BSc Economics programme

ECN 326: Monetary Economics

Module 5

THE DEMAND FOR MONEY

In Lecture 3, on the nature of money, we saw why there was a need for money: • to solve the double coincidence of wants problem associated with barter • to obviate the lack of trust between the payer and the payee in a transaction. However, what determines the quantity of money that individuals and economies demand is a separate question. It is the aim of this lecture to explain what determines the quantity of money we demand and also to present a number of models (or theories) of the demand for money. The lecture is majorly split into two main sections. The first part considers the demand for money from individuals or institutions/firms perspective, i.e., the microeconomic determinants of money demand. The second part examines the demand for money at the macroeconomic level, gives a brief history of money demand, focusing on the breakdown of the macroeconomic demand for money function.

The ultimate aim of the lecture is to study the money demand as one of the building blocks of the money market equilibrium.

The study of the demand for money function has long dominated empirical research in monetary economics. One is therefore tempted o inquire into the nature of this function that qualifies it for a special study. This is of particular importance as traditional microeconomics theory presents us with a generalized framework in which the demand for any good may be analyzed. Traditional theory approaches demand analysis by postulating that an individual derives satisfaction from the consumption of goods and services. Individual market demand for these goods is thus derived from this satisfaction or utility. Money, however, does not seem to fit neatly into this kind of analysis, and the demand for it does not appear to be adequately explained by utility theory.

What then are the various factors that distinguish money from other goods and services? As emphasized in earlier lectures, money is a for goods and services. Besides, its market value in general is predictable and stable. These two characteristics combine to give it liquidity. Because money is the most liquid of all assets, individuals hold it for day-to-day events to make transactions. If money is held for the reasons mentioned, why do we study the demand for money? One reason is the peculiar nature of money mentioned above (i.e. its liquidity). The other is the importance of money in economic activity. Specifically, a stable money demand function forms the core in the conduct of monetary policy as a stable money demand function enables a policy-driven change in monetary aggregates to have measurable or indeed predictable influence on output, interest rates and ultimately on the . The size of the interest elasticity of the demand for money provides a useful guide to the effectiveness of monetary policy and impact of money on the economy. Because of its importance, a steady stream of theoretical and empirical research has been carried out over several decades. Most of the earlier work concentrated on developed countries. In recent years, however, there have been a lot of analyses as well on developing countries.

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There are eight broad sections expected to be covered in this lecture on the demand for money. The first section deals with the basic theoretical analysis of the demand for money by the classical economists. Specifically considered are the Fisher's , and the Cambridge version of the quantity theory. The second section deals with the Keynesian theory of the demand for money. In the same section, we explore the demand for money in the Keynesian tradition. These include the regressive expectation model, and as behaviour towards risk. We discuss also the interest elasticity of the demand for cash. The third section deals with the Friedman analysis of the demand for money which is a restatement of the classical theory of the demand for money. The fourth section deals with the specification of the demand for money. Specifically, in this section, we deal with the basic questions about the theoretical and empirical analysis of the demand for money. The fifth section deals with the general issues in the specification as well as the empirical results of studies of the demand for money in developing countries. The sixth section outlines the modern general overview of the demand for money including: the inventory theoretic model of Baumol-Tobin and the portfolio selection model of Tobin; discuss why Tobin's model solves the `plunger' problem of the demand for money model of Keynes; describe the general set-up of macroeconomic money demand equations; discuss empirical evidence on money demand functions, especially on income and interest elasticities; and finally describe what happened and what is meant by `the case of the missing money' and give reasons for the breakdown of the estimated money demand equations.

Microeconomic determinants of the demand for money There are essentially four main determinants of money demand at the individual level. These are

1. Interest differentials: the difference between the yield on money, commonly assumed in the literature to be zero,1 and the rate of return on other assets. The greater the rate of return on assets other than money, the greater the opportunity cost of holding money, and so the fewer money balances will be demanded.

