The following points highlight the three main approaches to the demand for money. The approaches are: 1. The Classical Approach 2. The Keynesian Approach Liquidity Preference 3. The Post-Keynesian Approaches.
1. The Classical Approach:
The classical economists did not explicitly formulate demand for money theory but their views are inherent in the quantity theory of money. They emphasized the transactions demand for money in terms of the velocity of circulation of money. This is because money acts as a medium of exchange and facilitates the exchange of goods and services. In Fisher’s “Equation of Exchange”,
MV = PT
Where M is the total quantity of money, V is its velocity of circulation, P is the price level, and T is the total amount of goods and services exchanged for money.
The right hand side of this equation PT represents the demand for money which, in fact, “depends upon the value of the transactions to be undertaken in the economy, and is equal to a constant fraction of those transactions.” MV represents the supply of money which is given and in equilibrium equals the demand for money. Thus the equation becomes MV = PT
This transactions demand for money, in turn, is determined by the level of full employment income. This is because the classicists believed in Say’s Law whereby supply created its own demand, assuming the full employment level of income. Thus the demand for money in Fisher’s approach is a constant proportion of the level of transactions, which in turn, bears a constant relationship to the level of national income. Further, the demand for money is linked to the volume of trade going on in an economy at any time. Thus its underlying assumption is that people hold money to buy goods.
But people also hold money for other reasons, such as to earn interest and to provide against unforeseen events. It is, therefore, not possible to say that V will remain constant when M is changed. The most important thing about money in Fisher’s theory is that it is transferable. But it does not explain fully why people hold money. It does not clarify whether to include as money such items as time deposits or savings deposits that are not immediately available to pay debts without first being converted into currency.
It was the Cambridge cash balances approach which raised a further question: Why do people actually want to hold their assets in the form of money? With larger incomes, people want to make larger volumes of transactions and that larger cash balances will, therefore, be demanded. The Cambridge demand equation for money is Md = kPY
where Md is the demand for money which must equal the supply of money (Md=Ms) in equilibrium in the economy, k is the fraction of the real money income (PY) which people wish to hold in cash and demand deposits or the ratio of money stock to income, P is the price level, and Y is the aggregate real income. This equation tells us that “other things being equal, the demand for money in normal terms would be proportional to the nominal level of income for each individual, and hence for the aggregate economy as well.”
Its Critical Evaluation:
This approach includes time and saving deposits and other convertible funds in the demand for money. It also stresses the importance of factors that make money more or less useful, such as the costs of holding it, uncertainty about the future and so on. But it says little about the nature of the relationship that one expects to prevail between its variables, and it does not say too much about which ones might be important.
One of its major criticisms arises from the neglect of store of value function of money. The classicists emphasized only the medium of exchange function of money which simply acted as a go-between to facilitate buying and selling. For them, money performed a neutral role in the economy. It was barren and would not multiply, if stored in the form of wealth.
This was an erroneous view because money performed the “asset” function when it is transformed into other forms of assets like bills, equities, debentures, real assets (houses, cars, TVs, and so on), etc. Thus the neglect of the asset function of money was the major weakness of the classical approach to the demand for money which Keynes remedied.
2. The Keynesian Approach Liquidity Preference:
Keynes in his General Theory used a new term “liquidity preference” for the demand for money.
Keynes suggested three motives which led to the demand for money in an economy:
(1) The transactions demand,
(2) The precautionary demand, and
(3) The speculative demand.
The Transactions Demand for Money:
The transactions demand for money arises from the medium of exchange function of money in making regular payments for goods and services. According to Keynes, it relates to “the need of cash for the current transactions of personal and business exchange.” It is further divided into income and business motives.
The income motive is meant “to bridge the interval between the receipt of income and its disbursement.” Similarly, the business motive is meant “to bridge the interval between the time of incurring business costs and that of the receipt of the sale proceeds.”
If the time between the incurring of expenditure and receipt of income is small, less cash will be held by the people for current transactions, and vice versa. There will, however, be changes in the transactions demand for money depending upon the expectations of income recipients and businessmen. They depend upon the level of income, the interest rate, the business turnover, the normal period between the receipt and disbursement of income, etc.
Given these factors, the transactions demand for money is a direct proportional and positive function of the level of income, and is expressed as L=kY
where LT is the transactions demand for money, k is the proportion of income which is kept for transactions purposes, and Y is the income.
This equation is illustrated in Figure 1 where the line kY represents a linear and proportional relation between transactions demand and the level of income. Assuming k= 1/4 and income Rs1000crores, the demand for transactions balances would be Rs. 250crores, at point A. With the increase in income to Rs. 1200crores, the transactions demand would be Rs300crores at point B on the curve kY.
If the transactions demand falls due to a change in the institutional and structural conditions of the economy, the value of k is reduced to say, 1/5, and the new transactions demand curve is k’Y. It shows that for income of Rs. 1000 and 1200crores, transactions balances would be Rs. 200 and 240 crores at points C and D respectively in the figure.
“Thus we conclude that the chief determinant of changes in the actual amount of the transactions balances held is changes in income. Changes in the transactions balances are the result of movements along a line like kY rather than changes in the slope of the line. In the equation, changes in transactions balances are the result of changes in Y rather than changes in k.”
