Question

Discuss the relationship between the neutrality (and super-neutrality) of money and the quantity theory of money. Does either of them imply the other?

Answer 1

The Money Quantity Theory and Money Neutrality go hand in hand. Finding one without the other is very difficult. As mentioned above, QT and NM explicitly believe that (base) cash is exogenous, they are only valid under very strict conditions. But when cash is endogenous, it is easy to define variants of QT and NM that are appropriate. Suppose, for example, the central bank sets the exchange rate, which means endogenously changing the cash stock.

"If the central bank doubles the foreign exchange rate permanently: all nominal variables will double[ the quantity theory of money]; all real variables will remain unchanged. [that's the Neutrality of Money]

And, assume that the central bank targets NGDP, which also means endogenously changing the cash stock. "If the central bank increases the NGDP target level permanently: all nominal variables will double[ that's Quantity Theory of Money]; all real variables will remain the same[ that's Money Neutrality].

And so on. A doubling of the price of foreign exchange (or the NGDP target, or whatever nominal variable the central bank picks), will cause the stock of money to double, along with all other nominal variables. The stock of money is now endogenous, and the exchange rate (or NGDP) is now exogenous.

Whether true or false, the Quantity Theory of Money and the Neutrality of Money, are equally applicable in a world where the stock of money is determined endogenously. The same underlying idea of the classical dichotomy, that nominal variables (those with $ in the units) and real variables (those without $ in the units) are independent of each other (under some conditions), is equally applicable regardless of what is assumed exogenous.