Gold
Well, sort of. Most of these people would, I imagine, envision a return to gold coins and private bank notes backed up by 100% reserve requirements. Personally I think that gold is too valuable and will make small transactions tricky. The obvious answer is silver but then you can't go bimetallic with a fixed exchange rate or there will be trouble. The other problem with gold and silver, the most serious problem as I see it, is that they are quite soft and suffer wear, thus lowering their value over time. There are engineering solutions to this, and I believe I have come up with one of them.
Most coins of the last few centuries are pretty similar. Raised images and lettering on both sides, with a raised edge produced through rolling. These days the raised edge is just part of the work hardening of the piece, really, since most coins contain a large amount of copper, but in the past it was there to make coin clipping easily visible. Coin clipping is the practice of cutting pieces off a precious metal coin in order to sell the valuable metal or strike your own coins. Precious metal coins are supposed to be a particular weight and purity, which is certified by the fact that they are struck as coins. Leave most of the coin intact while removing a small piece of it, and you can spend the coin at the same value as before, plus you now have some extra gold to sell.
The fact that a substantial portion of the coin is proud gives us the chance to produce a more durable gold or silver coin. Simply replace the edge and the images with some superalloy like inconel, strike the whole thing together and you have a (mostly) gold coin with that attractive two tone finish that can really handle the ravages of everyday commerce.
Not exactly what I meant but you get the idea
Gold is so much more valuable than inconel that it will represent nearly all of the coin's value, and you may then produce coins with quite a small amount of gold set into them to make smaller denominations. Speaking of which, here comes engineering solution number two.

Now we come to the sticky subject of bank notes. Under the above monetary system, it would be most efficient to have each bank duly print its own notes or perhaps contract some excellent third party printer, which amounts to the same thing, but, crucially, the bank notes should have the same denomination as the precious metal currency they are standing in for. When someone presents a bank with one of its own notes, say a $5, it should give a $5 coin, or if both parties agree, $5 in other change at whatever floating exchange the two agree on. Banks should in general be willing to accept the notes of other banks, since they can then simply go to the bank in question and demand their specie for use as loans or reserves.
Loans and demand deposits are an interesting one. If all demand notes were to have a specified loan lifetime then the interest the bank earned loaning the money out could pay the storage fee. The note could then be redeemed at any time after the loan expiry but, critically, there would be an incentive to redeem the note as soon as it fell due, since banks could charge a storage fee or keep the money loaned out earning them nice interest for which the bearer could not demand a return. He would then want to redeem the note and perhaps loan the money out again at a better interest rate, save it in his own safe or just spend it. Banks could even redeem demand notes sooner than the due date, for a small fee of course.
All of that would mean that the total money supply might be about double the amount of the actual gold and silver. Now let's consider loans. In this economy, all bank loans would come out of savings in those banks of actual savers who have actually deposited the money there. They could not simply print more demand notes than there was metal, since other banks and people would certainly come to redeem them. They would, however, print loan notes. These would be interest bearing assets given to people who deposit money for a given time at a given interest rate. The loan's value, due date and interest rate would be on the loan note. If the depositor fell on hard times he could liquidate the note by selling it to a bank, or anyone really. The price paid for it would closely relate to all three essential features of a loan: interest, term and principal. These loan notes, then, would not circulate as currency but would be rapidly convertable, making them a kind of money. Their impact on the money supply would not be great, however. The borrower would be given demand notes or specie, what he preferred would make little difference to the bank. Large loans might require a fairly hefty amount of gold so it would be more convenient for someone borrowing money to build a power station, for instance, to get that money as demand notes, but in principle any form of money would be equal.
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