2. Cost of transfers: the costs associated with transferring between higher interest earning assets and money, needed to purchase goods and services. If the cost of transfers, known as brokerage fees, are high then it is unlikely that we will put our wealth into the higher interest earning assets as to do so will involve substantial costs. Demand for money will then be a positive function of these transfer costs.

3. Price uncertainty of assets: there is inevitably risk involved in holding assets. Even though there exists a risk in holding money as a , since we do not know for certain how many goods a given quantity of money can buy in the future due to inflation, the risk associated with holding other, interest earning, assets is generally considered to be greater. If the price of assets is likely to vary over time then, by the time we want to sell those assets in order to obtain money to undertake transactions, we may face considerable capital loss. If we are risk-averse then our demand for money will therefore be a positive function of the riskiness or price uncertainty of alternative assets.

4. The expected pattern of expenditures and receipts: if individuals were paid their wages in lump sums weekly then average cash balances would be less than if wages were paid monthly. If the pattern of payments and receipts was uncertain then cash balances would be likely to be higher; it may be

Page | 2 unwise to face the brokerage fees and transfer cash to bonds if there is a possibility that you will need to make a large cash payment in the near future.

These determinants are also related to Keynes' description of money demand motives. Keynes (1936) broke down the demand for money into three types: transactions, precautionary and speculative motives:

The transaction demand for money is essentially that needed to buy goods and services where money is needed as a medium of exchange.

Precautionary money balances are simply holdings of money kept in case of emergencies (an unexpectedly large hospital treatment bill or a domestic accident for example).

Finally, the speculative demand for money considers money as an alternative to interest earning assets. Due to the capital loss involved with holding bonds when the interest rate increases2 if an individual expects the interest rate to rise, then he will expect to experience a capital loss on his bond holdings. Knowing that the bond price will fall, he will want to hold a larger quantity of money.

In fact, Keynes originally assumed that individuals held their expectations of interest rate movements with certainty. When the interest rate was below what they expected in the long run, R* in Figure 3.1, then they would put all of their financial wealth in the form of money to avoid the capital loss associated with holding bonds. When the interest rate was above what was expected, then the expected interest rate fall would be associated with a capital gain from holding bonds. The individual would then hold as little money as possible, only covering the transactions and precautionary motives (T representing minimum cash required to conduct transactions). The individual's demand for money, as a function of the interest rate, would then be a step function, shown in Figure 1 below.

Figure 1:

Interest rate

R*

0 T

Quantity of money

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It has become standard to model each component of the demand for money separately. The transaction demand for money is typically modelled by allowing money to be a function of determinants 1, 2 and 4 above (i.e. ignoring asset price uncertainty). By allowing more flexible assumptions on the expected pattern of expenditures and receipts, similar analysis can incorporate a precautionary motive for money holdings. Analysis of the speculative demand for money, however, concentrates on determinant 3, asset price uncertainty, while dropping one or more of the other factors for tractability.

THE THEORETICAL ANALYSIS OF THE DEMAND FOR MONEY

This topic examines the demand for money at the macroeconomic level. On a more general level, the following theoretical analyses are considered.

1. The Classical Approach to the demand for money (or the ): Fisher’s Equation of Exchange 2. The Classical Approach to the demand for money (or the quantity theory of money): The Cambridge Version of the Quantity theory of money 3. Keynes Theory of the Demand for Money 4. Regressive Expectations Model 5. Liquidity Preference as Behaviour towards Risk 6. Baumol-Tobin Transactions Demand for Money 7. Tobin’s Model of Portfolio Selection 8. Macroeconomic Determinants of Money Demand 9. The Stability of the Money Demand function 10. Reasons for the breakdown of the Money Demand functions.

The Classical Approach to the Demand for Money

The economists in the classical tradition based their analyses on the major functions of money, which include: (i) medium of exchange, (ii) store of value, (iii) unit of account, and (iv) store of deferred payments. According to the classical economists, all markets for goods continuously clear and relative prices are flexible to ensure that the automatic adjustment to equilibrium is attained. In this tradition, the economy is always in full employment except for transitory real disturbances. The role of money in such an economy is simple since it serves as a numeraire.