Interest Rate and Transactions Demand:
Regarding the rate of interest as the determinant of the transactions demand for money, Keynes made the LT function interest inelastic. But he pointed out that the “demand for money in the active circulation is also to some extent a function of the rate of interest, since a higher rate of interest may lead to a more economical use of active balances.”
“However, he did not stress the role of the rate of interest in this part of his analysis, and many of his popularizes ignored it altogether.” Two post-Keynesian economists William J. Baumol and James Tobin have shown that the rate of interest is an important determinant of transactions demand for money. The have also pointed out that the relationship between transactions demand for money and income is not linear and proportional. Rather, changes in income lead to proportionately smaller changes in transactions demand.
Transactions balances are held because income received once a month is not spent on the same day. In fact, an individual spreads his expenditure evenly over the month. Thus a portion of money meant for transactions purposes can be spent on short-term interest-yielding securities. It is possible to “put funds to work for a matter of days, weeks, or months in interest-bearing securities such as U.S. Treasury bills or commercial paper and other short-term money market instruments.
The problem here is that there is a cost involved in buying and selling. One must weigh the financial cost and inconvenience of frequent entry to and exit from the market for securities against the apparent advantage of holding interest-bearing securities in place of idle transactions balances.
Among other things, the cost per purchase and sale, the rate of interest, and the frequency of purchases and sales determine the profitability of switching from ideal transactions balances to earning assets. Nonetheless, with the cost per purchase and sale given, there is clearly some rate of interest at which it becomes profitable to switch what otherwise would be transactions balances into interest-bearing securities, even if the period for which these funds may be spared from transactions needs is measured only in weeks. The higher the interest rate, the larger will be the fraction of any given amount of transactions balances that can be profitably diverted into securities.”
The structure of cash and short-term bond holdings is shown in Figure 2 (A), (B) and (C). Suppose an individual receives Rs.1200 as income on the first of every month and spends it evenly over the month. The month has four weeks. His saving is zero.
Accordingly, his transactions demand for money in each week is Rs. 300. So he has Rs900 idle money in the first week, Rs600 in the second week, and Rs300 in the third week. He will, therefore, convert this idle money into interest-bearing bonds, as illustrated in Panel (B) and (C) of Figure 2. He keeps and spends Rs.300 during the first week (shown in Panel B), and invests Rs .900 in interest-bearing bonds (shown in Panel C).
On the first day of the second week, he sells bonds worth Rs.300 to cover cash transactions of the second week and his bond holdings are reduced to Rs. 600. Similarly, he will sell bonds worth Rs. 300 in the beginning of the third week and keep the remaining bonds amounting to Rs. 300 which he will sell on the first day of the fourth week to meet his expenses for the last week of the month.
The amount of cash held for transactions purposes by the individual during each week is shown in saw-tooth pattern in Panel (B), and the bond holdings in each week are shown in blocks in Panel (C) of Figure 2.
The modern view is that the transactions demand for money is a function of both income and interest rates which can be expressed as
LT = f(Y,r).
This relationship between income and interest rate and the transactions demand for money for the economy as a whole is illustrated in Figure 3. We saw above that LT = kY. If Y=Rs1200crores and k= 1 /4, then LT=Rs300 crores.
This is shown as Y curve in Figure 3. If the income level rises to Rs. 1600 crores, the transactions demand also increases to Rs 400 crores, given k=1/4. Consequently, the transactions demand curve shifts to Y2 The transactions demand curves Y1 and Y2 are interest-inelastic so long as the rate of interest does not rise above r8 per cent. As the rate of interest starts rising above r8 the transactions demand for money becomes interest elastic.
It indicates that “given the cost of switching into and out of securities, an interest rate above 8 per cent is sufficiently high to attract some amount of transactions balances into securities.” The backward slope of the Y, curve shows that at still higher rates, the transaction demand for money declines. Thus when the rate of interest rises to r8, the transactions demand declines to Rs. 250crores with an income level of Rs1200crores. Similarly, when the national income is Rs. 1600 crores, the transactions demand would decline to Rs. 350 crores at r12interest rate. Thus the transactions demand for money varies directly with the level of income and inversely with the rate of interest.
The Precautionary Demand for Money:
The precautionary motive relates to “the desire to provide for contingencies requiring sudden expenditures and for unforeseen opportunities of advantageous purchases.” Both individuals and businessmen keep cash in reserve to meet unexpected needs. Individuals hold some cash to provide for illness, accidents, unemployment and other unforeseen contingencies.
Similarly, businessmen keep cash in reserve to tide over unfavourable conditions or to gain from unexpected deals. Therefore, “money held under the precautionary motive is rather like water kept in reserve in a water tank.” The precautionary demand for money depends upon the level of income, business activities, opportunities for unexpected profitable deals, availability of cash, the cost of holding liquid assets in bank reserves, etc.
Keynes held that the precautionary demand for money, like transactions demand, was a function of the level of income. But the post-Keynesian economists believe that like transactions demand, it is inversely related to high interest rates.
