According to the classical theory, interest, in real terms, is the reward for the productive use of capital, which is equal to the marginal productivity of physical capital.

In a money economy, however, as physical capital is purchased with monetary funds, the rate of interest is taken to be the annual rate of return over money capital invested in physical capital assets.

According to Keynes, true classical theory of interest rate is the savings investment theory. It was presented in a refined form by economists like Marshall, Pigou, Taussig, and others.

Basically, the theory holds the proposition based on the general equilibrium theory that the rate of interest is determined by the intersection of the demand for and supply of capital.

Thus, an equilibrium rate of interest is determined at a point at which the demand for capital equals its supply.

Demand for capital stems from investment decisions of the entrepreneur class. Investment demand schedule, thus, reflects the demand for capital, while the supply of capital results from savings in the community.

Savings schedule, thus, represents the supply of capital. It follows that savings and investment are the two real factors determining the rate of interest.

In technical jargon, the rate of interest is determined by the intersection of investment demand schedule and the savings schedule. At the equilibrium rate of interest, total investment and total savings are equal.

It should be noted that the theory assumes real savings and real investment. Real savings refer to those parts of real incomes which are left unconsumed to provide resources for investment purposes.

Reinvestment implies use of resources in producing new capital assets like machines, factory plants, tools and equipment, etc. It means investment in capital goods industries, in real terms.

**Demand for Capital**:

Demand for capital comes from entrepreneurs who wish to invest in capital goods industries. In fact, demand for capital implies the demand for savings.

Investors agree to pay interest on those savings because the capital projects, which will be undertaken with the use of these funds, will be so productive that the returns on investment realised will be in excess of the cost of borrowing, i.e., interest.

In short, capital is demanded because it is productive, i.e., it has the power to yield an income even after covering its cost, i.e., interest. The marginal productivity curve of capital, thus, determines the demand curve for capital.

Indeed the marginal productivity curve is, after a point, a downward sloping curve. While deciding about an investment, the entrepreneur, however, compares the marginal productivity of capital with the prevailing market rate of interest.

Marginal productivity of capital = marginal physical product of capital x the price of the product. Given marginal productivity, when the rate of interest falls, the entrepreneur will be induced to invest more till marginal productivity of capital is equal to the rate of interest.

Thus, investment demand expands when the interest rate falls and it contracts when the interest rate rises. As such, investment demand is regarded as an inverse function of the rate of interest. In symbolic terms:

I = f(r), in which ΔI/Δr < 0

Where, I = investment demand, r = rate of interest, and f = functional relationship panel (a) illustrates an investment demand schedule in graphical terms.

It can be seen that when the rate of interest is OR, the investment volume is OQ _{
1
} When the interest rate falls to OR _{
2
} , investment volume rises to OQ _{
2
} . It follows that the investment demand curve is a downward- sloping curve.

**Supply of Capital:**

Saving is the source of capital formation. Therefore, supply of capital depends basically on the availability of savings in the economy. Savings emerge out of the people's desire and capacity to save.

To some classical economists like Senior, abstinence from consumption is essential for the act of saving while economists like Fisher stress that time preference is the basic consideration of the people who save.

In both the views, rate of interest plays an important role in the determination of savings. The classical economists commonly hold that the rate of saving is the direct function of the rate of interest.

That is, savings expand with the rise in the rate of interest and, when the rate of interest falls, savings contract. In symbolic terms, the saving function may be stated as follows:

S = f (r), in which ΔS/Δr > 0

Where, S = volume of savings,

r = rate of interest, and

stands for functional relationship.

Panel (b) illustrates the savings schedule in graphical terms.

The savings schedule refers to the quantum of savings at alternative rates of interest. When the rate of interest is, OR _{
2
} , OQ _{
1
} is the savings; when the rate of interest rises to QR _{
1
} savings expand to OQ _{
2
} level. The saving-function or the supply of savings curve is an upward-sloping curve.

It must be noted that savings and investment, referred to in the above functions, are in real terms.

**Equilibrium Rate of Interest**:

The equilibrium rate of interest is determined at that point at which both demand for and supply of capital are equal. In other words, at the point at which investment equals savings, the equilibrium rate of interest is determined.

OR is the equilibrium rate of interest which is determined at the point at which the supply of savings curve intersects the investment demand curve, so that OQ amount of savings is supplied as well as invested.

This obviously implies that the demand for capital (OQ) is equal to the supply of capital (OQ) at the equilibrium rate of interest (OR).

Indeed, the demand for capital is influenced by the productivity of capital and the supply of capital. In turn, savings are conditioned by the thrift habits of the community.

Thus, the classical theory of interest implies that the real factor, thrift and productivity in the economy, are the fundamental determinants of the rate of interest.

**Criticisms:**

Keynes is a firm critic of the classical theory of the rate of interest. Major criticisms levelled against the classical theory are as follows:

1. Keynes attacks the classical view that interest is the reward for saving. He points out that one can get interest by lending money which has not been saved but has been inherited from one's forefathers.

Similarly, if a man hoards his savings in cash, he earns no interest. Further, the amount of saving depends not only on the rate of interest but also on the level of income, and hence the rate of interest cannot be a return on saving or waiting.

According to Keynes, interest is purely a money phenomenon, a payment for the use of money and that the rate of interest is a reward for parting with liquidity (i.e., dishoarding cash balances of money) rather than a return on saving.

2. Keynes further maintains that the classical theory of interest is indeterminate and confounding. Hence, we cannot know the rate of interest unless we know the savings and investment schedules, which again, cannot be known unless the rate of interest is known. Thus, the theory fails to offer a determinate solution.

3. Further, the classical theory looks upon money merely as a medium of exchange. It does not take into account the role of money as a store of value.

It assumes that income not spent on consumption should necessarily be diverted to investment; it ignores the possibility of savings being hoarded.

These factors make the classical theory unrealistic and inapplicable in a dynamic economy. It fails to integrate monetary theory into the general body of economic theory.

4. According to the classicists, the rate of interest is an "equilibrating" factor between savings and investment.

In the view of Keynes, "The rate of interest is not the price which brings into equilibrium the demand for resources to invest with the readiness to abstain from present consumption.

It is the price which equilibrates the desire to hold wealth in the form of cash with the available quantity of each."

5. Keynes also points out that equality between saving and investment was brought about by changes in the level of income and not by the rate of interest, as asserted by the classical economists.

6. It has been pointed out that the classical interest theory is narrow in scope. It considers only the capital meant for investment. It makes no consideration for consumption loans.

7. The classical theory pays no attention to the significance of newly created money and bank credit in the determination of interest.

According to it, if there is an increase in the demand for investment, the saving schedule remaining unchanged, the rate of interest will rise.

But today, savings are supplemented by credit and the rate of interest may not rise despite an increase in the investment demand.