The Classical approach to the demand for money (otherwise known as the quantity theory of money) was the theory of the value of money accepted by the classical economists. Starting in the hands of the French writer Jean Bodin, many economists in the classical tradition (e.g. John Locke, David Hume, David Ricardo and John Stuart Mill amongst others) contributed to the development of the theory which reached its highest level of sophistication in the hands of , Alfred Marshall and A. C. Pigou.

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1. FISHER'S EQUATION OF EXCHANGE

Fisher's equation is basically an identity which relates the volume of transactions at current prices to the stock of money multiplied by the turnover rate of money. The turnover rate of money which measures the average number of times money is used in transactions during the period is called the velocity of money (V). This identity is expressed as:

MV=PT (1) where M, V, P, and T are the quantity of money, the transactions velocity of money, price index of the items traded and volume of transaction, respectively. As a result of the expost definition of velocity, the above relationship is an identity. In the simple equation, Fisher related the stock of money to the amount of money expended in the economy during a given period of time.

Another exposition and development of the Fisherian equation which focused only on income transactions can be developed as follows:

If the average of prices of commodity i is pi, and the quantity bought and sold of that commodity is qi, the total amount of money spent on that commodity is the product of its price and quantity, that is piqi. For the entire economy, the total expenditure on goods and services can be written as follows if the number of goods in the economy is n:

p1q1 + p2q2 + p3q3 ... + pnqn = ∑piqi (2) we can now write that: ∑piqi = ∑PQ (3) where P,Q stands for the index of prices and quantity of goods and services during the period, respectively.

Then, it can be seen that PQ is the total monetary expenditures in an economy. If the quantity of money in the economy (M) is given, the average value of each good or service bought by each unit of money is equal to the product of price and quantity divided by the money stock. This is what Fisher called the average rate of turnover of money or the velocity of circulation (V): V= PQ M (4)

If we multiply both sides of equation (4) by M, we have:

MV = PQ (5)

Like in the equation (1) developed earlier, this is also an obviously true statement and cannot by itself explain the variables it contains. With the exception of the price level, all the equilibrium values of the elements of the equation are determined by other forces. An increase in the quantity of money (M) which is exogenous will not generally be expected, of itself, to change either the velocity of circulation (V) or indeed the volume of transactions (or quantity of goods and services), Q. According to Fisher, Page | 5 the equation of exchange served to determine the price level. This result as expressed by Fisher formed the basis of the quantity theory (Fisher, 1911, The purchasing power of money. New York: Macmillan. p.23):

"We find that, under conditions assumed, the price level varies (1) directly as the quantity of money in circulation (M); (2) directly as the velocity of its circulation (V); and (3) inversely as the volume of trade done by it (T). The first of these three relations is worth emphasis. It constitutes the quantity theory of money"

The importance of the equations can be seen if the trends of thought of the classical economists are considered in details. First, if both the velocity and quantity of output are fixed, it is easy to see an equi- proportionate (equi-proportional) relationship between money and prices. Solving for the price level from the equation of exchange,

P = V (6) M Q

This can be written as:

P=cM (7)

The total differential of equation (7) given that c is fixed is:

dP = c dM (8)

Dividing through by P we have:

dP = c dM P M (9)

When the value of P as previously defined is substituted into the right hand of equation (9), we have that:

dP = dM P M (10)

Equation (10) says that there is equi-proportional relationship between money and prices.

Alternatively, we can write:

MV=Py (11)

The new variable y is real income and all other variables are as defined previously.

For small changes, we can write:

dM = dP dy + = π+ g M P y (12)

Where π is the rate of inflation and g is the rate of growth of real income.

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If an increase in y is not feasible as a result of supply or other constraints, then the equi-proportionate relationship between money and prices stand.

