if you use the monetarist frame. For instance, remember of Friedman (1) setting down wages as a determinant of the velocity of money. According to this, a rise in wages (as in a policy of rising minimum wages) could not necessarily be reflected in unemployment but could rather put pressure on prices. In the extreme case, we would have:

(↑w)L+rK=
(↑v)M=
(↑P)Q

This is: we could have, following the necessary logic consequences of Friedman representation of v, a cost pushing on prices within the equation of exchange (or at least the Friedmanite version of it).

(1) Friedman, Milton. The Quantity Theory of Money−A Restatement. 1956 -University of Chicago Press, 1987-. Page 293. See particularly equation 13.