Why isn't the Fed funds rate greater than interest rate on loans to the pubic First of all, fed funds rate is the rate banks borrow reserves' from each other. Interest rate on loans is the rate the bank charges to public for its loan. From one line of logic, we think of the rate bank charges to public should clearly be greater than the interest rate itself bear to borrow since banks are making a margin. And empirical data clearly support it.

However, another line of logic does not quite support it. We know the banks borrow reserve money in fed funds market, which is clearly better than the money it lends to the public in the following sense: one unit of fed funds can support 10 units of additional deposit if the reserve-deposit ratio is 10%. So the banks with this addtional 1 unit of reserve, can theoretically make 10 more units of loans and therefore creating 10 more units of deposit. So reserve is better money. Hence, theoreticaly, the fed funds rate should at leastbe higher than the rate banks make loans to the public, if not 10 folds.

My question being whether there is a logical fallacy in my understanding and if not, what kind of reality deviated it from theory.
I think you are missing the credit risk attached to any loan. You, as an individual borrower, are far more likely not to reimburse your loan than a bank. Thus the loan is far less risky.

Central bank money could only be qualified as "better" (even that does not mean much) because it is issued by the Central bank, deposits are issued by commercial bank, so you bear the risk that your bank fail, but it happens that in most country individual deposits are insured by some state agency. So I cannot really see why central bank money would be better than deposits.

Nowadays, the amount of reserves that a bank must hold does not actually play a big role in the economy (as opposed to what most of economic textbooks and economic professors are teaching in undergrad schools). The most important part is the interest rate that is paid on those reserve, which is fixed by the central bank and which act as an opportunity cost for the bank when it decides to lend to an individual rather than holding reserves.

However I see your point, but the fact is that this way of thinking is misleading. Banks create (in theory) as many loans as they want, because there are no physical constraints, if you want, that prevent them to do so. The only constraint is a regulatory constraint that states that in order to remain solvent (in order to be able to repay the depositors) banks should invest x% of the assets in reserves. Those reserves would be held on a central bank account in central bank money, and the return on those reserves will be the fed fund rate decided by the central bank (the same way a commercial bank decide how much interest it will pay on your savings account). So it is true that one more unit of reserves gives the right to issue more than one unit of loans but this does not mean that one money is better or worse than another. It's is just a matter of regulation.

It may be hard to get, but the point is really that central bank money is safer so cheaper than deposits, no matter what regulatory constraints apply to banks.

You may want to read this paper which may be a bit complicated but you should get the intuition. This two docs may be simpler (with nice pictures) : doc 1, doc 2.