According to Fisher and other classical economists, the quantity of money (M) is independent of the other variables. The quantity of M is determined by the monetary authorities (CBN). The velocity of circulation (V) is thought to be fixed because the various factors which influence it change only very slowly and are unlikely to change velocity in the short run. Based on this logic, velocity can be considered a constant. The factors which basically influence velocity are institutional factors which can change only in the long run. These are public's payments habits and the payments technology of the society, institutional arrangements for the settlement of debt in particular using charge accounts or bank charge cards, the extent of the use of cheques and the availability of credit facilities among businesses. If payment periods are short, the average money holding over the payment period for any given income level will be smaller and hence an increase in velocity. Similarly, frequent use of charge accounts by consumers or trade credit by business will increase velocity. The value of Q can also be treated as a constant because of the classical economists' argument that the economy is always at full employment or tending towards it. Given this, the economy's output level will be constant at all times.

From the equations above, given the fact that the demand for money is purely for transaction, the demand for money will therefore depend on the value of transactions to be undertaken in the economy. Indeed, we can then state that the demand for money is a constant proportion of the transactions to be undertaken. In our simple case above, the demand for money will be proportional to the nominal income. This approach has a lot to recommend it. For one thing, it links demand for money to the volume of trade in an economy, leading as it were, to the realm of macroeconomic theory, where it properly belongs. For another, the theory is directly estimable, making it easy to establish the size of the various coefficients in the demand-for- money function.

2. THE CAMBRIDGE VERSION OF THE QUANTITY THEORY

The Cambridge approach or the cash balance approach as it is often called is another variant of the quantity theory. The Cambridge version which is named after the academic institution, Cambridge University, where the two primary originators, Alfred Marshall and A.C. Pigou, were based demonstrated the equi-proportional relationship between money and prices. The function of the relationship was however less mechanistic than the Fisherian version. The Cambridge economists held the view that money is capable of yielding utility in itself and of itself. Money provides convenience and security. Money is a good which when held confers some satisfaction on the holder. The focus then is examining what it is that determines an individual's optimum money holdings. Money, according to the Cambridge school provides two needs for individuals who have it

First, money is held because of the convenience money provides in transactions compared to other stores of value. Second, money provides security because it lessens the possibility of inconvenience or at worst bankruptcy from failure to meet unexpected obligations. As Pigou notes [Pigou (1917). The value of money. Quarterly Journal of Economics, Vol. 32 (November), p. 41]:

" ... everybody is anxious to hold enough of his resources in the form of titles to legal tender (money) both to enable him to effect the ordinary transactions of life without trouble, and to secure him against unexpected demands, due to a sudden need, or to a rise in the price of something he cannot easily dispense with" Page | 7

The Cambridge economists did not inquire, as did Fisher, into the determinants of the amount of money that an economy needs to carry out a given volume of transactions. Instead, they inquired into the determinants of the amount of money that an individual will wish to hold. The question, as it stands, is basically microeconomic in nature, and an answer to it will necessarily derive from the theory of choice. In such a choice-framework the central factors are constraints and opportunity costs, all of these interacting with the individual's taste. To the Cambridge economists, the principal determinants of "taste" for money holding is that it is a convenient asset to hold, since it is universally acceptable in exchange for goods and services. The more transactions an individual has to undertake, the more cash he would want to hold. It is in this last sentence that the similarity between the Cambridge approach and the Fisherian approach lies. Beyond that, they are basically different. The emphasis of the Cambridge is on wanting to hold money rather than having to hold money as emphasized by economists in the Fisherian tradition.

The Cambridge economists realized however that any amount of money held in hand yields no income. As a result, money will be held as long as the utility derived from holding it in terms of both convenience and security outweighs the income loss from not holding the money in interest earning assets or satisfaction lost by using the money to purchase goods for consumption. From the point of view of an individual's behaviour in making choices, the important variables in the desire to hold money are; (1) The convenience that one desires from holding money for purposes of transactions, (2) An individual’s wealth; and (3) The rate of interest

The Cambridge economists did not elaborate on the kind of functional relationship that one may expect from these variables and money balances. Rather, they took the simplistic view that for an individual, the level of wealth, the volume of transactions and the level of income will, at least in the short run, be in stable proportion to one another.

