This is the oldest economic theory and dates back to the 16th century. V has been increasing with technology and varies with the interest rate, but in a short time period is approximately constant. If you make a small change in the money supply it could result in a myriad of possible changes in P and Y and exactly what might happen can not be determined. For example, in the 70s with OPEC creating cost push inflation, labor unions insisted on COLA, cost of living adjustments, in their labor contracts. With COLA, labor's wages are automatically adjusted to inflation so that they maintain constant purchasing power.
Manufacturers also adjust to inflation in the manner in which they adjust prices.
Before the inflation of the 70s auto manufacturers adjusted prices once a year. With inflation to avoid sticker shock they adjust prices many times during the year in small increments. All economists agree that economic actors adjust the strategies with respect to their expectations of inflation. Where economists disagree is how well economic agents are able to forecast inflation. A weaker assumption is adaptive expectations that assumes economic actors adapt towards rational expectations.