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Thanks for this wonderful article. These kinds of changes in focusing length are usually reflected within the viewfinder and on massive display screen right at the back of your camera. It containsconsists ofincludescarries nicepleasantgoodfastidious stuffinformationdatamaterial. If prices and income are free to change, the attempt to spend more will raise the nominal volume of expenditures and receipts, which will lead to a bidding up of prices and perhaps also to an increase in output.
The initial excess of money balances will therefore tend to be eliminated, even though there is no change in the nominal quantity, by either a reduction in the real quantity held through price rises or an increase in the real quantity desired through output increases. Conversely, if nominal balances happen to correspond to a smaller real quantity at current prices than people wish to hold, people will seek to spend less than they are receiving.
They cannot in the aggregate do so. But their attempt will in the process lower nominal expenditures and receipts, driving down prices or output and either raising the real balances held or lowering the real balances desired. It is clear from this discussion that changes in prices and nominal income can be produced either by changes in the real balances that people wish to hold or by changes in the nominal balances available for them to hold.
Indeed it is a tautology, summarized in the famous quantity equation to which we shall return that all changes in nominal income can be attributed to one or the other—just as a change in the price of any good can always be attributed to a change in either demand or supply.
The quantity theory is not, however, this tautology. It is, rather, the empirical generalization that changes in desired real balances in the demand for money tend to proceed slowly and gradually or to be the result of events set in train by prior changes in supply, whereas, in contrast, substantial changes in the supply of nominal balances can and frequently do occur independently of any changes in demand.
The conclusion is that substantial changes in prices or nominal income are almost invariably the result of changes in the nominal supply of money. Variants of the quantity theory of money are distinguished by the variables that are regarded as most important in determining the real quantity of money that people desire to hold and by the analysis of the process whereby any discrepancy between actual and desired real balances works itself out.
The chief issues that have occasioned controversy and conflict are perhaps the definition of money, the importance of transactions motives versus asset motives in the holding of money, the importance of substitution between money and other assets expressed in nominal terms as compared with substitution between money and real goods and services, and the speed and character of the dynamic process of adjustment.
We shall have occasion to comment on these below. Every payment made by one economic unit in an economy—household, business enterprise, or governmental organization—to another can be regarded as the product of a price and a quantity: Let P be a suitably chosen average of the prices, and let T be a suitably chosen aggregate of the quantities.
The total volume of transactions can also be viewed in terms of the medium of exchange used to effectuate them. Let M be the total quantity of money in the economy and V the average number of times each unit of money is used to effectuate a transaction during the year the transactions velocity. Each side of this equation can be broken into subcategories: Fisher and later writers emphasized in particular the subdivision of the left-hand side into two categories of payments, those effected by the transfer of hand-to-hand currency including coin and those effected by the transfer of deposits.
We then can write. As they stand, equations 3 and 4 are identities: If P changes from one time period to the next, then so must one or more of the other terms in the equations. That is an arithmetic necessity, not an economic proposition. The identities are useful for economic analysis because they offer a useful classification of the factors at work, a classification into categories each of which contains factors largely independent of those in the other categories.
The physical volume of transactions is denoted by T. It is determined by the resources available to the economy, the efficiency with which they are used, the degree of integration or disintegration of the economy which determines the number of transactions involved in the production and sale of final goods , and so on.
These are the basic physical and operational characteristics of the economy. All quantity theorists, at least since Hume, have recognized that changes in the stock of money may have transitional effects on T. However, they have generally regarded the average level of T and long-run changes in T as largely independent of the quantity of money, although not of the existence of a money economy. The price level, which is the object of investigation, is denoted by P.
It has generally been regarded as the resultant of other forces rather than as itself having any important element of autonomy. Cost-push or profit-push theories of inflation treat it as being to some extent independently determined.
Under a regime of widespread government price fixing, it clearly does have some measure of autonomy. The stock of money in nominal units is denoted by M. Its precise definition, as noted before, has been the subject of much controversy.
The transactions approach makes it seem natural to define money in terms of its function as a medium of exchange and to include only those means of payments generally acceptable in discharge of debts. Under a gold standard, specie was regarded as money par excellence, and questions were raised about extending the definition to include paper money and then demand deposits transferable by check.