The transactions and precautionary demand for money will be unstable, particularly if the economy is not at full employment level and transactions are, therefore, less than the maximum, and are liable to fluctuate up or down. Since precautionary demand, like transactions demand is a function of income and interest rates, the demand for money for these two purposes is expressed in the single equation LT = f (Y,r).9 Thus the precautionary demand for money can also be explained diagrammatically in terms of Figures 2 and 3.
The Speculative Demand for Money:
The speculative (or asset or liquidity preference) demand for money is “for securing profit from knowing better than the market what the future will bring forth” .Individuals and businessmen having funds, after keeping enough for transactions and precautionary purposes, like to make a speculative gain by investing in bonds. Money held for speculative purposes is a liquid store of value which can be invested at an opportune moment in interest-bearing bonds or securities.
Bond prices and the rate of interest are inversely related to each other. Low bond prices are indicative of high interest rates, and high bond prices reflect low interest rates. A bond carries a fixed rate of interest. For instance, if a bond of the value of Rs. 100 carries 4 per cent interest and the market rate of interest rises to 8 per cent, the value of this bond falls to Rs50 in the market. If the market rate of interest falls to 2 per cent, the value of the bond will rise to Rs. 200 in the market.
This can be worked out with the help of the equation.
V = R/r
where V is the current market value of a bond, R is the annual return on the bond, and r is the rate of return currently earned or the market rate of interest. So a bond worth Rs100 (V) and carrying a 4 per cent rate of interest (r), gets an annual return (R) of Rs4, that is, V=Rs.4/0.04=Rs.100. When the market rate of interest rises to 8 per cent, then V=Rs.4/0.08=Rs.50; when it falls to 2 per cent, then V=Rs. 4/0.02=Rs.200.
Thus individuals and businessmen can gain by buying bonds worth Rs. 100 each at the market price of Rs. 50 each when the rate of interest is high (8 per cent), and sell them again when they are dearer (Rs. 200 each when the rate of interest falls (to 2 per cent).
According to Keynes, it is expectations about changes in bond prices or in the current market rate of interest that determine the speculative demand for money. In explaining the speculative demand for money, Keynes had a normal or critical rate of interest (rc) in mind. If the current rate of interest (r) is above the “critical” rate of interest, businessmen expect it to fall and bond prices to rise.
They will, therefore, buy bonds to sell them in future when their prices rise in order to gain thereby. At such times; the speculative demand for money would fall. Conversely, if the current rate of interest happens to be below the critical rate, businessmen expect it to rise and bond prices to fall.
They will, therefore, sell bonds in the present if they have any, and the speculative demand for money would increase. Thus when r>rc, an investor holds all his liquid assets in bonds, and when r<rc his entire holdings go into money. But when r = rc he becomes indifferent to hold bonds or money.
This relationship between an individual’s demand for money and the rate of interest is shown in Figure 4 where the horizontal axis shows the individual’s demand for money for speculative purposes and the current and critical interest rates on the vertical axis. The figure shows that when r is greater than r c, the asset holder puts all his cash balances in bonds and his demand for money, is zero.
This is illustrated by the LM portion of the vertical axis. When r falls below rc, the individual expects more capital losses on bonds as against the interest yield. He, therefore, converts his entire holdings into money, as shown by OW in the figure. This relationship between an individual asset holder’s demand for money and the current rate of interest gives the discontinuous step demand for money curve LMSW.
For the economy as a whole the individual demand curve can be aggregated on this presumption that individual asset-holders differ in their critical rates rc. It is a smooth curve which slopes downward from left to right, as shown in Figure 5.
Thus the speculative demand for money is a decreasing function of the rate of interest. The higher the rate of interest, the lower the speculative demand for money, and the lower the rate of interest, the higher the speculative demand for money. It can be expressed algebraically as Ls = f (r), where Ls is the speculative demand for money and r is the rate of interest.” Geometrically, it is shows in Figure 5.
The figure shows that at a very high rate of interest r12, the speculative demand for money is zero and businessmen invest their cash holdings in bonds because they believe that the interest rate cannot rise further. As the rate of interest falls to say, r8 the speculative demand for money is OS. With a further fall in the interest rate to r6, it rises to OS1 But at a very low rate of interest r2, the Ls curve becomes perfectly elastic.
This is known as the liquidity trap when people prefer to keep money in cash rather than invest in bonds and the speculative demand for money is infinitely elastic. Thus the shape of the Ls curve shows that as the interest rate rises, the speculative demand for money declines, and with the fall in the interest rate, it increases. Thus the Keynesian speculative demand for money function is highly volatile, depending upon the behaviour of interest rates.
Keynes visualised conditions in which the speculative demand for money would be highly or even totally elastic so that changes in the quantity of money would be fully absorbed into speculative balances. This is the famous Keynesian liquidity trap. In this case, changes in the quantity of money have no effects at all on prices or income.
According to Keynes, this is likely to happen when the market interest rate is very low so that yields on bonds, equities and other securities will also below.
