13

Demand for Money and the Rate of Interest: The Classical Approach

INTRODUCTION

This section of the book is devoted to the monetary sector. The last two chapters analysed money and the determinants of the theory of money supply. In the next three chapters, we examine the theories of demand for money. The present chapter examines the classical approach to the demand for money, known as the quantity theory of money (QTM). The QTM has several versions. Two versions, which have gained importance, are Irving Fisher’s transaction approach and the Cambridge cash balance approach. In the chapter, we also focus on the determination of the rate of interest in the classical theory.

FISHER’S TRANSACTIONS APPROACH TO THE QUANTITY THEORY OF MONEY

This approach was formulated by the famous American economist Irving Fisher. The crux of Fisher’s quantity theory is his famous equation of exchange,

where,

M = total quantity of money in circulation

VT	=	transactions velocity of money or the average number of times a unit of money changes hands to perform transactions during a given period of time
PT	=	average price of all kinds of market transactions
T	=	aggregate or sum of all transactions of goods and services during a given time period The equation of exchange is a truism in that it depicts something that is self evident and holds at all times. Each side of the above equation depicts the value (in terms of money) of the total transactions during a given period of time. A look at the left hand side of the equation shows that while M is the total quantity of money in the economy, VT is the transactions velocity of money. Thus, MVT is the money value of the total transactions during the given period of time.

A look at the right hand side of the equation shows that for a single transaction i, the price is p_i while the quantity is t_i. Thus, p_it_i is the money value of the transaction i. The total money value of all transactions will be Σ p_it_i, which can be denoted as P_TT.

Fisher’s QTM is a tautology and does not make any assertions about the relationships among the variables in the real world. It is unable to express as to what the cause is and what the effect is. In spite of all these criticisms, it is called a theory. The reason is because the equation of exchange is one equation with four variables. It is possible to express the value of one variable in terms of the other three variables. To develop the theory, certain assumptions are necessary; which are as follows:

Transactions, T: It is assumed that the total volume of transactions is a function of the basic physical and operational characteristics of the economy, namely capital, labour, the factors of production and technology which are all independent of M, V_T and P_T.

Money, M: The assumption here is that the stock of money is determined by the monetary system.

Velocity of circulation, V_T: V_T is assumed to be constant because payment practices (including the frequency with which people are paid and the irregularity in payments, etc.) change quite slowly.

Prices, P_T: In the QTM, P_T is the only variable that is influenced by the changes in M, Hence, we get from Eq. (1)

The above analysis shows that

1. Given V_T and T, changes in M lead to changes in P_T
2. A doubling of M will lead to a doubling of P_T Thus, changes in M lead to equiproportionate changes in P_T

The Quantity Theory: The Income Version

Due to the dissatisfaction with the transactions approach to the quantity theory, a modified form of the theory was put forward where the quantity equation was expressed in terms of the real income. The other variables in the equation got a similar treatment.

The income version of the quantity theory can be expressed as:

where,

M = total quantity of money in circulation

V =	income velocity of money or the average number of times a unit of money changes hands to perform income transactions or transactions relating to final goods and services, during a given period of time
P =	average level of prices of only the final goods and services
y =	real income

 

Similar to the earlier version of the quantity theory, the income version is also an identity. However, it is a genuine equation where the variable P can be determined, given y, V and M. Assuming that V is a constant, and that y is determined by the forces in the real sector, the theory arrives at the conclusion that autonomous changes in the supply of money, M lead to equiproportionate changes in the price level, P.

Demand for Money

The focus of this chapter is on the demand for money. Though Fisher had as such not expressed it, the demand for money in an economy is determined by the value of transactions (since money is demanded for the very purpose of carrying on transactions). It is a constant fraction of the value of the transactions. Thus,

In equilibrium, the supply of money is equal to the demand for money.

Thus,

Combining the Eqs. (4) and (5), we get

 

M^s = M^d

or

or

where

The transactions approach leads to the hypothesis that the demand for money is a constant proportion of the level of transactions.

Shortcoming of the QTM Approach

The variables T and P_T are ambiguous, and difficult to measure with the given data. Also V_T, the velocity of circulation, is influenced by consumer and business spending which are not constant.

