It is important to distinguish the cause and effect of the twovariables - you are asking why a decrease inmoney supplyleads to an increase ininterest rates,and the replies have so far been telling you why an increase ininterest rates leads to a decrease in moneysupply.
So, can you change the money supply to have an effect on interestrates? Yes. Let's see what happens.
First, you have a decrease in money supply. This is usually theresult of a central bank policy (although we shall not go into howexactly they do this - might be confusing). Assuming that we are inthe short run, prices are given (i.e. do not change) and moneydemand remains the same. Now, there is a disequilibrium in themoney market, where money demand is greater than moneysupply.
Keeping that in mind, we now look at the initial equilibriuminterest rate, r*. Now, at this currentinterest rate,people are holding less money than they desire, so they sell theirassets (that pay interests) to have greater liquidity. However, aswe have mentioned earlier, money demand is greater than moneysupply, there will be more people wanting to sell assets to obtainliquidity than people willing to buy assets and giving upliquidity.
As a result, the interest rates get pushed up slowly, so as toreflect the market mechanism of creating a greater incentive forpeople to hold on to / buy assets. The interest rate will then riseto a point where there are equal number of assets being bought /sold. At this same point, money demand would also have decreased tomatch the lower money supply.
Hope that helps, and let me know if it doesn't. It probably means Iwasn't clear enough.
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