At a very low rate of interest, such as r2, in Figure 5, the Ls curve becomes perfectly elastic and the speculative demand for money is infinitely elastic. This portion of the Ls curve is known as the liquidity trap. At such a low rate, people prefer to keep money in cash rather than invest in bonds because purchasing bonds will mean a definite loss. People will not buy bonds so long as the interest rate remains at the low level and they will be waiting for the rate of interest to return to the “normal” level and bond prices to fall.
According to Keynes, as the rate of interest approaches zero, the risk of loss in holding bonds becomes greater. “When the price of bonds has been bid up so high that the rate of interest is, say, only 2 per cent or less, a very small decline in the price of bonds will wipe out the yield entirely and a slightly further decline would result in loss of the part of the principal.” Thus the lower the interest rate, the smaller the earnings from bonds. Therefore, the greater the demand for cash holdings. Consequently, the Ls curve will become perfectly elastic.
Further, according to Keynes, “a long-term rate of interest of 2 per cent leaves more to fear than to hope, and offers, at the same time, a running yield which is only sufficient to offset a very small measure of fear.” This makes the Ls curve “virtually absolute in the sense that almost everybody prefers cash to holding a debt which yields so low a rate of interest.”
Prof. Modigliani believes that an infinitely elastic Ls curve is possible in a period of great uncertainty when price reductions are anticipated and the tendency to invest in bonds decreases, or if there prevails “a real scarcity of investment outlets that are profitable at rates of interest higher than the institutional minimum.”
The phenomenon of liquidity trap possesses certain important implications:
First, the monetary authority cannot influence the rate of interest even by following a cheap money policy. An increase in the quantity of money cannot lead to a further decline in the rate of interest in a liquidity trap situation.
Second, the rate of interest cannot fall to zero.
Third, the policy of a general wage cut cannot be efficacious in the face of a perfectly elastic liquidity preference curve, such as Ls in Figure 5. No doubt, a policy of general wage cut would lower wages and prices, and thus release money from transactions to speculative purpose, the rate of interest would remain unaffected because people would hold money due to the prevalent uncertainty in the money market.
Last, if new money is created, it instantly goes into speculative balances and is put into bank vaults or cash boxes instead of being invested. Thus there is no effect on income. Income can change without any change in the quantity of money. Thus monetary changes have a weak effect on economic activity under conditions of absolute liquidity preference.
The Total Demand for Money:
According to Keynes, money held for transactions and precautionary purposes is primarily a function of the level of income, LT =f (Y), and the speculative demand for money is a function of the rate of interest, Ls = f (r). Thus the total demand for money is a function of both income and the interest rate:
LT+Ls =f (Y)+f (r)
or L =f(Y)+f (r)
or L =f(Y,r)
where L represents the total demand for money. Thus the total demand for money can be derived by the lateral summation of the demand function for transactions and precautionary purposes and the demand function for speculative purposes, as illustrated in Figure 6 (A), (B) and (C). Panel (A) of the Figure shows OT, the transactions and precautionary demand for money at Y level of income and different rates of interest. Panel (B) shows the speculative demand for money at various rates of interest.
It is an inverse function of the rate of interest. For instance, at r. rate of interest it is OS and as the rate of interest falls to r2, the Ls curve becomes perfectly elastic. Panel (C) shows the total demand curve for money L which is a lateral summation of LT and Ls curves: L=LT+LS. For example, at r rate of interest, the total demand for money is OD which is the sum of transactions and precautionary demand OT plus the speculative demand TD, OD=OT+TD, where TD = OS. At r2 interest rate, the total demand for money curve also becomes perfectly elastic, showing the position of liquidity trap.
3. The Post-Keynesian Approaches:
Keynes believed that the transactions demand for money was primarily interest inelastic. Prof. Baumol has analysed the interest elasticity of the transactions demand for money on the basis of his inventory theoretical approach. Further, in the Keynesian analysis the speculative demand for money is analysed in relation to uncertainty in the market. Prof. Tobin has given an alternative theory which explains liquidity preference as behaviour towards risk.
The two approaches to the liquidity preference theory are discussed below:
1. Baumol’s Inventory Theoretic Approach:
William Baumol has made an important addition to the Keynesian transactions demand for money. Keynes regarded transactions demand for money as a function of the level of income, and the relationship between transactions demand and income as linear and proportional.
Baumol shows that the relation between transactions demand and income is neither linear nor proportional. Rather, changes in income lead to less than proportionate changes in the transactions demand for money. Further, Keynes considered transactions demand as primarily interest inelastic. But Baumol analyses the interest elasticity of the transactions demand for money.
Baumol’s theory is based on the following assumptions:
1. The transactions between money and bonds are transparent and occur in a steady stream.
2. The bond market is perfect where there is easy conversion of bonds into cash and vice versa.
3. There is a fixed cost in exchanging bonds for cash and vice versa.
4. The holding of cash involves interest cost and non-interest costs.
5. The interest cost (or rate of interest) is constant over the year.
6. The non-interest costs such as brokerage fee, mailing expenses, etc. are also fixed over the year.
Given these assumptions, Baumol’s analysis is based on the holding of an optimum inventory of money for transactions purposes by a firm or an individual. He writes: “A firm’s cash balance can usually be interpreted as an inventory of money which its holder stands ready to exchange against purchase of labour, raw materials, etc.”
