Economics is the science of confusing stocks with flows.
What is the market of loanable funds? It is supposed to be the market that equilibrates the demand for savings with the demand for investment. But if such a market existed, it would be a market for flows, not stocks.
However the bond market is a market of stocks. The capital market is a market for stocks. Both bonds and capital persist across periods and can be re-sold. Everyone who owns a bond (or who owns capital) is a potential supplier of bonds or capital at some rate. Everyone is also a potential demander of bonds or capital at some rate.
As the interest rate changes, some suppliers become demanders, so that at equilibrium, supply (of the stock) is equal to the demand (for the stock). This is the equilibrating process for stocks that can be re-sold by their current owner in any period.
But lending and investment are the derivatives of these quantities with respect to time — they are flows.
Can the interest rate equilibrate both flows and stocks?
A flow of investment — say capital goods producing firms or borrowing — leaves the current period stock of capital or bonds unchanged, but the growth rate of these stocks changes. In future periods, there will be a greater stock of capital or bonds as a result of an increase in the flow of investment or borrowing. And we can imagine that there might be a demand for a flow of savings or a demand for a flow of lending.
As a simple example, suppose that all bonds are consols — to avoid issues with changes to the quantity of bonds due to bond repayment. The equivalent assumption for capital would be no depreciation.
In that case, let be the total quantity of bonds or capital. Then the growth rate of bonds or capital will be .
If the rate, is such that the quantity of bonds demanded is the quantity of bonds supplied:
Where are the interest-elasticities of supply and demand (for the stock).
At the market clearing rate, we have , so dividing both equations yields:
Therefore the interest rate that equilibrates stocks will only equilibrate flows in one of three special cases:
- Supply and demand for flows is zero ()
- The interest-elasticities are zero ()
- Flows are stocks. I.e. all capital depreciates to zero instantly and all bonds are repaid instantly.
None of these assumptions hold in any economy. Nor is plausible to believe that they should hold in simple models.
Therefore the interest rate can only equilibrate the level (stock) of bonds or capital so that at that rate, agents are just as likely to buy the capital from someone else as they are to sell it to someone else. But interest rates cannot clear flows — they cannot clear lending and borrowing, savings and investment.
The flows will be whatever is profitable at the rate, which may not be what is demanded at that rate.