What then is the optimal amount of money to hold? The assumption by the Cambridge economists is that the demand for money would be a proportion of income and wealth. The distinction between income and wealth was not clearly stated.

Money demand in the Cambridge version (Md) is assumed to be a proportion k of nominal income, the price level p multiplied by real income, y. The proportion of income that is optimal to hold in the form of money k is assumed to be relatively stable in the short run. In equilibrium, the exogenously determined must be equal to money demand, hence: Ms = Md = kY= kPy (13)

It can be seen from equation (13) that the demand for money is a constant proportion of the level of income. With k fixed and the y determined by supply conditions in such a way that an increase is not feasible, the Cambridge equation reduces to a proportional relationship between the price level and the money stock. Then as in Fisher, the quantity of money determines the price level.

The formal relationship between the Cambridge and the Fisher equation can be shown by rewriting equation (13) as follows: Page | 8

M 1 = Py (14) K It can be seen that the two equations are equivalent with: V = 1 (15) k Alternatively, let

M = kY (16)

We can reconcile with Fisher's formulation. Let Q' be the level of' real output in economy (i.e. real gross national product) rather than a measure of total transactions (the latter includes transfers of used goods, financial assets, etc.). This latter measure is represented by Q in Fisher's formulation. Therefore, Q' < Q. In addition, let V' be the income velocity of circulation of money. The equation of exchange can then be written to mean only transactions in final goods and services:

MV'= PQ' (17) Since Q' = Q in the Cambridge model, M = kY = kPQ = kPQ' (18) M = kPQ 1 And M = PQ' (19) 푘

Therefore, the reciprocal of k, the proportionality factor, is equal to V', the income velocity of circulation. It is therefore apparent that, while Fisher was concerned with the length of time for which an average unit of the money stock will be held, the Cambridge economists focused on the proportion of income that will be held in the form of money.

Fisher's framework implies that the velocity of circulation is constant, at least in the short run. This is not so with the Cambridge approach, which emphasizes the influence of the rate of interest and expectations on the demand-for-money function. Interest rates and expectations are both volatile; they change significantly even in the short run, so that the velocity circulation can no longer be taken as given constant. Furthermore, Fisher’s theory seems to imply that the rate of interest has no effect on the demand for money. This is not true of the Cambridge approach, whose chief contribution was to call attention to the fact that the rate of interest may be very important.

Although the exact relationship between the rate of interest and the demand for money was not specified by the Cambridge economists, at least not as we know it today, it was left to their successors to investigate this relationship in more detail.

Pigou (1917), the leading proponent of the Cambridge approach, commented on the relationship between his approach and that of Fisher as follows:

…there is no conflict between my formula and that embodied in the quantity theory. But it does not follow that there is nothing to choose between them… The claim that I make on behalf of mine is that it is a somewhat more effective engine of analysis. It focuses attention on the proportion of their resources that people choose to hold in the form of legal tender instead of focusing it on 'velocity and circulation'. This fact gives it, as I Page | 9

think, a real advantage, because it brings us at once into relation with volition - an ultimate cause of demand - instead of with something that seems at first sight accidental and arbitrary. (p. 54).

While it can be said that the two formulations of the quantity theory are equivalent, the Cambridge version as a result of the questions it raises provides more inquiry into the theory of the demand for money. While the emphasis of the Fisherian equation is on money and its velocity (the rate of turnover of money), the emphasis of the Cambridge equation is that the quantity theory is a theory of the demand for money. It also recognizes that in equilibrium, money demand must be equal to money supply. The emphasis therefore is on money demand and money supply. The focus by the Cambridge equation on the quantity theory as a theory of the demand for money leads naturally to an answer to the question: through which mechanism does money affect the price level?

