If banks do not loan out all their excess reserves, then the real world multiplier is

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The real world multiplier is equal to 1/R_d if all excess reserves are loaned out by banks. However, if banks do not loan out all their excess reserves, the multiplier will be smaller than 1/R_d. This is because the amount of new money created by the banking system depends on the amount of excess reserves that are loaned out. If banks hold onto some of their excess reserves, then the amount of new money created will be lower than it would have been otherwise, reducing the multiplier.

If Banks Do Not Loan Out All Their Excess Reserves