Do current Central Banks need to target a monetary aggregate as they set interest rates for a target inflation? [closed]

On reading a textbook, the author state that after the 80's, and the serious consequences of thinking that inflation could be controlled by just targeting a monetary aggregate, modern central banks(CB) have shifted their paradigm to a targeting inflation by setting the interest rate. My question is if the CB sets the interest rate, does he need to target M0? Or does the CB just print money according to money demand?

Any help would be appreciated.

closed as unclear what you're asking by EnergyNumbers, cc7768, Kitsune Cavalry♦, optimal control, VicAcheFeb 1 '16 at 12:32

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• It's very difficult to work out what you are asking. What do you mean by "the interest rate" - which one? Which Central Bank? – EnergyNumbers Jan 29 '16 at 10:23

The demand for liquidity is usually defined as $$L(Y,i)$$ where $Y$ is income and $i$ is the nominal interest rate. In equilibrium this equals the aggregate money supply $M$ which is function of several things, like $M_0$ the reserve rate, etc. Let us assume that everything except $i$, $M_0$ and $M = f(M_0)$ is constant. Then $$L(Y,i) = M = f(M_0).$$ Demand for liquidity decreases in $i$ and $M$ increases in $M_0$. Thus for any given value of $i$ there is at most one equilibrium value of $M_0$, hence the central bank cannot simoultaneously set both $i$ and $M_0$ and always expect an equilibrium outcome. Lacking equilibrium either $i$ or $M$ will shift.