3 KEYNES THEORY OF THE DEMAND FOR MONEY

As an economist in Cambridge himself, Keynes was not unfamiliar with the work of his colleagues. Indeed it was said that he participated actively in the development of the theory. As a starting point it is usual to begin the Keynesian analysis from the perspectives of the motives for holding money. Keynes's treatment gives the impression that there were separate money demands for each of the motives. While an individual might not exactly keep money in watertight components for each of the motives, Keynes nevertheless thought it useful to consider the various overall motives for holding money in general. According to Keynes, there are three motives for holding money. First, since money serves as a medium of exchange, it is held to effect transactions. This is referred to as the transactions motive. Second, money may be held as a precaution or to meet unforeseen contingencies or circumstances. Such emergencies include paying unexpected medical bills, making purchase at unexpectedly favorable prices. Within the context of developing economies, emergencies will include paying for a car battery that suddenly goes flat, or undertaking funeral expenses for an old relation etc. This is what Keynes referred to as the precautionary motives for holding money. Third, within an investment portfolio, money can be held to balance against risk. This is what is referred to as the speculative motive. Both the transaction and the precautionary motives for holding money are functions of income while the speculative demand is a function of interest rate.

The store of value role or function of money implies that money is one form in which wealth can be held. Thus, an individual can have in his portfolio money and alternative assets. The alternative assets in which wealth/income be held, Keynes labeled 'bonds'. According to Keynes, the important variables determining how much money as opposed to bond an individual holds in his portfolio is the rate of interest on bonds. At higher interest rate, the opportunity cost of holding money would be high. When the interest rate is high relative to a fixed view of the nominal interest rate, a future decline in the interest rate would be expected by the public. Thus, such a decline in interest rate would mean capital gain on bonds. Keynes believed that when the interest rate is high, this would result in a low demand for money as a store of value. This is because of the high interest payments, and because at a high interest rate a future capital gain on bonds was likely. The demand for money as an asset would increase as the interest rate declines. According to Keynes therefore the demand for money would vary inversely with the rate of interest. This is Keynes' theory of speculative demand money, and represents Page | 10 a great innovation to the classical theory or the demand for money as developed by Marshall and Pigou. Even though the Cambridge economists suggested that uncertainty might play a role in the demand for money, it was Keynes who formalized it in the theory of the demand for money in terms of uncertainty about the future rate of interest.

There was not much that was new in this approach. What was new was the use of the term 'transactions' to define that class of motive for holding money which takes place to bridge the gap between receipts and payments. The term 'precautionary motive' was reserved for payments that cannot be considered regular. Such payments include the payment of unexpected bill making purchases at unexpectedly favourable prices and meeting sudden emergencies. The demand for money to hold for this motive, according to Keynes, is also proportional to the level of income

What can really be described as new in the Keynesian theory speculative demand for money. Cambridge economists like Pigou and Marshall had suggested that uncertainty may play a crucial role in the demand-for-money function. In particular, they suggested that about the future may influence the demand for money. It was Keynes who really formalised it in terms of uncertainty about the future rare of interest.

In Keynesian theory an individual is assumed to hold all of his wealth either in bonds or in money. Money is a financial asset that is perfectly liquid but earns no rate of interest. A bond, on the other hand, is an asset that carries with it the promise to pay the owner a certain income per annum. This income is fixed in money terms. Hence, a decision to buy such a bond is a decision to buy a claim to a future income stream. The price that a wealth-holder will be prepared to pay for a bond (i.e. its market value) will depend upon the rate of interest, for he will wish to earn at least the going rate of interest on that portion of his wealth held in bonds. For example, if the rate of interest is 5 per cent, he will be willing to pay up to, but not more than, Nl00 for a bond that offers an income of NS per annum in perpetuity. lf the rate of interest rises to 10 per cent, he will not be willing to pay more than N50 for the same bond.

It follows therefore that the price of a bond varies inversely with the rate of interest; a rise in the rate of interest means a fall in its market value, and vice versa. This relationship makes it possible for bond- holders to earn capital gains or losses. But changes in the rate of interest do not involve changes in the value of money. In the two-asset world of Keynes, bonds offer the attraction of income plus the possibility of capital gain 'when the interest rate is expected to fall. In the opposite case of a rise in the interest rate, it also offers the possibility of capital loss.