Cash balances are held because income and expenditure do not take place simultaneously. “But it is expensive to tie up large amounts of capital in the form of cash balances. For that money could otherwise be used profitably elsewhere in the firm or it could be invested profitably in securities.”
Thus the alternative to holding cash balances is bonds which earn interest. A firm would always try to keep minimum transactions balances in order to earn maximum interest from its assets. The higher the interest rate on bonds, the lesser the transactions balances which a firm holds.
Baumol assumes that a firm receives V dollars once per time period, say a year, which are spent at a constant rate over the period. It is, therefore, always profitable for the firm to spend idle funds on buying bonds which can be sold when it needs cash for transactions purposes.
The structure of cash for holdings and bond holdings by a firm is shown in Figure 7. Suppose the firm has $ 1,200 which it has to spend every quarter at a constant rate over the year. Out of this, it keeps $ 400 in cash for transactions purposes and buys bonds with the remaining amount of $800.
Half the bonds purchased carry maturity of 1 /3t (4 months) and the other (half) bonds carry maturity of 2/31 (8 months). Further suppose that K is the sum received from the sale of bonds and the firm’s average cash holdings equal half the sum (1 /2K) received from the sale of bonds.
Given these assumptions, the firm buys bonds with 2/3K ($800) of its income at time f=0 and keeps 1/3K ($400) in cash, as shown in the figure. At time 1 /3f, the first half of the bonds purchased ($400) mature which it sells for cash until time 2/3f. At time 2/3f, the remaining bonds mature which the firm sells for transactions purposes until time t1 At time t1 when the year is over, the cash balance is zero and the firm is again ready for fresh receipts in the new year. Now the problem is how to hold assets by a firm, “given that there exist interest-yielding bonds that can be owned as well as cash, and given that there is a fixed cost involved in exchanging bonds for cash.”
The solution of this problem requires minimising the cost of holding cash balances over the year. The holding of cash balances consists of interest cost and non-interest costs. Interest cost is in the nature of opportunity cost because when a firm holds cash balances for transactions purposes it forgoes interest income.
On the other hand, non-interest costs include such items as brokerage fees, mailing expenses, book-keeping expenses, etc. for converting cash into bonds, and vice versa.
Thus whenever a firm holds money for transactions purposes, it incurs interest costs and brokerage fees (non-interest costs). Let r be the rate of interest which is assumed to be constant over the year and b the brokerage fee which is also assumed to be fixed. Assume that at the beginning of the year, Y is the income of the firm which is equal to the real value of the transactions performed by it, and K is the size of each cash withdrawal at intervals over the year when the bonds are sold.
Thus Y/K is the number of withdrawals that occur over the year. The cost on brokerage fees during the year will equal b(Y/K). Since the average cash withdrawal are K/2, the interest cost of holding cash balances is rK/2.
Then the total cost of making transactions, C, may be written in equation form as:
C = r K/2+ b Y/K â€¦. (1)
The optimal value of K is that which minimizes the total inventory cost C. By differentiating C with respect to K, setting the derivative dC/dK equal to zero, and solving for C, we obtain
Equation (2) shows that if the brokerage fee increases, the number of withdrawals will decrease. In other words, the optimal cash balance will increase because the firm will invest less in bonds. On the other hand, if the rate of interest on bonds rises, the firm will find it profitable to invest in bonds and the optimal cash balance will be lower, and vice versa.
Baumol’s analysis points toward another important fact about the behaviour of demand for transactions balances. When a firm or an individual purchases large number of bonds, it is left with small transactions balances and vice versa. But every purchase involves non-interest costs in the form of brokerage fee, mailing, etc. which the purchaser has to pay.
He has, therefore, to balance the income to be forgone by making fewer bond purchases against the expenses to be incurred by making large bond purchases. This decision depends upon the rate of interest on bonds.
The higher the rate of interest, the larger the expenses which a firm can absorb in making bond purchases. A more important factor which determines this decision is the amount of money involved in transactions because brokerage fees of buying and selling bonds are relatively fixed and do not change much in relation to the former. When the money involved in transactions is larger, the smaller will be the brokerage costs. “On a $ 1000 bond purchase, minimum brokerage fees can be costly.
On a million dollar transaction they are negligible. Hence, the larger the total amounts involved, the less significant will be the brokerage costs, and the more frequent will be optimal withdrawals.” This is because of the operation of economies of scale in cash management or use of money.
It implies that at higher levels of income, the average cost of transactions i.e. brokerage fees are lower. As income increases, the transactions demand for money also increases but by less than the increase in income. If income increases fourfold, optimal transactions balances only double.
Since Baumol takes the income elasticity of demand for money to be one-half (1/2), the demand for money will not increase in the same proportion as the increase in income. This is because of the economies of scale that encourage larger investment in bonds when the amount of money involved in transactions is larger due to increase in income.
In this inventory theory of the demand for money, Baumol also emphasises that the demand for money is a demand for real balances. Since the value of average cash holdings over the year is K/2, the demand for real balances for transactions purposes becomes
where MD is the demand for money and P is the price level.
