Suppose the Fed reduces the money supply and the demand for money is fixed. Will the interest rate increase or decrease as a result of the Fed selling bonds?

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In the scenario that you give here, the interest rates that banks charge will go up, all other things being equal.

In this scenario, the Fed is reducing the money supply by selling bonds.  When the Fed sells bonds, banks are buying the bonds with their reserves.  When the banks...

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In the scenario that you give here, the interest rates that banks charge will go up, all other things being equal.

In this scenario, the Fed is reducing the money supply by selling bonds.  When the Fed sells bonds, banks are buying the bonds with their reserves.  When the banks do this, there is less money in the money supply.  When the money supply goes down, the laws of supply and demand tell us that the price of money will go up.  The price of money is the interest rate.  Therefore, the interest rates will be going up because the supply of money is decreasing while demand for money remains constant.

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