Indeterminacy of the Theories of Interest (With Diagram)

In this article we will discuss about the indeterminacy of the theories of interest.

Keynes criticised the classical theory of interest for being indeterminate because it failed to relate the rate of interest with the income level. To Hansen, “Keynes’s criticism of the classical theory applies equally to his own theory and to the loanable funds theory.”

We illustrate below the indeterminate nature of these theories:

In the classical formulation, since savings depend upon the level of income, it is not possible to know the rate of interest unless the income level is known beforehand. And the income level cannot be known without already knowing the rate of interest. A lower rate of interest will increase investment, output, employment, income and savings. So, for each income level a separate supply curve will have to be drawn.

The same reasoning applies to the loanable funds formulation of the rate of interest. The supply schedule of loanable funds is composed of savings, dishoarding and bank money supply. Since savings vary with past income and the new money and activated balances with the current income, it follows that the total supply schedule of loanable funds also varies with income. Thus this theory is indeterminate unless the income level is already known.

The indeterminate nature of both the theories is explained with the help of Figure 6. All that the classical formulation gives us is a family of saving schedules, and the loanable funds formulation a family of investment schedules at various income levels relating them to different interest rates.

We take saving and investment (or demand and supply of loanable funds) on the X-axis and the rate of interest on the vertical axis. The savings schedules (for both the formulations) are shown as S₁Y₁ and S₂Y₂ and II is the investment demand schedule.

When income is Y₂, given the investment demand schedule and II, and the savings schedule S₂Y₂, savings equal investment at interest rate r. Similarly when income is Y, the savings schedule S₂Y₂ equals the investment demand schedule II at interest r_t.

These equilibrium positions tell us about the various levels of income associated with different rates of interest, but not about the rate of interest itself. They show that interest is a function of savings, investment and the level of income. Unless the level of income is known, it is not possible to determine the rate of interest. Hence the classical and the loanable funds theories of interest rate are indeterminate.

The Keynesian theory of interest rate is also indeterminate because the liquidity preference schedule is not related to the level of income. Unless the income level is known beforehand, the demand and supply curves of money cannot tell us what the rate of interest will be.

All that the Keynesian formulation provides us is a family of liquidity preference schedules at various income levels relating them to different interest rates. In Figure 7, a family of liquidity preference schedules LY, L_tY₁ and L₂Y₂ is drawn at various income levels.

A perfectly inelastic money supply curve QM is drawn on the assumption that the supply of money is fixed by the monetary authority. If Y is the income level, the liquidity preference schedule LY equals the money supply schedule QM at interest rate r.

If the income level rises to Y₁, the liquidity preference schedule also shifts upward to L₁M_t and equals the QM curve at the interest rate r. If income falls to Y₂ level, the liquidity preference curve shifts to L₂Y₂ and equals QM curve, at the interest rate r₂. Thus the Keynesian theory simply relates different income levels to various interest rates, but does not show what the rate of interest will be. Hence it is an
indeterminate theory.