Equation (3) shows that the demand for real transactions balances “is proportional to the square root of the volume of transactions and inversely proportional to the square root of the rate of interest.” It means that the relationship between changes in the price level and the transactions demand for money is direct and proportional. The pattern of a firm’s purchases remaining unchanged, the optimal cash balances (Y) will increase in exactly the same proportion as the price level (P). If the-price level doubles, the money value of the firm’s transactions will also double.
When all prices double, brokerage fee (b) will also double “so that larger cash balances will become desirable in order to avoid investments and withdrawals and the brokerage costs which they incur.” Thus the increase in the money value of transactions and in brokerage fees leads to a rise in the optimal demand for money in exactly the same proportion as the change in the price level. Thus Baumol’s analysis of the demand for real balances implies that there is no money illusion in the demand for money for transactions purposes.
Its Superiority over the Classical and Keynesian Approaches:
Baumol’s inventory theoretic approach to the transactions demand for money is an improvement over the classical and Keynesian approaches.
1. The cash balances quantity theory of money assumed the relationship between the transactions demand and the level of income as linear and proportional. Baumol has shown that this relationship is not accurate. No doubt it is true the transactions demand increases with increase in income but it increases less than proportionately because of the economies of scale in cash management.
2. Baumol’s theory also has the merit of demonstrating the interest elasticity of the transactions demand for money as against the Keynesian view that it is interest inelastic.
3. Baumol analyses the transactions demand for real balances thereby emphasizing the absence of money illusion.
4. Baumol’s inventory theoretic approach is superior to both the classical and Keynesian approaches because it integrates the transactions demand for money with the capital-theory approach by taking assets and their interest and non-interest costs into account.
5. Baumol’s theory removes the dichotomy between transactions and speculative demand for money of the Keynesian approach.
2. Tobin’s Portfolio Selection Model: The Risk Aversion Theory of Liquidity Preference:
James Tobin in his famous article “Liquidity Preference as Behaviour Towards Risk,” formulated the risk aversion theory of liquidity preference based on portfolio selection. This theory removes two major defects of the Keynesian theory of liquidity preference.
One, Keynes’s liquidity preference function depends on the inelasticity of expectations of future interest rates; and two, individuals hold either money or bonds. Tobin has removed both the defects. His theory does not depend on the inelasticity of expectations of future interest rates but proceeds on the assumption that the expected value of capital gains or losses from holding interest- bearing assets is always zero. Moreover, it explains that an individual’s portfolio holds both money and bonds rather than only one at a time.
Tobin starts his portfolio selection model of liquidity preference with this presumption that an individual asset holder has a portfolio of money and bonds. Money neither brings any return nor imposes any risk on him. But bonds yield interest and also bring income.
However, income from bonds is uncertain because it involves a risk of capital losses or gains. The greater the investment in bonds, the greater is the risk of capital loss from them. An investor can bear this risk if he is compensated by an adequate return from bonds.
If g is the expected capital gain or loss, it is assumed that the investor bases his actions on his estimate of its probability distribution. It is further assumed that this probability distribution has an expected value of zero and is independent of the level of the current rate of interest, r, on bonds.
His portfolio consists of a proportion M of Money and B of bonds where both M and Badduptol. They do not have any negative values. The return on portfolio R is R = B (r+g) where O < B < 1
Since g is a random variable with expected value zero, the expected return on the portfolio is
RE = mR =Br.
The risk attached to a portfolio is measured by the standard deviation of R, that is, Ïƒ R-
Tobin describes three types of investors. The first category is of risk lovers who enjoy putting all their wealth into bonds to maximise risk. They accept risk of loss in exchange for the income they accept from bonds. They are like gamblers. The second category is of plungers. They will either put all their wealth into bonds or will keep it in cash. Thus plungers either go all the way, or not at all.
But the majority of investors belong to the third category. They are risk averters or diversifies. Risk averters prefer to avoid the risk of loss which is associated with holding bonds rather than money. They are prepared to bear some additional risk only if they expect to receive some additional return on bonds, provided every increase in risk borne brings with it greater increase in returns.
They will, therefore, diversify their portfolios, and hold both money and bonds. Although money neither brings any return nor any risk, yet it is the most liquid form of assets which can be used for buying bonds any time.
In order to find out risk averter’s preference between risk and expected return, Tobin uses indifference curves having positive slopes indicating that the risk averter demands more expected returns in order to take more risk.
This is illustrated in Figure 8 where the horizontal axis measures risk (sR) and the vertical axis the expected returns (smR). The line or is the budget line of the risk averter. It shows the combinations of risk and expected return on the basis of which he arranges his portfolio of wealth consisting of money and bonds and l2 are indifference curves.
An indifference curve shows that he is indifferent between all pairs of expected return and risk that lie on I1 curve. Points on I2 curve are preferred to those on I1 curve. But the risk averter will achieve an equilibrium position between expected return and risk where his budget line is tangent to the indifference curve. It is point T on the budget line Or and I1 curve.
In the lower portion of the figure, the length of the vertical axis shows the wealth held by the risk averter in his portfolio consisting of money and bonds. The line OC shows risk as proportional to the share of the total portfolio held in bonds. Thus point E on this line drawn as perpendicular from point T determines the portfolio mix of money and bonds. It is OP of bonds shown as B, and PW of money shown as M in the figure.
