Principles of Economics/Liquidity trap
Normally, monetary policy works because a change in the money supply changes interest rates, which then goes on to change most other things in the economy. However, there is a possibility that in certain situations, most often during financial crises (especially banking crises), an economy may enter a liquidity trap, in which an increase in the money supply does not further lower the interest rate. The demand for money is so responsive, or elastic, that it completely consumes all the additional money, without helping to boost the economy. In this situation, monetary policy is futile (unless it is practiced at a point above (to the left of) the liquidity trap, which would be even worse for the economy).
Beyond a certain point (the liquidity trap line), L(r,y), the money demand, becomes perfectly horizontal. Shifts in (M/P)S, the money supply, in this area have no effect on interest rate r. This is what the diagram shows.