Comprehensive Notes on the Modern Theory of Interest

Neo-Keynesian economists like Hicks, Lerner and Hansen are of the opinion that loanable funds formulation and the Keynesian liquidity preference formulation taken together do supply us with an adequate theory of the rate of interest.

This is referred to as “the neo-Keynesian synthesis.” It provides a determinate theory of interest. It successfully combines all the four factors savings, liquidity preference, investment and the quantity of money into a well-integrated theory.

It combines monetary and real factors to seek an explanation of the determination of the rate of interest.

It should be noted here that earlier, the loanable fund version had made an unsuccessful attempt to combine these real and monetary factors in explaining the interest rate determinations. This task was successfully carried out by the neo-Keynesians.

In expounding the modern theory of interest, Professor Hansen, in his Monetary Theory and Fiscal Policy, points out that there are four determinants of the rate of interest:

1. The investment demand schedule;

2. The consumption function;

3. The liquidity preference schedule; and

4. The quantity of money.

Using the classical terminology, there are, four determinants of income and the rate of interest: (1) productivity; (2) thrift; (3) the desire for holding cash; and (4) the quantity of money or money supply.

The equilibrium condition of these four variables together determines the rate of interest. According to Hansen, “an equilibrium condition is reached when the desired volume of cash balances equals the quantity of money.

When the marginal efficiency of capital is equal to the rate of interest, and finally, when the volume of investment is equal to the normal or desired volume of saving. And these factors are interrelated.”

In short, according to the modern theory of interest, when the four variables, viz. saving, investment, liquidity preference and the quantity of money, are integrated with income, we get a fairly satisfactory explanation of the rate of interest.

For this purpose, a synthesis between the loanable funds formulation and the liquidity preference theory is evolved by neo-Keynesian economists (Hicks, Lerner and Hansen).

In fact, the aim of such a synthesis was to combine the real sector and the monetary sector as well as the flow and stock variables of these distributive theories (loanable funds and liquidity preference) together as an explanation of interest rate determination.

Thus, the neo-Keynesian synthesis evolved two schedules, the IS schedule and the LM schedule the former showing the equilibrium between the flow variables in the real sector and the latter representing the equilibrium of the stock variables.

When the IS and LM schedules are plotted graphically, their respective curves (the IS curve and the LM curve) give us the equilibrium rate of interest at the point of their intersection. At this equilibrium rate of interest:

(i) Total saving = total investment;

(ii) Total demand for money = total supply of money; and

(iii) The real as well as the monetary sectors are in equilibrium.

Let us now see, how these two schedules (IS and LM) and the respective curves are constructed.

The IS Schedule:

From the loanable funds formulation, we get a family of loanable fund schedules or saving schedules at various income levels. These together with the investment demand schedule gives us the IS schedule, and when represented diagrammatically we get the IS curve.

The IS curve denotes equilibrium in the real sector, showing various combinations of the levels of income (Y) and interest rate (r) at which there is equilibrium between aggregate real saving and real investment.

It is a commonly accepted dictum that investment is a decreasing function of the rate of interest (i.e., when the rate of interest is high, the investment is low and vice versa) and that saving is an increasing function of the level of income (i.e., saving increases as income increases).

Now, in order to derive the IS schedule, we have to find out those rates of interest and those levels of income corresponding to which investment is equal to saving from a given investment schedule and a given saving schedule. For this, let us construct hypothetical schedules.

To present the above schedules diagrammatically in a generalised form, let Y ₁ , Y ₂ , Y ₃ , Y ₄ and V ₅ represent respectively the income levels of Rs.1000, 1500, 2000, 2500 and 3000 crores in the economy.

We may assume that at these income levels, S ₁ , V ₁ , S ₂ , Y ₂ , S ₃ , V ₃ , S ₄ , Y ₄ , and S ₅ , V ₅ curves represent volumes of savings of Rs. 100, 200, 300, 400 and 500 crores respectively.

It is the investment curve when the income level is Y ₁ ; the equilibrium between saving and investment is established at R ₁ M ₁ rate of interest (7% in the given illustration).