Thus the risk averter diversifies his total wealth OW by putting partly in bonds and partly keeping in cash. That is why he is called a diversifier. He is not prepared to accept more risk unless he can also expect greater expected return.
However, the risk averter possesses an intrinsic preference for liquidity which can be only offset by higher interest rates. The higher the interest rate, the lower the demand for money, and the higher the incentive to hold more bonds. On the contrary, the lower the interest rate, the higher the demand for money, and the lower the willingness to hold bonds. This is illustrated in Figure 9.
The slope of the budget line increases with the increase in the interest rate. This is shown by the budget line r1 rotating upward to r2 and r3 Consequently, returns increase in relation to risk with increase in the interest rate, and the budget line touches higher indifferences curves.
In Figure 9, budget lines r1 r2 and r3are tangents to I1, I2 and I3 curves at points T1, T2 and T, respectively. These points trace out the optimum portfolio curve, OPC, in the figure which shows that as the tangency points move upward from left to right, both the expected return and risk increase.
These tangency points also determine the portfolio selection of risk averters as shown in the lower portion of Figure 9. When the rate of interest is râ€ž they hold OB, bonds and B1 W money. As the rate of interest increases, from r1 to r2 and r3, risk averters hold successively more bonds OB2 and OB3 and reduce money to B2W and B3W in their portfolios.
The figure also shows that as the rate of interest increases by equal increments from r1, to r2 to r3 risk averters hold bonds by decreasing increments, B2B3<B2B1<OB1. This also means that the demand for money falls by smaller amounts, as the rate of interest increases. This is because the total wealth in the portfolio consists of bonds plus money.
The demand for money curve can thus be drawn on the basis of figure 9. This is depicted in Figure 10 as the Ls curve. The curve shows that when the rate of interest falls from a higher level, there is a smaller increase in the demand for money.
For instance, when the interest rate falls from r10 to r8, the demand for money increases by AB which is smaller than OA. This is because risk averters prefer to hold more bonds than money. But when the rate of interest falls at a lower level from r4 to r2, the increase in the demand for money is much larger. It is CD in Figure 10. This demand for money curve relates to the speculative demand for money and not to the aggregate demand for money.
Its Superiority over Keynesian Theory:
Tobins’ risk aversion theory of portfolio selection is superior to the Keynesian liquidity preference theory of speculative demand for money on the following counts:
First, Tobin’s theory does not depend on inelasticity of expectations of future interest rates, but proceeds from the assumption that the expected value of capital gain or loss from holding interest-bearing assets is always zero. In this respect, Tobin regards his theory as a logically more satisfactory foundation for liquidity preference than the Keynesian theory.
Second, this theory is superior to Keynes’s theory in that it explains that individuals hold diversified portfolios of bonds and money rather than either bonds or money.
Third, like Keynes, Tobin regards the demand for money as closely dependent on interest rates and inversely related to interest rates and his theory provides a basis for liquidity preference.
Fourth, Tobin is more realistic than Keynes in not discussing the perfect elasticity of demand for money (the liquidity trap) at very low rates of interest.
Fifth, according to David Laidler, the real importance of the portfolio theory lies in “not what it tells directly about the aggregate economy, but rather it represents an interesting approach to the problem of relating demand for money to the existence of uncertainty, an approach that probably has scope for considerable development in the future.”
3. Friedman’s Theory of Demand for Money:
Friedman’s theory of demand for money is a capital or wealth theory, because he regards money as an asset or capital good.
For ultimate wealth holders, the demand for money, in real terms, may be expected to be a function primarily of the following variables:
1. Total Wealth:
The total wealth is the analogue of the budget constraint. It is the total that must be divided among various forms of assets. In practice, estimates of total wealth are seldom available. Instead, income may serve as an index of wealth. Thus, according to Friedman, income is a surrogate of wealth.
2. The Division of Wealth between Human and Non-Human Forms:
The major source of wealth is the productive capacity of human beings which is human wealth. But the conversion of human wealth into non- human wealth or the reverse is subject to institutional constraints. This can be done by using current earnings to purchase non-human wealth or by using non-human wealth to finance the acquisition of skills.
Thus the fraction of total wealth in the form of non-human wealth is an additional important variable. Friedman calls the ratio of non-human to human wealth or the ratio of wealth to income as w.
3. The Expected Rates of Return on Money and Other Assets:
These rates of return are the counterparts of the prices of a commodity and its substitutes and complements in the theory of consumer demand. The nominal rate of return may be zero as it generally is on currency, or negative as it sometimes is on demand deposits, subject to net service charges, or positive as it is on demand deposits on which interest is paid, and generally on time deposits.
The nominal rate of return on other assets consists of two parts: first, any currently paid yield or cost, such as interest on bonds, dividends on equities, and costs of storage on physical assets, and second, changes in the prices of these assets which become especially important under conditions of inflation or deflation.
