This unit discusses some of the important theories of interest rate such as the

classical, the loanable funds, the Keynesian, and the modern theory of interest

are also examined in this unit.

At the end of this unit, the student should be able to;

i. Recognize both saving and consumption functions.

ii. Derive saving function from consumption function

iii. Know those factors that determine saving.

iv. Understand relationship between saving and investment.

### INTRODUCTION TO THEORY OF INTEREST RATE.

Of all the theories discussed below, the Keynesian liquidity preference theory

that determines the interest rate by the demand for and supply of money is stock

theory. It emphasises that the rate of interest is a purely monetary phenomenon.

It is a stock analysis because its takes the supply of money as given during the

short run and determines the interest rate by liquidity preference or demand for

money. On the other hand the loanable funds theory is a flow theory that

determines the interest rate by the demands for and supply loanable funds. It

involves the linking of the interest rate with the dis-savings, investment and

hoarding of funds on the demand side with savings, dishoarding and bank money

on the supply side. These are all flow variables. Hicks and Hansen have

reconciled and synthesized these stocks and flow theories in a general equilibrium framework and presented a determinate theory of interest rates in

terms of the IS-LM formulation.

### THE CLASSICAL THEORY OF INTEREST

According to the classical theory, rate of interest is determined by the supply and

demand of capital. The supply of capital is governed by the time preference and

the demand for capital by the expected productivity of capital. Both time

preference and productivity of capital depend upon waiting or saving or thrift.

The theory is therefore, also known as the supply and demand theory of savings.

Demand side. The demand for capital consists of the demand for productivity

and consumptive purpose. Ignoring the letter, capital is demanded by the

investors because it is productive. But the productivity of the capital is subject to

the law of variable proportion. Additional unit of capital are not as productive as

the earlier unit. A stage comes when the employment of an additional unit of

capital in the business is just worthwhile and no more. Suppose an investor

invest Rs 1, 00,000 in a factory and expects a yield of 20%. Another instalment

of an equal amount would not be as productive as the first one and might bring in

15%. While a third instalment might yield 10%. If he has borrowed the money at

10% he will not venture to invest more. For the rate of interest is just equal to the

marginal productivity of capital to him. It shows that at a higher rate of interest

the demand for capital is low and it is high at a lower rate of interest. Thus the

demand is inversely related to the rate of interest and the demand schedule for

capital or investment curve slope down ward from left to right. There are,

however, certain other factors which govern the demands for capital, such as the

growth of population, technical progress, process of rationalization, the standard

of living of the community, etc.

Supply side. The supply of capital depends upon savings, rather upon the will to

save and the power to save and the community. Some people save irrespectively

of the rate of interest. They would continue to save even if the rate of interest

were zero. There are others who save because the current rate of interest is just

enough to induce them to save. They would reduce their savings if the rate of

induced to save if the rate of interest were raised. To the last two categories of

savers, saving involves a sacrifice, abstinence or waiting when they forgo present

consumption in order to earn interest. The higher the rate of interest, the larger

will be the community savings and more will be the supply of funds. The supply

curve of capital or the savings curve thus moves upward to the right.

Self Assessment Exercise

i. Discuss the classist theory of rate of interest

### THE LOANABLE FUNDS THEORY OF INTEREST

The neo-classical or the loan able funds theory explains the determination of

interest in terms of demand and supply of loan able funds or credit.

According to this theory, the rate of interest is the price of credit which is

determined by the demand and supply of ‗credit‘, or saving plus the net increase

in the amount of money in a period, to the demand for ‗credit‘, or investment

plus net ‗hoarding‘ in the period.‖ Let us analyze the force behind the demand

and supply of loanable funds.