How do all these affect the demand for money to hold? Keynes argued that wealth-holders have formed firm expectations about the movement of interest rates, and also about what they consider the 'normal' rate of interest. Thus, when the rate of interest is expected to fall (i.e. the current rate is higher than that considered normal), the demand for money is relatively low, since people hold bonds in anticipation of capital gains. But when it is expected to rise (i.e. the current rate is lower than that considered normal), the demand for money is greater, as people attempt to avoid making capital loss by not holding bonds and holding money instead.

As postulated, the demand-for-money function of an individual is a discontinuous function of the Page | 11 current level of the rate of interest. There is some level of the current rate of interest above which the expected bond yield is positive, below which it is negative and at which it is zero. These coincide respectively with zero demand for money, a demand for money equal to an individual's wealth and any demand for money between these two extremes. Let us illustrate this graphically.

In Figure 1 the individual’s wealth (w) is measured on the horizontal axis and the rate of interest (r) on the vertical axis. Let Or, be the rate of interest considered normal by wealth-holders. At any rate of interest higher than Or, the demand for money is equal to zero (so that all his wealth is held in bonds). AB is thus a segment of the demand curve for money. At a rate of interest lower than Or the individual holds all his wealth is held in money and CD is another segment of the demand curve. At point D all wealth is held in money. Joining BC, we get a discontinuous demand curve for money given by ABCD.

How then do we get the usual continuous demand-for-money curve? Given the ‘normal’ rate of interest, individuals have divergent expectations about the movement of the rate of interest towards the rate considered normal. The lower the current rate of interest, the more rapidly wealth-holders expect it to rise and, by implication, the more individuals will want to hold all their wealth in money. It to rise and, by implication. the more individuals will want to hold all their wealth in money. Similarly, the higher the rate of interest. the smaller the amount that individuals will want to hold. If we assume that money and bond holdings of each individual are small relative to the rest of the economy, if we assume further that there is some diversity of opinion about the expected chance of the rate of interest, the aggregate demand-for-money function becomes a continuous and negative function oft he rate of interest. Figure 9.2 Demand for money function

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This is shown graphically in Figure 9.2. The inverse relationship between the rate of interest and the demand for money can be read off the graph. When the rate of interest is r,, the demand for money is M'; but when the rate of interest falls to r, the demand for money increases to M',.

According to Keynes, the demand for money is a function of income and the rate of interest. The transactions and precautionary motives are functions of income, while the speculative demand for money is a function of the rate of interest. Thus,

M' = L1(Y) + L1(r) (20) where L1 represents the transactions and precautionary demands for money and L1, represents the speculative demand for money. Combining both functions, we get

M' = f(Y1r) (21)

Relation (9.2 I) is a testable function, and economists have lost no time in performing statistical tests to estimate the parameters of this function. Some of the results of that test are provided below.

4. Regressive Expectations Model

As mentioned earlier, the most novel part of the Keynes's analysis is the speculative demand for money. Even though the Cambridge economists recognized the existence of uncertainty and its likely effects on the demand for money, it was Keynes who as said earlier formalized the demand for money in terms of uncertainty about the future interest rate. The additional demand for money (additional to transactions and precautionary motives) exist according to Keynes because of the uncertainty about future interest rates and the relationship between changes in interest rate and the market price of bonds. If interest rates move in such a way as to cause capital losses to outweigh the interest earnings on the bonds and cause an investor to hold money instead of bonds, future changes in the interest rate would affect whether bond or money is held. The return on money is zero since no interest is earned by holding it. On the other hand, bonds will earn interest, r. The expected return on bonds is equal this interest rate, r plus or minus expected capital gain or loss. An investor will expect a capital gain if a fall in interest rate is expected, and a capital loss if he expected interest rates to rise. It is the uncertainty about the future cause of interest rates that is very crucial t Keynes's analytical framework. This is often referred to as the regressive expectations model. Essentially it says that people hold money when th y expect bond prices to fall (that is, interest rates to rise) and in this way expe t that a loss would be sustained if they were to hold bonds. Given the variation in people's estimates of the possibility of a rise or fall in interest rates and their magnitudes, there would be people who at any given time will expect it to ris and thus hold money.

