Given the liquidity preference, an increase in the supply of money leads to a fall in the rate of interest. But, can the rate of interest fall to zero per cent or around that level? The answer is no. This is because the liquidity preference curve becomes flat and parallel to X-axis around an interest rate of 2 per cent, indicating, that at this low interest rate, the demand for money becomes almost infinite. Hence, whatever be the quantum of increase in money supply, it is entirely held by the people in their cash balances and, thus, does not lead to any further fall in the rate of interest. Thus, rate of interest cannot fall to zero, in fact it may fall below say 2 per cent. This is shown in the fig below.
With the given liquidity preference curve LP and money supply OQ0 as shown by the SM curve, the equilibrium rate of interest is Oi0, which may be as low as say 2 per cent. Now, if the money supply curve shifts to SM1 increasing the money supply to OQ1, the new equilibrium at E1 also gives the same rate of interest Oi. The rate of interest, thus, remains unchanged. This is because the liquidity preference curve becomes flat in the range E0E1 onwards. This flattening of the liquidity preference curve at lower interest levels is known as liquidity trap. Any increase in money supply over this range cannot further push down the rate of interest.
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