Demand for Loanable Funds. The demand for loan able funds has primarily

tree sources: government, businessmen and consumer who need them for

purpose of investment, hording and consumption. The government borrows

funds for construction public works or for war preparation. The businessmen

borrow for purchase of capital goods and for stating investment projects. Such

borrowing is interest elastic and depends mostly on the expected rate of profit as

compared with the rate of interest. The demand for loan able funds on scooters,

houses, etc. individual borrowings are also interest elastic. The tendency to

borrow is more at a lower rate of interest that at a higher in order to enjoy their

consumption soon. Since this demand for funds is mostly met out of past savings

or through dis-savings,

Supply of Loanable Funds. The supply of loan able funds comes from savings

dishoarding and bank credit. Private individuals and corporate savings are the

main sources of savings. Though personal savings depends upon the income

level yet taking the level of income as given they regarded as interest elastic. The

higher the rate of interest, the greater will be the inducement to save and vice

versa. Corporate savings are the undistributed profits of firm which also depends

on the current rate of interest to some extent. If the interest rate is high it will act

as a deterrent to borrowing and thus encourage savings.

#### Total Demand for Money

If the total liquid money is denoted by M, the transactions plus precautionary

motive by M1 and the speculations motive for holding by M2, then M=M1+M2.

Since M1=L1(y) and M2=L2 (r), the total liquidity preferences functions is

expressed as M=L(Y,r).M1 is idle or passive money. Though M1 is a function of

income and M2 of the rate of interest, yet they cannot be held in water-tight

compartments. Even M1 is interest elastic at high interest rates.

Self Assessment Exercise

i. Explain what is meant by loanable fund theory

ii. Is income a major determinant of rate of interest

### Indeterminancy of The Classical, the Loanable Funds and the

Keynesian Theories of Interest

Keynes criticized 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. Here, we illustrate the in determinant nature of this

theory.

In the classical formulation, since savings depends upon the level of income, it is

not possible to know the rate of interest unless the income level is known before hand. And the income level cannot behold. 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 formulations on 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

new money and activated balance 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.

Self Assessment Exercise

i. explain clearly what is meant by indeterminate

### Modern Theory of Interest

We have seen above that no single theory of interest is adequate and determinate.

An adequate theory to be determinant must take into consideration both the real

and monetary factors that influence the interest rate. Hicks has utilized the

Keynesian tools in a method of presentation which shows that productivity,

thrift, liquidity preference and money supply are all necessary elements in a

comprehensive and determinate interest theory. According to Hansen, ―An

equilibrium condition is reached when the desired volume of cash balance 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 ,‖ Thus in the

modern theory of interest, savings, investment, liquidity preference and the

quality of money are integrated at various levels of income for a synthesis of the

loanable funds with the liquidity preference theory. The four variable of the

formulation have been combined, to construct two new curves, the IS curve

representing flow variable of the loanable funds formulation (or the real factors

of the classical theory) and the LM curve representing the stock variable of

liquidity preference formulation. The equilibrium between IS and LM curves

provides a determinate solution.

The IS/LM model was born at the econometric conference held in Oxford during

September, 1936. Roy Harrod, John R. Hicks, and James Meade all presented

papers describing mathematical models attempting to summarize John Maynard

Keynes' General Theory of Employment, Interest, and Money. Hicks, who had

seen a draft of Harrod's paper, invented the IS/LM model (originally using

the abbreviation "LL", not "LM"). He later presented it in "Mr. Keynes and the

Classics: A Suggested Interpretation".

Hicks later agreed that the model missed important points of Keynesian theory,

criticizing it as having very limited use beyond "a classroom gadget", and

criticizing equilibrium methods generally: "When one turns to questions of

policy, looking towards the future instead of the past, the use of equilibrium

methods is still more suspect." The first problem was that it presents the real and

monetary sectors as separate, something Keynes attempted to transcend. In

addition, an equilibrium model ignores uncertainty – and that liquidity

preference only makes sense in the presence of uncertainty "For there is no sense

in liquidity, unless expectations are uncertain." A shift in one of the IS or LM

curves will cause a change in expectations, which shifts the other curve. Most

modern macroeconomists see the IS/LM model as being - at best - a starting

approximation for understanding the real world.