• According to Fisher’s transactions approach, changes in M lead to equiproportionate changes in P_T.
• The equation of exchange is a truism as it depicts something that is self evident and holds at all times.
• The transactions approach leads to the hypothesis that the demand for money is a constant proportion of the level of transactions.

THE CAMBRIDGE CASH BALANCE APPROACH

Given by the economists Marshall and Pigou, this early neoclassical theory hypothesized the following demand function for money:

where,

M^d = the amount of money demanded
K = a constant
Y = national income in money terms

Now,

Thus, K gives the demand for money for every rupee of income per unit time. In fact, K depicts the proportion of money income, which the public likes to hold as money. This is, in fact, the most important feature of the Cambridge theory in that the demand for money is a function of money income.

We have

where,

y = the real national income
P = general price level

Combining Eqs. (6) and (7), we get

The equilibrium condition for the money market is

Thus, we get from Eqs. (8) and (9),

 

M^s = KP_y

Hence,

The above equation looks very similar to the Fisher’s equation, except for V, which represents the income velocity (and not the transactions velocity).

A comparison of the two approaches depicts the conceptual differences between the two approaches, which are as follows:

1. The transactions approach lays emphasis on the medium of exchange function of money and thus defines money in terms of whatsoever is included as the medium of exchange. On the other hand, the cash balance approach lays emphasis on the store of value function of money and is therefore consistent with the broader meaning of money.
2. The transactions approach lays stress on the mechanical aspects of the payments practices while examining the determinants of the transactions velocity of money. In contrast, the cash balance approach is influenced by K, which is a behavioural ratio.
3. The cash balance approach can be easily expressed in terms of the simple demand supply analysis whereas the same cannot be said for the transactions approach.

• The cash balance approach lays emphasis on the store of value function of money.
• The cash balance approach can be easily expressed in terms of the simple demand supply analysis.

THE CLASSICAL THEORY OF INTEREST

Interest is the price, which is paid by the borrower to the lender of borrowed funds. When this price is expressed in terms of a rate per cent per unit time, it becomes a rate of interest. The interest rate exercises a strong influence on all economic activities like investment, saving and international capital flows.

 

The reason for discussing it here in the present chapter (with the demand for money) is the influence of Keynes, who had argued that the rate of interest is determined by the demand and supply of money.

Before the advent of Keynes on the economic scenario, the classical theory was considered to be a satisfactory theory for the determination of the rate of interest. According to the classical theory, the rate of interest is determined by the demand and the supply of capital.

Demand for Capital

The proponents of the classical theory believed that capital is demanded only for purposes of investment. It is inversely related to the rate of interest. Other things being equal, the lower the rate of interest higher will be the investment. For every new investment project that a firm undertakes, the firm will have to first estimate the rate of return and then compare it with the interest rate. At a higher interest rate, relatively fewer projects will be undertaken unless they yield a return at least equal to, if not greater than, the interest rate. Thus, at higher rates of interest investment is low. In contrast, at lower rates of interest investment is comparatively high. Hence, there exists an inverse relationship between the investment and the rate of interest.

In Figure 13.1, the investment demand schedule, I is downward sloping from left to right. Keynes had accepted that investment is a function of the rate of interest.

Supply of Capital

As far as the supply of capital is concerned, its source is saving. Saving is income that is withheld from consumption. According to the classical theory, saving is a function of the rate of interest. The classical theory had emphasized that the normal state for an economy is full employment. Hence, income cannot be taken as a variable and it cannot have an influence on savings in the short run. Therefore at the full employment level of income, saving is a direct function of the rate of interest. The higher the rate of interest, the larger is the amount of the income that is saved. In Figure 13.1, the saving schedule, S is upward sloping.

Figure 13.1 Determination of the Rate of Interest: The Classical Theory

Interest Rate Determination

In Figure 13.1, saving and investment curves are represented by curves S and I. They intersect each other at point E. Thus, the equilibrium rate of interest is r*. At all other rates of interest, there will exist disequilibrium and forces will be at work to push the rate of interest back until the equilibrium rate of interest is achieved at r*.

If the rate of interest were above r*, the funds supplied by the savers would be more than those demanded by the investors and this would push down the rate of interest. If the rate of interest were below r*, demand for funds from the investors would be more than those supplied by the savers and this would push up the rate of interest. It is only at the equilibrium rate r* that every rupee of saving is matched by a rupee of investment.