Today these would generally be included in the definitions, but there is much controversy about the treatment of other deposits, such as time deposits and savings deposits. On transactions lines, it is argued that such deposits cannot be used to discharge debts without first being converted into either currency or demand deposits.
One answer to this argument is that it is also true of some items that all are willing to regard as money. Such a currency note can be used to effectuate few transactions without first being converted into smaller denominations. No issue of principle is involved. However M is defined, equation 3 remains valid, provided V is appropriately defined.
The issue is one of the usefulness of one or another definition: Whatever the precise definition of M , the factors determining it depend critically on the monetary system and are largely independent of the forces determining T. Two main cases should be distinguished: Under a gold standard the amount of money in the gold standard world is determined by the total existing amount of gold, the fraction used as money, and the institutional arrangements determining the superstructure of claims to gold, in the form of currency or deposits, that can be erected on any given stock of gold.
Changes in the amount of money depend on costs of producing various quantities of gold, the demand for gold for non-monetary purposes, and the financial arrangements for issuing fiduciary claims to gold. For any one country the situation is somewhat different: It must be whatever quantity is consistent with levels of prices and incomes that will maintain balance in its international payments. Gold inflows or outflows tend to keep it at that quantity. Under a fiduciary standard the amount of money is ultimately under the control of the monetary authorities.
In practice these authorities have always been governmental agencies. Although they have had the power to control the stock of money, they frequently have not stated their objectives in these terms but have let the stock of money be whatever was consistent with some alternative objective e.
Under either the gold or the fiduciary standard the factors determining M are connected only loosely, if at all, with those we have considered as affecting directly either P or T. It is precisely this clearly perceived independence of the factors determining the quantity of money that has rendered the quantity theory so attractive to economists.
We now come to V , the velocity of circulation. This is the core of the quantity theory. It is determined by whatever factors affect, on the one hand, the amount of money people want to hold and, on the other, their ability to make their actual money balances equal their desired balances.
The transactions approach makes it natural to emphasize payment practices: However, such payment practices themselves seem to be largely explained by the willingness of people to hold money. For example, during periods of rapid inflation, when it is costly to hold money, pay periods consistently tend to become more frequent. It is convenient to postpone a fuller consideration of the factors determining velocity until we discuss the post-Keynesian formulation in terms of the demand for money.
Here it suffices to point out that Fisher and other earlier quantity theorists explicitly recognized that velocity would be affected by, among other factors, the rate of interest and also the rate of change of prices. They recognized that both high rates of interest and rapidly rising prices would give people an incentive to economize on money balances and so tend to raise velocity and that low rates of interest and falling prices would have the opposite effect.
They were never guilty of the crude fallacy—with which critics have often charged them—of regarding velocity as something of a natural constant. Despite the large amount of empirical work done on these equations, notably by Fisher and Carl Snyder, these ambiguities and deficiencies of data have never been satisfactorily resolved.
Should capital transfers, such as purchases and sales of real estate and securities, be included? What is the relevant price and quantity in these transactions? As noted before, the data on volume of transactions have been satisfactory only for transactions effected by check. For these, debits to bank accounts or bank clearings provide a statistically reliable total, although even then there are problems involved in separating out money-changing transactions.
However, even for check transactions, there is no satisfactory way to break down the other side of the equation into price and quantity components. With the development of national or social accounting, which has stressed income transactions rather than gross transactions and which has explicitly and satisfactorily dealt with the conceptual and statistical problems of distinguishing between changes in prices and changes in quantities, there has been a tendency to express the quantity equation in terms of income rather than of transactions.
Let Y be money national income, P the price index implicit in estimating national income at constant prices, and y national income in constant prices, so that. Let M represent, as before, the stock of money, but define V as the average number of times per year that the money stock is used in making income transactions that is, payments for final productive services rather than all transactions.
We then can write the quantity equation in income form as. Although the symbols P and V are used both in eqs. Equation 6 is both conceptually and empirically more satisfactory than equation 3.
Nonetheless, the earlier discussion of the fourfold classification implicit in the quantity equation applies, except for changes that are nearly self-evident, such as the very different relevance for y than for T of the degree of integration or disintegration of industry. Equation 6 is also closer in conception to the Cambridge approach, to which we now turn.
