1. Money Supply
Even though the Federal Reserve system in the US or any other central bank cannot control the money supply very accurately, we will assume, for the sake of simplicity, that it can do so regardless of the interest rates.

2. Increase in Money Supply
m1=M1 / P1
m2=M2 / P1
m=M / P

3. Increase in Money Supply: Real Balance Effect P2 < P1
m1=M1 / P1
m2=M1 / P2
m=M / P

4. Decrease in Money Supply: Real Balance Effect P1 < P2
m1=M1 / P2
m2=M1 / P1
m=M / P

5. Equilibrium Nominal Interest Rate
m1=M1 / P1 r
md(y1)
m=M / P
M1 / P1

6. Equilibrium Nominal Interest Rate
m1=M1 / P1 r2
md(y2) r1
md(y1)
m=M / P
M1 / P1

7. Liquidity Effect and the Interest Rate
Initial liquidity effect of an increase in the money supply r
m1=M1 / P1
m1=M2 / P1 r1 r2
md(y1)
m=M / P
M1 / P1