Changes in Saving and Investment

A shift in either the saving or the investment curves will move the economy to a new equilibrium. Suppose that the recipients of the income become thriftier and save more of their income at each rate of interest. The saving curve in Figure 13.2 will shift outwards from S to S₁. The equilibrium would change from E* to E₁ and there would occur a decrease in the interest rate from r* to r₁. A shift of the saving function in the opposite direction, indicating that less is saved at each rate of interest, would lead to a rise in the interest rate.

The effects of a shift in the investment curve can be analysed in a similar manner.

The Classical Theory: A Critical Appraisal

The negative points of the classical theory are:

1. Keynes had criticized the classical theory in classicists’ belief that saving is a unique function of the interest rate. According to Keynes, there does not exist a significant relationship between savings and the interest rate. He also emphasized that savings function will shift whenever there is a change in the income level.
2. The classical theory assumed that a shift in the investment curve can take place without causing a change in the income level. Thus, the classical theory fails to recognize the relationship between investment and income.

However, in spite of all these shortcomings, we do study the classical theory for many reasons, which are as follows:

1. It is incorrect to say that the classical theory is unacceptable or wrong. Without the refinements in the theory which would give us a more correct picture, it is wrong to categorize the theory as correct or incorrect.
   

   Figure 13.2 A Change in Saving and its Effect on the Rate of Interest

2. To be able to understand a new theory in a better way, it is necessary to study even an old theory which is not totally incorrect but nevertheless which was accepted world wide for over a hundred years.
3. Even today despite the success faced by the Keynesian theory, many people still have faith in the classical theory.

• The proponents of the classical theory believed that capital is demanded only for purposes of investment, which is inversely related to the rate of interest.
• As far as the supply of capital is concerned, its source is saving, which, according to the classical theory is a direct function of the rate of interest.
• The intersection of the saving and investment curves determines the equilibrium rate of interest.
• A shift in either the saving or the investment curves will move the economy to a new equilibrium position.

THE LOANABLE FUNDS THEORY

Till Keynes had arrived on the scene, the classical theory of the rate of interest was the accepted theory for the determination of the interest rate. Later, it was reconstructed as the loanable funds theory. Hence, the theory can be said to be an extension of the classical saving investment theory.

While the classical theory had incorporated only the non-monetary (real) factors, the loanable funds theory incorporates both the monetary as well as the non-monetary factors in the analysis. It is associated with Wicksell, D. H. Robertson and others.

The theory is based on the following assumptions:

1. The market for loanable funds is fully integrated with perfect mobility of funds.
2. There exists perfect competition in the market and so each borrower and lender is a price taker. There will be only one rate of interest and that will be the market clearing rate of interest.
3. All factors, other than the rate of interest, are assumed to be constant. The rate of interest does not respond to or interfere with the other macroeconomic variables. In other words, the theory uses a partial equilibrium analysis.
4. The theory is in ‘flow’ terms where the flow demand and supply of loanable funds are analysed to determine the rate of interest.

The rate of interest is determined by standard demand supply analysis. According to the loanable funds theory, the rate of interest, which is the price of loanable funds, is determined by the demand for and supply of loanable funds.

Demand for Loanable Funds, LD

The demand for loanable funds can be expressed as

	LD	= I + ΔMD
where,	LD	= Demand for loanable funds
	I	= Gross investment expenditure
	ΔMD	= Incremental demand for money

Since both, I and ΔMD are a decreasing function of the rate of interest so LD is also a decreasing function of the rate of interest. Investment (which was present in the classical theory also) is a real factor whereas the incremental demand for money is a monetary factor. Hence, both real and monetary factors are included in the demand for money.

Supply of Loanable Funds, LS

The sources of supply of loanable funds are

 

LS = S + DH + ΔM

LS = Supply of loanable funds

S = Aggregate saving of all the households and firms in the economy, net of their dissaving

DH = Aggregate dishoarding of previously accumulated cash balances

ΔM = Incremental supply of money

Since both S and DH are increasing functions of the rate of interest, while ΔM is given autonomously, LS is also an increasing function of the rate of interest. While S, the aggregate saving of all the households and firms (which was present in the classical theory also) is a real factor, DH the aggregate dishoarding of previously accumulated cash balances and ΔM, the incremental supply of money are both monetary factors. Hence, both real and monetary factors are included in the supply of money.