4. Other Variables:
Variables other than income may affect the utility attached to the services of money which determine liquidity proper. Besides liquidity, variables are the tastes and preferences of wealth holders. Another variable is trading in existing capital goods by ultimate wealth holders. These variables also determine the demand function for money along with other forms of wealth. Such variables are noted as u by Friedman.
Broadly, total wealth includes all sources of income or consumable services. It is capitalized income. By income, Friedman means “permanent income” which is the average expected yield on wealth during its life time.
Forms of Wealth:
Wealth can be held in five different forms: money, bonds, equities, physical goods, and human capital. Each form of wealth has a unique characteristic of its own and a different yield.
1. Money is taken in the broadest sense to include currency, demand deposits and time deposits which yield interest on deposits. Thus money is luxury good. It also yields real return in the form of convenience, security, etc. to the holder which is measured in terms of the general price level (P).
2. Bonds are defined as claim to a time stream of payments that are fixed in nominal units.
3. Equities are defined as a claim to a time stream of payments that are fixed in real units.
4. Physical goods or non-human goods are inventories of producer and consumer durables.
5. Human capital is the productive capacity of human beings.
Thus each form of wealth has a unique characteristic of its own and a different yield either explicitly in the form of interest, dividends, labour income, etc., or implicitly in the form of services of money measured in terms of P, and inventories. The present discounted value of these expected income flows from these five forms of wealth constitutes the current value of wealth which can be expressed as:
W = y/r
where W is the current value of total wealth, y is the total flow of expected income from the five forms of wealth, and r is the interest rate. This equation shows that wealth is capitalized income. Friedman in his latest empirical study Monetary Trends in the United States and the United Kingdom (1982) gives the following demand function for money for an individual wealth holder with slightly different notations from his original study of 1956 as:
where M is the total stock of money demanded; P is the price level; Y is the real income; W is the fraction of wealth in non-human form; Rm is the expected nominal rate of return on money; Rb is the expected rate of return on bonds, including expected changes in their prices; Re is the expected nominal rate of return on equities, including expected changes in their prices; gp =(1 /P) (dP/dt) is the expected rate of change of prices of goods and hence the expected nominal rate of return on physical assets; and u stands for variables other than income that u may affect the utility attached to the services of money.
The demand function for business is roughly similar, although the division of total wealth and human wealth is not very useful since a firm can buy and sell in the market place and hire its human wealth at will. But the other factors are important.
The aggregate demand function for money is the summation of individual demand functions with M and y referring to per capita money holdings and per capita real income respectively, and w is the fraction of aggregate wealth in non-human form.
The demand function for money leads to the conclusion that a rise in expected yields on different assets (Rb, Re and) reduces the amount of money demanded by a wealth holder, and that an increase in wealth raises the demand for money. The income to which cash balances (M/P) are adjusted is the expected long-term level of income rather than current income being received.
Empirical evidence suggests that the income elasticity of demand for money is greater than unity which means that income velocity is falling over the long run. This means that the long-run demand for money function is stable and is relatively interest inelastic, as shown in Fig. 11 where MD is the demand for money curve. If there is change in the interest rate, the long-run demand for money is negligible.
Its Superiority over Keynesian Theory:
Friedman’s theory of demand for money is superior to Keynes’ Theory in the following ways:
First, Friedman uses a broader definition of money than that of Keynes in order to explain his demand for money function. He treats money as an asset or capital good capable of serving as a temporary abode of purchasing power. It is held for the stream of income or consumable services which it renders. On the other hand, the Keynesian definition of money consists of demand deposits and non-interest bearing debt of the government.
Second, Friedman postulates a demand for money function quite different from that of Keynes. The demand for money on the part of wealth holders is a function of many variables. These are Rm, the yield on money; Rb, the yield on bonds; Re, the yield on securities; gp, the yield on physical assets; and u referring to other variables. In the Keynesian theory, the demand for money as an asset is confined to just bonds where interest rates are the relevant cost of holding money.
Third, there is also the difference between the monetary mechanisms of Keynes and Friedman as to how changes in the quantity of money affect economic activity. According to Keynes, monetary changes affect economic activity indirectly through bond prices and interest rates. The monetary authorities increase the money supply by purchasing bonds which raises their prices and reduces the yield on them.
Lower yield on bonds induces people to put their money elsewhere, such as investment in new productive capital that will increase output and income. On the other hand, in Friedman’s theory monetary disturbances will directly affect prices and production of all types of goods since people will buy or sell any asset held by them. Friedman emphasises that the market interest rates play only a small part of the total spectrum of rates that are relevant.
Fourth, there is the difference between the two approaches with regard to the motives for holding money balances. Keynes divides money balances into “active” and “idle” categories. The former consist of transactions and precautionary motives, and the latter consist of the speculative motive for holding money.
On the other hand, Friedman makes no such division of money balances. According to him, money is held for a variety of different purposes which determine the total volume of assets held such as money, physical assets, total wealth, human wealth, and general preferences, tastes and anticipations.
Fifth, in his analysis, Friedman introduces permanent income and nominal income to explain his theory. Permanent income is the amount a wealth holder can consume while maintaining his wealth intact. Nominal income is measured in the prevailing units of currency. It depends on both prices and quantities of goods traded. Keynes, on the other hand, does not make such a distinction.