Or at Y ₁ income level, R _l M ₁ is the equilibrium rate of interest which brings about equality between saving and investment (in our example, at 7% rate of interest S = 100 crores and / = 100 crores. (S – I).

Likewise, at the income level Y ₃ , R ₂ M ₂ rate of interest establishes equilibrium between saving and investment. And in the same manner, at income levels Y ₂ , Y ₄ and Y ₅ , the equilibrium between saving and investment is established by R ₃ M ₃ , and R ₄ M ₄ and R ₅ M ₅ rates of interest respectively.

Now, connecting together the various rates of interest equalising saving and investment at the corresponding levels of income, Y ₁ ,Y ₂ Y ₅ etc., we then get a curve called the IS.

It is easy to see from the diagram that each point along the IS curve gives different income levels at which the savings and investment are in equilibrium.

Thus, as Hansen points out, the non-classical formulation reveals that the various levels of income will be (given the investment-demand schedule and a family of loanable funds or saving schedules) at different rates of interest. But it does not show what the rate of interest will be.

The IS curve slopes downward to the right for the simple reason that at higher levels of income, saving is greater, but the greater the saving, the lower the rate of interest.

Thus, as the level of income rises, the rate of interest declines, with increasing saving. And, as the rate of interest declines, investment rises till saving equals investment.

Thus, the downward-sloping IS curve shows the relation that given the investment function, the consumption function from given income is high at low rates of interest, and low at high rates of interest.

It goes without saying that the position of the IS curve depends on the position of the saving and investment curves, so that any change in the relative position of two curves will change the position of the IS curve accordingly.

Hansen points out that the IS curve depends upon the level (and shape) of the marginal efficiency of investment schedule and equally upon the level (and slope) of the consumption function (which in turn determines the saving schedule).

This means that the slope of the marginal efficiency of investment curve, the II curve, at different levels of interest rate, together with the slope of the consumption function (which in turn determines the saving schedule).

This means that the slope of the marginal efficiency of investment curve, the II curve, at different levels of interest rate, together with the slope of the consumption function (or saving schedule – SY curves) at different levels of income, determine together the slope of the IS curve.

An upward movement in the marginal efficiency schedule (II curve) or in the consumption function or both will raise the level of income corresponding to each given rate of interest; hence the IS curve will also be shifted upward.

The LM Schedule:

In order to observe the monetary sector equilibrium in the theory, neo-Keynesians have derived the LM schedule or curve from Keynes’ liquidity preference theory.

It has been pointed out that the liquidity preference function L and the money supply M also establish a relation between the income and the rate of interest. Hansen states that from the Keynesian formulation we get a family of liquidity preference schedules at various income levels.

These, together with the supply of money fixed by the monetary authority, give us the LM schedule. The LM schedule tells us what the various rates of interest will be (given the quantity of money and the family of liquidity preference schedules) at different levels of income.

It should be remembered that the liquidity preference schedule alone cannot tell us what the rate of interest will be.

In fact, the LM schedule shows the relation that (given a certain liquidity or demand schedule for money) and a certain quantity of money fixed by the monetary authority; the rate of interest will be low when income is low and high when income is high.

Thus, the LM schedule is the schedule showing the relation between income and interest (given the L function and the supply of M) when the desired cash equals the actual cash, or when L – M.

This means, the LM schedule presupposes equilibrium between L and M, just as the IS schedule presupposes equilibrium between I and S ⁴ .

We construct a hypothetical LM schedule on the next page.

For a diagrammatic representation in a generalised form, we assume that Y ₁ , Y ₂ , Y ₃ , Y ₄ , Y ₅ represent respectively the income levels Rs. 1,000, 1,500, 2,000, 2,500 & 3,000 crores, and L ₁ Y _V L ₂ Y ₂ , L ₃ Y ₃ , L ₄ Y ₄ , L ₅ Y ₅ are the liquidity preference curves at different income levels Y ₁ , Y ₂ etc.

The LY curve represents the demand for cash at different income levels. Further, it has been assumed that the supply of money is fixed and interest inelastic. This is represented by OM.