Interest Rate Determination

In Figure 13.3, S represents the saving curve and LS represents the supply of loanable funds. The horizontal distance between the S and LS curves is the sum of DH and ΔM. This distance increases as r increases because while ΔM is given exogenously, DH is an increasing function of r. Similarly, I represents the investment curve and LD represents the demand for loanable funds. The horizontal distance between I and LD curves is ΔMD. This distance increases as r decreases because ΔMD is a decreasing function of r.

According to the standard demand supply theory, equilibrium is determined at the level where

Demand for loanable funds = Supply of loanable funds

or

LD = LS

or

I + ΔMD = S + DH + ΔM

On the other hand, in the classical theory equilibrium is determined at the level where

 

I(r) = S(r)

Figure 13.3 Interest Rate Determination in the Loanable Funds Theory

In Figure 13.3, the LD and LS curves intersect each other at point E. The equilibrium rate of interest is r**. The S-I equilibrium of the classical theory yields r* as the equilibrium rate of interest.

The Loanable Funds Theory: A Critical Appraisal

The positive points of the loanable funds theory are as follows.

1. It is an improvement over the classical theory in that it recognizes the fact that loanable funds are demanded for purposes other than investment expenditures and also that besides saving there exist other sources of loanable funds also.
2. The classical theory considers only the real factors in the determination of the interest rate whereas the loanable funds theory takes into consideration both the real and the monetary factors.
3. The theory recognizes that like saving and investment, the aggregate dishoarding of previously accumulated cash balances and the incremental demand for money also exercise a strong influence on the rate of interest.

The negative points of the loanable funds theory are mentioned below. The theory is unable to specify in a clear manner the different sources of the supply and demand for loanable funds.

On the supply side:

1. Some savings may not come through the loan market. Firms and households may invest their savings directly into physical assets.
2. Not all dishoarding of cash balances are lent out. The dishoarders may spend them directly.

On the demand side:

1. Investments or hoardings may be financed from owned funds and not necessarily from borrowed funds.
2. Funds may be borrowed not only for investment and hoarding but also for the buying of old financial and non-financial assets, and for consumption spending.
3. The flow equilibrium approach of the theory has also been subjected to a lot of criticism. In the bond market at least in the short period, the amount of outstanding bonds (a stock concept) is much more than the demand and supply of bonds (a flow concept). Hence, in the short period the stock equilibrium exercises a strong influence on the behaviour of the interest rate. What is required is a stock flow analysis to determine the interest rate.
4. The rate of interest not only has a strong influence on the different macro variables like savings, investment, prices, supply and demand for money, but in turn, it is also affected by these variables. So what is required is a general equilibrium approach, and not a partial equilibrium approach, for the determination of the interest rate.
5. Like all other theories, the basic tenet of the loanable funds theory is that there exists a fully integrated market where all the lending and borrowing activities are performed through perfectly homogenous bonds at a single rate of interest. This does not present a true picture of even the most well developed financial markets where there exists a variety of interest rates.

• The demand for loanable funds is a decreasing function of the rate of interest.
• The supply of loanable funds is an increasing function of the rate of interest.
• The equilibrium rate of interest is determined by the intersection of the demand for loanable funds schedule and the supply of loanable funds schedule.

INTRODUCTION

The chapter examines the quantity theory of money (QTM) and its two versions, Irving Fisher’s transaction approach and the Cambridge cash balance approach.

FISHER’S TRANSACTIONS APPROACH TO THE QUANTITY THEORY OF MONEY

1. The crux of Fisher’s quantity theory is his famous equation of exchange, MV_T = P_TT.
2. The equation of exchange is a truism. In spite of all these criticisms, it is called a theory. To develop the theory, certain assumptions are necessary: T is assumed to be a function of the basic physical and operational characteristics of the economy; M is assumed to be determined by the monetary system; and V_T is assumed to be constant.
3. P_T is the only variable that is influenced by the changes in M. Hence, we get the equation
4. The analysis shows that given V_T and T, changes in M lead to equiproportionate changes in P_T.
5. The main shortcoming of the QTM approach is that the variables T and P_T are ambiguous and with the given data it is difficult to measure them.