Within the Keynesian analytical framework, an individual holds all liquid assets in either money or bonds but not some of each. When bond is held, th · holder is entitled to a stream of income into the future. The expected return on bonds is from two sources: the interest payments on the bonds and a potential capital gain. Let the yield on bond be YB and the price of bond be PB. The market interest rater is:

r = YB Page | 13

PB (22) The market price of the bond (PB) is:

PB = YB r (23)

The expected percentage capital gain (g) is the percentage increase in pric from the purchase price of the bond PB to the expected sales price PB*. The expression for the capital gain is:

g = PB* - PB PB (24) ilizing equations (9.22) and (9.23), with a fixed YB on the bond, an expected price PB* corresponds to an expected interest rate (re) which can be expressed as:

re = YB PB* (25)

Thus capital gains g can be stated in terms of expected and current interest rates as:

The total return on a bond (RB) is equal to the sum of the market interest rate (r) and the capital gain g. That is

RB = r + g (27)

Substituting the value of g, this is:

RB = r + r - 1 re (28)

Given the above what is the choice of the individual asset holder? If the total rate of return on bonds (RB) is greater than zero, the liquid wealth will put rnto bonds. On the other hand if the total return (RB) is less than zero, the total liquid wealth will be put into money. In the development of this formulation, Keynes assumed that each individual has formed expectations about the rate of interest such that the expected rate corresponds to some normal long run average rate. If the rate of interest rises above this long run expectations, the asset holder expects the interest rate to fall and vice-versa. Thus in this kind of framework, expectations are regresive. Hence this is called a regressive expectations model.

The total rate of return on bond (RB) is etermmed by the expected rate of interest r and the observable interest rate r. It is possible to compute the critical interest rate (r) which entitles an individual asset holder to a net return of zero such that when the rate of interest is greater than the critical rate r, all wealth is held in bonds and when it is below it all wealth is held in money. In order to find the critical value re equation (9 28) is set equal to zero:

O = r – r - 1 re r(1 + re) = re Page | 14

r = re = re 1 + re (29) where r,, the critical rate of interest is the value of the market interest rate r that makes RB= 0 is given as:

re 1 + re (30)

The individual’s demand for money can be shown as in the following fig 9.1 below. Measured on the vertical axis is the current rate of interest and total wealth is measured on the horizontal axis When the in greater than re, the asset holder holds only bonds and the demand for money is zero. When the rate of interest is below re so that the total return on bonds is less than zero that is RB< 0 and the expected capital losses on bonds is greater than the interest yield, the asset holder moves entire wealth into money. We thus derive a demand for money curve for an individual that looks like a step function as shown in figure 9.3 below. It should be noticed that when the rate of interest r is equal to the critical rate re, RB=0 and the asset holder is indifferent between bonds and money. At any other value of r, the asset holder is either holding bonds and nothing else or holding money and nothing else.

Review Questions

1. What is meant by Quantity theory of money? What are its shortcomings?

2. Compare and contrast Fisher’s equation of exchange and Cambridge version of the quantity theory of exchange.

3. Discuss as exhaustively as possible the Quantity theory of money highlighting its major elements and its contributions to the role of money in the economy.

4. “The demand for money and the demand for other economic goods are the same.” Do you agree? Discuss fully.

5. What are the microeconomic determinants of the demand for money? What are Keynes contributions to the demand for money? How are these microeconomic determinants related to Keynes' description of money demand motives?

Edited and compiled by the Course Instructor:

Ajibade Moses Anderson ADEOYE Phone: 0802 454 4444, 0803 435 4647 Email: [email protected], and [email protected]

Office: SMS B 020 BSc Economics Programme College of Social and Management Sciences Bowen University Iwo, Osun State, Nigeria Website: www.bowen.edu.ng

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