In Y ₁ income level, the equilibrium between the demand for and supply of money is established at R ₁ M rate of interest. At Y ₂ income level, the equality between the demand for and supply of cash is established at R ₂ M rate of interest.

In the same manner, R ₃ M, R ₄ M and R ₅ M rates of interest bring about equilibrium between the demand and supply of money at Y ₃ , Y ₄ and Y ₅ income levels respectively.

When we draw a curve relating various levels of income to the corresponding demand for the limited money supply (as it is fixed) and so the rate of interest rises steeply; the LM curve becomes highly inelastic with respect to the rate of interest at high income level, at low income levels there rates of interest, which equalise the demand and supply of money, we get the LM curve.

Thus, the LM curve shows the various rates of interest which equalise the demand for money (liquidity preference) of the people with the supply of money at various income levels. Thus, the LM curve denotes equilibrium in the monetary sector as such.

The LM curve slopes upward to the right for the simple reason that, as the income increases, the liquidity preference or the demand for money, increases and, consequently, the rate of interest also increases.

On the other hand, when the level of income falls, the liquidity-preference of the people also diminishes, hence the rate of interest declines.

It should be noted that at high levels of income there is a large “transactions” is relatively a small transactions demand for money, so that a larger part of the money may be held as idle balances; the effect is to lower the rate of interest.

But since the liquidity preference function L is highly elastic at low interest rates due to the speculative demand for money, the relative super-abundance of the money supply at low income levels cannot drive the rate of interest much below a certain minimum. Thus, the LM curve at low income levels becomes interest-elastic.

A shift in the LM curve is caused by either: (1) an increase in the quantity of money (M) or (2) a decrease in the liquidity preference function. Thus, either a decrease in the liquidity preference function or an increase in the quantity of money will shift the LM curve to the right, as shown in LM ₁ .

Determination of the Rate of Interest:

According the modem theory of interest, the intersection of the IS and LM curves determines the rate of interest. Y” is how the real sector and the monetary sector are integrated by the neo-Keynesian synthesis in explaining interest rate determination.

It is easy to see that the changes (shift) in the IS curve or changes the LM curve or both and their respective positions determine the equilibrium rate of interest accordingly.

The IS curve which denotes equilibrium in the real sector shows the various combinations of the levels of income and interest rate at which there is equilibrium between aggregate real saving and real investment.

It may be interest-elastic at high levels of income and interest-inelastic at low income levels.

On the other hand, the LM curve which denotes equilibrium in the monetary sector shows those various combinations of the levels of income and interest rates corresponding to which the supply of and demand for money are in equilibrium.

The LM curve is interest-inelastic at high income levels and interest-elastic at low income levels. Income and the rate of interest are, thus, determined together at the point of intersection of these two curves.

In the rate of interest is RM, determined by the intersection of the IS and the LM curves at point R. At this point, income and the rate of interest stand in such relation to each other that: (1) investment and saving are at equilibrium and (2) the demand for money is in equilibrium with the supply of money. This Changes in IS and LM curves and the rate of interest.

It appears from this figure that:

1. With a given LM curve, when the IS is shifted to the right, income rises and the rate of interest also rises.

2. When the IS curve is constant and the LM curve is shifted to the right, the rate of interest falls and so on.

Thus, for a determinate theory of interest, we should view the interaction of the following factors: (1) the investment-demand function, (2) the saving function, (3) the liquidity preference function, and (4) the supply of money. Hansen, states that the Keynesian analysis, in a broad sense, involves all these.

In this sense, Keynes, unlike the neo-classicists, did formulate a determinate interest theory. But he failed to bring all the elements together in a comprehensive manner to formulate plainly an integrated theory of interest.

He, however, did not realise that liquidity preference plus the quantity of money can furnish not the rate of interest but only an LM schedule.

Thus, the credit goes to Professor Hicks for using the Keynesian tools in a proper manner to construct a comprehensive and determinate theory of interest.

In short, the modern theory of interest holds that productivity, thrift, liquidity preference, and the money supply are all important determinants of the rate of interest.