Although generally accepted as being imperfect, the model is seen as a useful

pedagogical tool for imparting an understanding of the questions that

macroeconomists today attempt to answer through more nuanced approaches. As

such, it is included in most undergraduate macroeconomics textbooks, but

omitted from most graduate texts due to the current dominance of real business

cycle and new Keynesian theories.

The IS–LM model is also a macroeconomic tool that demonstrates the

relationship between interest rates and real output, in the goods and services

market and the money market. The intersection of the IS and LM curves is the

"general equilibrium" where there is simultaneous equilibrium in both

markets. Two equivalent interpretations are possible: first, the IS-LM model

explains changes in national income when the price level is fixed in the short�run; second, the IS-LM model shows why the aggregate demand

curve shifts. Hence, this tool is sometimes used not only to analyse the

fluctuations of the economy but also to find appropriate stabilisation policies.

#### FORMATION

The model is presented as a graph of two intersecting lines in the first quadrant.

The horizontal axis represents national income or real gross domestic

product and is labelled Y. The vertical axis represents the real interest

rate, i. Since this is a non-dynamic model, there is a fixed relationship between

the nominal interest rate and the real interest rate (the former equals the latter

plus the expected inflation rate which is exogenous in the short run); therefore

variables such as money demand which actually depend on the nominal interest

rate can equivalently be expressed as depending on the real interest rate.

The point where these schedules intersect represents a short-run equilibrium in

the real and monetary sectors (though not necessarily in other sectors, such as

labor markets): both the product market and the money market are in

equilibrium. This equilibrium yields a unique combination of the interest rate

and real GDP.

### THE EXPLANATION OF IS CURVE AND FUNCTION

For the investment—saving curve, the independent variable is the interest rate

and the dependent variable is the level of income. (Note that economics graphs

like this one typically place the independent variable (interest rate, in this

example) on the vertical axis rather than the horizontal axis.). The IS curve is

drawn as downward-sloping with the interest rate (i) on the vertical axis and

GDP (gross domestic product: Y) on the horizontal axis. The initials IS stand for

"Investment and Saving equilibrium" but since 1937 have been used to represent

the locus of all equilibria where total spending (consumer spending + planned

private investment + government purchases + net exports) equals an economy's

total output (equivalent to real income, Y, or GDP). To keep the link with the

historical meaning, the IS curve can be said to represent the equilibria where

total private investment equals total saving, where the latter equals consumer

saving plus government saving (the budget surplus) plus foreign saving (the

trade surplus). In equilibrium, all spending is desired or planned; there is no

unplanned inventory accumulation. The level of real GDP (Y) is determined

along this line for each interest rate.

Thus the IS curve is a locus of points of equilibrium in the "real" (non-financial)

economy. Each point on the curve represents the equilibrium between the

Savings and Investment (S=I).

Given expectations about returns on fixed investment, every level of the real

interest rate (i) will generate a certain level of planned fixed investment and other

interest-sensitive spending: lower interest rates encourage higher fixed

investment and the like. Income is at the equilibrium level for a given interest

rate when the saving that consumers and other economic participants choose to

do out of this income equals investment (or, equivalently, when "leakages" from

the circular flow equal "injections"). The multiplier effect of an increase in fixed

investment resulting from a lower interest rate raises real GDP. This explains the

downward slope of the IS curve. In summary, this line represents the causation from falling interest rates to rising planned fixed investment (etc.) to rising

national income and output.

The IS curve can also be summarised as follows; it is defined by the equation

where Y represents income, C represents consumer spending as an increasing

function of disposable income (income, Y, minus taxes, T(Y), which themselves

depend positively on income), I, represents investment as a decreasing function

of the real interest rate, G represents government spending, and NX(Y)

represents net exports (exports minus imports) as an increasing function of

income (increasing because exports are increasing function of income). In this

equation, the level of G (government spending) is presumed to be exogenous,

meaning that it is taken as a given.