The essential feature of a money economy is that it enables the act of purchase to be separated from the act of sale. An individual who has something to exchange need not seek out the double coincidence—someone who both wants what he has and offers in exchange what he wants. He need only find someone who wants what he has, sell it to him for general purchasing power, and then find someone else who has what he wants and buy it with general purchasing power.
In order for the act of purchase to be separated from the act of sale, there must be something which can serve as a temporary abode of purchasing power in the interim. It is this aspect of money which is emphasized in the cash-balances approach.
How much money will people or enterprises want to hold for this purpose? We then add up the cash balances held by all holders of money in the community and express the total as a fraction of their total income. We can then write. In either case, k is clearly equal numerically to the reciprocal of the V of equation 6 , the V in one case being interpreted as measured velocity and in the other as desired velocity.
Most writers who have used one of the two approaches regarded them in this way and tended to cover much the same ground. Yet to a far greater extent than is reflected in the writings of the early expositors, the two approaches stress different aspects of money, make different definitions of money seem natural, and lead to emphasis being placed on different variables and analytical techniques.
Consider the definition of money. The transactions approach makes it natural to define money in terms of whatever serves as the medium of exchange in discharging obligations. By stressing the function of money as a temporary abode of purchasing power the cash-balances approach makes it seem entirely appropriate to include also such stores of value as demand and time deposits not transferable by check, although it clearly does not require their inclusion.
Similarly, the transactions approach leads to stress being placed on such variables as payments practices, the financial and economic arrangements for effecting transactions, and the speed of communication and transportation as it affects the time required to make a payment—essentially, that is, to emphasis on the mechanical aspects of the payments process.
The cash-balances approach, on the other hand, leads to stress being placed on variables affecting the usefulness of money as an asset: Stress on the first set of variables led most early writers—both those using the Fisher equation and those using the Cambridge equation—to predict that velocity would increase over time as a result of technological improvements in transportation and communication, which would facilitate the payments process. In fact, velocity has shown no tendency to rise over time.
If anything it has rather tended to decline in economically progressive countries along with rises in real income, although this tendency is less pronounced when money is defined narrowly than when it is defined to include some deposits not transferable by check. Finally, with regard to analytical techniques, the cash-balances approach fits in much more readily with the general Marshallian demand—supply apparatus than the transactions approach does.
Equation 7 can be regarded as a demand function for money, with P and y on the right-hand side being two of the variables on which demand for money depends, and with k symbolizing all the other variables, so that k is to be regarded not as a numerical constant but as itself a function of still other variables.
For completion the analysis requires another equation showing the supply of money as a function of other variables. The price level is then the resultant of the interaction of the demand and supply functions. From this point of view the quantity theory of money as embodied in equation 7 is a theory of the demand for money, not a theory of the price level or of money income.
The Keynesian income—expenditure analysis developed in the General Theory of Employment, Interest and Money offered an alternative approach to the interpretation of changes in money income that emphasized the relation between money income and investment or autonomous expenditures rather than the relation between money income and the stock of money. The success of the Keynesian revolution in economic thought led to a temporary eclipse of the quantity theory of money and to perhaps an all-time low in the amount of economic research and writing devoted to monetary theory and analysis, narrowly interpreted.
It became a widely accepted view that money does not matter, or, at any rate, that it does not matter very much, and that policy and theory alike should concentrate on investment, government fiscal policy, and the relation between consumer expenditures and income.
Keynes did not, of course, deny the validity of the quantity equation. What he did was something very different. He argued that under conditions of underemployment equilibrium the V in equation 6 and the k in equation 7 were highly unstable and would, for the most part, passively adapt to whatever changes independently occurred in money income or the stock of money. Hence, under such conditions these equations, although entirely valid, were largely useless for policy or prediction.
Moreover, he regarded such conditions as prevailing much, if not most, of the time. Keynes reached this conclusion by giving a highly specific form to equation 7. He regarded M 1 as a roughly constant fraction of income. Keynes, of course, emphasized that there was a whole complex of interest rates. Although expectations are given great prominence in developing the liquidity function expressing the demand for M 2 , they do not enter explicitly into that function.
