# The Theories of Interest Rate

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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