THE QUANTITY THEORY: THE INCOME VERSION

1. Here, the quantity equation is expressed in terms of the real income.
2. The income version of the quantity theory can be expressed as:

    

   MV = Py

3. Similar to the earlier version of the quantity theory, the income version is also an identity.
4. It is a genuine equation where the variable P can be determined, given y, V and M.
5. The theory arrives at the conclusion that autonomous changes in the supply of money lead to equiproportionate changes in the price level.

DEMAND FOR MONEY

1. The demand for money in an economy is determined by the value of transactions and is a constant fraction of the value of the transactions.
2. Thus, M^d = kPT

SHORTCOMING OF THE QTM APPROACH

The variables T and P_T are ambiguous, and V_T is influenced by consumer and business spending.

THE CAMBRIDGE CASH BALANCE APPROACH

1. Given by the economists Marshall and Pigou, this early neoclassical theory hypothesized the following demand function for money:
2. Here K depicts the proportion of money income, which the public likes to hold as money. This is, in fact, the most important feature of the Cambridge theory in that the demand for money is a function of money income.
3. The equation

   The above equation looks very similar to the Fisher’s equation, except for V which represents the income velocity.

A COMPARISON OF THE TWO APPROACHES:

1. The transactions approach lays emphasis on the medium of exchange function of money whereas the cash balance approach lays emphasis on the store of value function of money.
2. The transactions approach lays stress on the mechanical aspects of the payments practices while examining the determinants of the transactions velocity of money. In contrast, in the cash balance approach K is more of a behavioural ratio.
3. While the cash balance approach can be easily expressed in terms of the simple demand supply analysis, the same cannot be said for the transactions approach.

THE CLASSICAL THEORY OF INTEREST

1. Interest is the price, which is paid by the borrower to the lender of borrowed funds. When this price is expressed in terms of a rate per cent per unit time, it becomes a rate of interest.
2. The rate of interest is determined by the demand and the supply of capital.
3. As far as the demand for capital is concerned, it is demanded only for purposes of investment.
4. There exists an inverse relationship between investment and the rate of interest. Thus, the investment demand schedule is downward sloping.
5. As far as the supply of capital is concerned, its source is saving that is income withheld from consumption.
6. Saving is a direct function of the rate of interest. Thus, the saving schedule, S is upward sloping.

INTEREST RATE DETERMINATION

1. Saving and investment curves intersect to determine the equilibrium rate of interest at r*.
2. At all other rates of interest there will exist disequilibrium and forces will be at work to push the rate of interest back until the equilibrium rate of interest is achieved at r*.

CHANGES IN SAVING AND INVESTMENT

1. A shift in either the saving or the investment curves will move the economy to a new equilibrium.
2. Suppose that the recipients of the income become thriftier and save more of their income at each rate of interest, the saving curve will shift outwards and there would occur a decrease in the interest rate.
3. The effects of a shift in the investment curve can be analysed in a similar manner.

THE CLASSICAL THEORY: A CRITICAL APPRAISAL

The negative points of the classical theory are as follows:

1. According to Keynes, there does not exist a significant relationship between savings and the interest rate.
2. The classical theory fails to recognize the relationship between investment and income.
3. In spite of all these shortcomings, we do study the classical theory because to be able to understand a new theory in a better way it is necessary to study even an old theory which may not be totally correct.

THE LOANABLE FUNDS THEORY

1. The theory can be said to be an extension of the classical saving investment theory.
2. While the classical theory had incorporated only the non-monetary (real) factors, the loanable funds theory incorporates both the monetary as well as the non-monetary factors in the analysis.
3. The theory is based on the following assumptions:
   1. The market for loanable funds is fully integrated with perfect mobility of funds.
   2. There exists perfect competition in the market and so each borrower and lender is a price taker.
   3. There will be only one rate of interest and that will be the market clearing rate of interest.
   4. All factors, other than the rate of interest, are assumed to be constant.
   5. The theory is in ‘flow’ terms.
4. The rate of interest, which is the price of loanable funds, is determined by the demand for and supply of loanable funds.

