Establish Money Market Equilibrium
Assume an increase in the nominal money supply.
Because there is a change in a nominal variable this time, the short- and long-run predictions differ.
In the short run, you assume sticky prices. At the same prices, if the initial nominal money supply of M1 increases to M2, the real money supply also increases. As a result, the real money supply curve increases (shifts to the right). Therefore, in the short run, you predict a lower real interest rate (r2) and a higher quantity of real money (m2).
To express your long-run predictions, make use of the Quantity Theory of Money. This theory states that, in the long run, the price level increases at the same rate at which the nominal money supply increased. Therefore, you expect the percent increase from P1 to P2 to match the increase in the nominal money supply from M1 to M2.
In this case, the real money supply curve returns to its original position, indicating r1 as the equilibrium real interest rate and m1 as the equilibrium real quantity of money. The real quantity of money is the same as before m1 because the price level and the nominal money supply have increased by the same proportion (M1 / P1 = M2 / P2).