# I don't understand the MV = PY

I'm not a native speaker so please excuse my English.

When they draw the result that the central bank's monetary supply determine the inflation rate, didn't they suppose many variables sticky?

With money supply matching up with the demand, they start their train of logic as follows. MV = PY, here the Y is fixed since it's exogenous, and V is fixed for the convenience of computation, so M controls the P... Okay I get that part, but what I wonder is that, when you fix the V, doesn't that make the k also fixed, which means kY, the money demand function is eventually fixed.

Then, how can they manipulate the M when they assumed M equals to the fixed demand of money?

Money demand is fixed because it depends on the real economy....that's an assumption. So when M changes only P can change. That's the theory. It's not really a theory. Just an accounting equality, since V is never defined exogenously. It's bad economics. :/

$$M\cdot V=P\cdot Y \Leftrightarrow M=\frac{P}{V}\cdot Y\\ \frac{1}{V}=k \Leftrightarrow M=kPY$$ So suppose we keep $$V$$ and $$Y$$ fixed and vary $$M$$, $$P$$ varies as well and this means $$kPY$$ also varies (because of P). More specifically when money supply goes up while keeping velocity and output constant, the price level has to rise,(raising money demand to equal money supply).

• In my text book, Macroeconomics 7th edition by Gregory Mankiw, it says V = 1/k, there's no P there. What am I missing? – dolco Mar 22 '19 at 10:44
• i have edited the answer – Milton Keynes Mar 22 '19 at 11:48

I'm the OP. I've solved it. What I was missing was that the fixed supply is nothing but the 'real supply'.

1.real demand = kY (fixed)

2.real supply = M/P (fixed)

When they said "the central bank controls the money supply", it meant it manipulate the M only. So P should also change by the same rate to make the whole 'real' supply, M/P, equal to kY. It was so easy. I kind of feel stupid now :D