DEMAND FOR LOANABLE FUNDS, LD

1. The demand for loanable funds can be expressed as

    

   LD = I + ΔMD

2. Since both I and ΔMD are a decreasing function of the rate of interest, so LD is also a decreasing function of the rate of interest.

SUPPLY OF LOANABLE FUNDS, LS

1. The sources of supply of loanable funds are

    

   LD = S + DH + ΔM

2. Since both S and DH are increasing functions of the rate of interest, while ΔM is given autonomously, LS is also an increasing function of the rate of interest.

INTEREST RATE DETERMINATION

1. The horizontal distance between the S and LS curves is the sum of DH and ΔM. This distance increases as r increases.
2. The horizontal distance between I and LD curves is ΔMD. This distance increases as r decreases.
3. Equilibrium is determined at the level where the demand for loanable funds is equal to the supply of loanable funds.

THE LOANABLE FUNDS THEORY: A CRITICAL APPRAISAL

1. The positive points of the loanable funds theory are as follows:
   1. It recognizes the fact that loanable funds are demanded for purposes other than investment expenditures and also that besides saving, there exist other sources of loanable funds also.
   2. The loanable funds theory takes into consideration both the real and the monetary factors.
2. The negative points of the loanable funds theory are as follows:
   1. The theory is unable to specify in a clear manner the different sources of the supply and demand for loanable funds.
   2. The flow equilibrium approach of the theory has also been subjected to a lot of criticism. What is required is a stock flow analysis to determine the interest rate.
   3. For the determination of the interest rate, a general equilibrium approach and not a partial equilibrium approach is required.
   4. The basic tenet of the loanable funds theory is that there exists a fully integrated market, which does not present a true picture of reality.

TRUE OR FALSE QUESTIONS

1. According to Fisher’s transactions approach to the quantity theory of money, changes in M lead to equiproportionate changes in P_T.
2. The most important feature of the Cambridge cash balance approach is that the demand for money is a constant fraction of the value of the transactions.
3. The demand for loanable funds is an increasing function of the rate of interest.
4. The classical theory had incorporated only the monetary factors in the determination of the rate of interest.
5. The loanable funds theory incorporated both the monetary as well as the non-monetary factors in the determination of the rate of interest.

VERY SHORT-ANSWER QUESTIONS

1. ‘The transactions approach leads to the hypothesis that the demand for money is a constant proportion of the level of transactions.’ Comment.
2. Discuss the income version of the quantity theory of money.
3. Compare Fisher’s transactions approach and the Cambridge cash balance approach.
4. What is interest? Discuss.
5. How does a shift in either the saving or the investment curves move the economy to a new equilibrium? Explain.

SHORT-ANSWER QUESTIONS

1. ‘Fisher’s quantity theory of money is a tautology and does not make any assertions about the relationships between the variables in the real world.’ Explain.
2. Give a critical appraisal of the loanable funds theory.
3. ‘According to the classical theory, the rate of interest is determined by the demand and the supply of capital.’ Explain.
4. Discuss briefly the Cambridge cash balance approach to the demand for money.
5. Discuss briefly the following approaches to the demand for money bringing out the special features of each approach:
   1. Fisher’s transactions approach to money
   2. The Cambridge cash balance approach
   3. The classical theory of interest
   4. The loanable funds theory

LONG-ANSWER QUESTIONS

1. What is the rate of interest? How is it determined in the classical theory of interest?
2. How is the rate of interest determined in the loanable funds theory? Explain.
3. Give a critical appraisal of the loanable funds theory.
4. Compare the loanable funds theory with the classical theory of the determination of the rate of interest.
5. Write a short note on Fisher’s transactions approach to money.

TRUE OR FALSE QUESTIONS

1. True. A doubling of M will lead to a doubling of P_T. Thus, changes in M lead to equiproportionate changes in P_T.
2. False. The most important feature of the Cambridge cash balance approach is that the demand for money is a function of money income.
3. False. The demand for loanable funds is a decreasing function of the rate of interest.
4. False. The classical theory had incorporated only the non-monetary (real) factors in the determination of the rate of interest.
5. True. Unlike the classical theory, the loanable funds theory incorporated both the monetary as well as the non-monetary or real factors in the determination of the rate of interest.