For the most part, Keynes and his followers in practice treated the amount of M 2 demanded simply as a function of the current interest rate, the emphasis on expectations serving only as a reason for their attribution of instability to the liquidity function. Except for somewhat different language, the analysis up to this point differs from that of earlier quantity theorists, such as Fisher, only by its subtle analysis of the role of expectations about future interest rates and its greater emphasis on current interest rates and by restricting more narrowly the variables explicitly considered as affecting the amount of money demanded.
Let the interest rate fall sufficiently low, he argued, and money and bonds would become perfect substitutes for one another; liquidity preference, as he put it, would become absolute.
The liquidity-preference function, expressing the quantity of M 2 demanded as a function of the rate of interest, would become horizontal at some low but finite rate of interest. Under such circumstances, he held, if the amount of money is increased by whatever means, the holders of money might seek to convert the additional cash balances into bonds.
This would, however, tend to lower the rate of return on bonds. Even the slightest lowering would, he argued, lead holders of money to desist from trying to convert it into bonds.
The result would simply be that people would be willing to hold the increased quantity of money; k would be higher and V lower. Conversely, if the amount of money were decreased, holders of bonds would seek to convert them into money, but this would tend to raise the rate of interest, and even the slightest rise would reconcile them to holding the bonds instead of the money. Or, again, suppose there is an increase in money income for whatever reason. That will require an increase in M 1 , which can come out of M 2 , without any further effects.
Conversely, any decline in M 1 , can be added to M 2 , without any further effects. The conclusion is that under circumstances of absolute liquidity preference income can change without a change in M and M can change without a change in income.
The holders of money are in metastable equilibrium, like a tumbler on its side on a flat surface; they will be satisfied with what-ever the amount of money happens to be.
But, since he regarded interest rates as frequently being not far above the level at which liquidity preference would become absolute, he treated velocity as if in practice its behavior frequently approximated that which would prevail in this limiting case. They were readier than he was to accept absolute liquidity preference as the actual state of affairs. More important, many argued that when liquidity preference was not absolute, changes in the quantity of money would affect only the interest rate on bonds and that changes in this interest rate in turn would have little further effect.
They argued that both consumption expenditures and investment expenditures were nearly completely insensitive to changes in interest rates, so that a change in M would merely be offset by an opposite and compensatory change in V or a change in the same direction in k , leaving P and y almost completely unaffected. In essence their argument consists in asserting that only paper securities are substitutes for money balances—that real assets never are see Tobin The issues raised for the quantity theory by the Keynesian analysis are clearly empirical rather than theoretical.
Is it a fact that the quantity of money demanded is a function primarily of current income and of the rate of interest on fixed-money-value securities?
Is it a fact that the amount demanded is highly elastic with respect to the rate of interest on such securities at a low but finite rate of interest? Is it a fact that expenditures are highly inelastic with respect to such a rate of interest? Or, to put the issue in an equivalent but more readily observable form, is it a fact that velocity is a highly unstable and unpredictable magnitude that generally varies in a direction opposite to that of the quantity of money?
Experience with monetary policy after World War II very quickly produced a renewed interest in money and a renewed belief that money matters. Under the influence of Keynesian ideas, country after country followed an easy-money policy designed to keep interest rates low in order to stimulate, if only slightly, the investment regarded as needed to offset the shortage of demand that was universally feared.
The result was an intensification of the strong inflationary pressure inherited from the war, a pressure that was brought under control only when countries undertook so-called orthodox measures to restrain the growth in the stock of money, as in Italy, beginning in August , in Germany in June , in the United States in March , in Great Britain in November , and in France in January The effect of experience was reinforced by developments in economic theory, especially by the explicit analysis of the so-called real-balance effect as a channel through which changes in prices and in the quantity of money could affect income, even when investment and consumption were insensitive to changes in interest rates or when absolute liquidity preference prevented changes in interest rates see Haberler ; Tobin ; Pigou ; ; Patinkin Many economists continue to use Keynesian analysis but have revised their empirical presumptions.
They grant that liquidity preference is not absolute and that investment does have a sizable elasticity with respect to interest rates. They continue, however, to regard analysis in terms of the quantity equation as less useful and meaningful than analysis in terms of autonomous expenditures and the multiplier, with monetary changes being taken into account as one factor among many that can affect these magnitudes. The postwar period has also seen a return to analysis in terms of the quantity equation accompanied by a reformulation of the quantity theory that has been strongly affected by the Keynesian analysis of liquidity preference Johnson The reformulation emphasizes the role of money as an asset and hence treats the demand for money as part of capital or wealth theory, concerned with the composition of the balance sheet or portfolio of assets.