### THE EXPLANATION OF LM CURVE AND FUNCTION

For the liquidity preference and money supply curve, the independent variable is

"income" and the dependent variable is "the interest rate." The LM curve shows

the combinations of interest rates and levels of real income for which the money

market is in equilibrium. It is an upward-sloping curve representing the role of

finance and money

The LM function is the set of equilibrium points between the liquidity

preference (or demand for money) function and the money supply function (as

determined by banks and central banks). Each point on the LM curve reflects a

particular equilibrium situation in the money market equilibrium diagram, based

on a particular level of income. In the money market equilibrium diagram, the

liquidity preference function is simply the willingness to hold cash balances

instead of securities. For this function, the nominal interest rate (on the vertical

axis) is plotted against the quantity of cash balances (or liquidity), on the

horizontal. The liquidity preference function is downward sloping. Two basic

elements determine the quantity of cash balances demanded (liquidity

preference) and therefore the position and slope of the function:

Transactions demand for money: this includes both (a) the willingness to hold

cash for everyday transactions and (b) a precautionary measure (money demand

in case of emergencies). Transactions demand is positively related to real GDP

(represented by Y,and also referred to as income). This is simply explained – as

GDP increases, so does spending and therefore transactions. As GDP is

considered exogenous to the liquidity preference function, changes in GDP shift

the curve. For example, an increase in GDP will increase transactions which will

increase the demand for money for given interest rates, and cause the Liquidity

preference curve to shift to the right. Imply willingness to hold cash instead of

securities as an asset for investment purposes. Speculative demand is inversely

related to the interest rate. As the interest rate rises, the opportunity cost of

holding cash increases – the incentive will be to move into securities.

The money supply function for this situation is plotted on the same graph as the

liquidity preference function. The money supply is determined by the central

bank decisions and willingness of commercial banks to loan money. Though the

money supply is related indirectly to interest rates in the very short run, the

money supply in effect is perfectly inelastic with respect to nominal interest rates

(assuming the central bank chooses to control the money supply rather than

focusing directly on the interest rate). Thus the money supply function is

represented as a vertical line – money supply is a constant, independent of the

interest rate, GDP, and other factors. Mathematically, the LM curve is defined by

the equation , where the supply of money is represented as the real amount M/P

(as opposed to the nominal amount M), with P representing the price level, and L

being the real demand for money, which is some function of the interest rate i

and the level Y of real income. The LM curve shows the combinations of interest

rates and levels of real income for which money supply equals money demand—

that is, for which the money market is in equilibrium.

For a given level of income, the intersection point between the liquidity

preference and money supply functions implies a single point on the LM curve:

specifically, the point giving the level of the interest rate which equilibrates the

money market at the given level of income. Recalling that for the LM curve, the

interest rate is plotted against real GDP (whereas the liquidity preference and

money supply functions plot interest rates against the quantity of cash balances), an increase in GDP shifts the liquidity preference function rightward and hence

increases the interest rate. Thus the LM function is positively sloped.

Self Assessment Exercise

0 Y1 Y2

i. In a clear term, explain what is meant by IS-LM

### CONCLUSION

This unit conclude that earlier interest rate theories are indeterminate but the

modern theory which makes use of IS-LM model is adequate and determinate.

### SUMMARY

This unit looked at theories of interest rate which include classical theory of

interest rate, the loanable fund theory, Keynesian liquidity theory and the modern

theory of rate of interest.

### MARKED ASSIGNMENT

i. What do understand by price of saving

ii. List and explain any three theories of interest rate

iii. Give reason why some theories are assumed to be indeterminate.

iv. Explain the difference between classical and Keynesian theory of

interest rate.

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Delhi, India

Lipsey R.G, (1979); An Introduction to Positive Economics, Hayper & Raw,

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