Othyem, the problem is pp. 61-62, of professor Selgin’s Theory of Free Banking.
i. Mises took the 100% reserves position, because he uses Bohm-Bawerk’s capital theory. Selgin does not link money theory to capital theory, which allows him to avoid what he believes to be “mistaken view” of Mises.
However, this cannot be done, and Mises is not mistaken. Separation of meeting demand for loanable funds independent of operation and success of whole economic system cannot be considered.
So long as market interest rate, determined by quantity of loanable funds and demand for loanable funds, is used as representitive to quantity of capital at immediate future, which is something no-one can directly observe, since each person has his own individual time-preference, expressed in their respective saving and spending habits.
ii. Express this problem in another way, minus ecomic jargon, as one mathematician I respect greatly did.
Every ADAPTIVE SYSTEM has:
(1) variable quantity Z which is citerion of fitness (e.g., profitability);
(2) variable quantity X determining fitness of system at time T, which is not directly observable, as function of system’s behavior B; if it was, then there would be no problem and no reason for adaptation, would there?;
(3) vector Y, which is directly observable, which is linked in predictable way to X;
(4) system itself, which is function of Y;
(5) system’s behavior B;
(6) variable quantity, decreasing as absolute deviation of X from Z is increasing, which determines probability that this whole system continues to function in next time period.
Every adaptive system’s survival hinges, thus, upon step number (3).
Edit: As I mentioned in earlier post, an alternative to 100% reserve is one currency per bank, exclusive to each particular bank, which cannot be eliminated by competition. All credit expansion causes change in value and acceptability of that currency, discounting it to such extent that it would be if banks had 100% reserves of one common currency. Exactly same as adding a point (7), variable quantity C mapping to Y, such that system is now function of C, not of Y directly.