The classical theory of the rate of interest [the loanable funds theory] seems to suppose that, if the demand curve for capital shifts or if the curve relating the rate of interest to the amounts saved out of a given income shifts or if both these curves shift, the new rate of interest will be given by the point of intersection of the new positions of the two curves. But this is a nonsense theory. For the assumption that income is constant is inconsistent with the assumption that these two curves can shift independently of one another. If either of them shift, then, in general, income will change; with the result that the whole schematism based on the assumption of a given income breaks down … In truth, the classical theory has not been alive to the relevance of changes in the level of income or to the possibility of the level of income being actually a function of the rate of the investment.Read the rest here.
There are always (at least) two parts in an economic transaction. Savers and investors have different liquidity preferences and face different choices — and their interactions usually only take place intermediated by financial institutions. This, importantly, also means that there is no “direct and immediate” automatic interest mechanism at work in modern monetary economies. What this ultimately boils done to is — iter — that what happens at the microeconomic level — both in and out of equilibrium — is not always compatible with the macroeconomic outcome. The fallacy of composition has many faces — loanable funds is one of them.