For ultimate wealth-holders the demand for money, in real terms, may be expected to be a function of the following variables. This is the analogue of the budget constraint in the usual theory of consumer choice.
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. However, it should be recognized that income as measured by statisticians may be a defective index of wealth because it is subject to erratic year-to-year fluctuations and that a longer term concept, like the concept of permanent income developed in connection with the theory of consumption, may be more useful.
Friedman ; , p. The major asset of most wealth-holders is their personal earning capacity, but the conversion of human into nonhuman wealth or the reverse is subject to narrow limits because of institutional constraints. It can be done by using current earnings to purchase nonhuman wealth or by using nonhuman wealth to finance the acquisition of skills but not by purchase or sale and to only a limited extent by borrowing on the collateral of earning power.
Hence, the fraction of total wealth that is in the form of nonhuman wealth may be an additional important variable. This is the analogue of the prices of a commodity and its substitutes and complements in the usual theory of consumer demand. The nominal rate of return on money may be zero, as it generally is on currency, or negative, as it some-times is on demand deposits subject to net service charges, or positive, as it sometimes is on demand deposits on which interest is paid and generally is 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 storage costs on physical assets, and, second, changes in their nominal prices.
The second part will, of course, be especially important under conditions of inflation or deflation. Another variable, one that is likely to be important empirically, is the degree of economic stability expected to prevail in the future. Wealth-holders are likely to attach considerably more value to liquidity when they expect economic conditions to be unstable than when they expect them to be highly stable.
This variable is likely to be difficult to express quantitatively even though the direction of change may be clear from qualitative information.
For example, the outbreak of war clearly produces expectations of instability, which is one reason why war is often accompanied by a notable increase in real balances—that is, a notable decline in velocity.
We can symbolize this analysis in terms of the following demand function for money for an individual wealth-holder:. Each of the four rates of return stands, of course, for a set of rates of return, and for some purposes it may be important to classify assets still more finely—for example, to distinguish currency from deposits, long-term from short-term fixed-value securities, risky from relatively safe equities, and different kinds of physical assets from one another.
The usual problems of aggregation arise in passing from equation 8 to a corresponding equation for the economy as a whole—in particular, they arise from the possibility that the amount of money demanded may depend on the distribution of such variables as y and w and not merely on their aggregate or average value.
If we neglect these distributional effects, 8 can be regarded as applying to the community as a whole, with M and y referring to per capita money holdings and per capita real income, respectively, and w to the fraction of aggregate wealth in nonhuman form.
The major problems that arise in practice in applying 8 are the precise definitions of y and w , the estimation of expected rates of return as contrasted with actual rates of return, and the quantitative specification of the variables designated by u. Business enterprises are not subject to a constraint comparable to that imposed by the total wealth of the ultimate wealth-holder. The total amount of capital embodied in productive assets, including money, is a variable that can be determined by the enterprise to maximize returns, since it can acquire additional capital through the capital market.
Hence, there is no reason on this ground to include total wealth, or y as a surrogate for total wealth, as a variable in their demand function for money. It is by no means clear what the appropriate variable is: The lack of availability of data has meant that much less empirical work has been done on the business demand for money than on an aggregate demand curve encompassing both ultimate wealth-holders and business enterprises.
As a result there are as yet only faint indications about the best variable to use. The division of wealth between human and non-human form has no special relevance to business enterprises, since they are likely to buy the services of both forms on the market. Rates of return on money and on alternative assets are, of course, highly relevant to business enterprises. These rates determine the net cost to them of holding the money balances.
However, the particular rates that are relevant may be quite different from those that are relevant for ultimate wealth-holders. For example, rates charged by banks on loans are of minor importance for wealth-holders yet may be extremely important for businesses, since bank loans may be a way in which they can acquire the capital embodied in money balances. The counterpart for business enterprises of the variable u in 8 is the set of variables other than scale affecting the productivity of money balances.
At least one of these—namely, expectations about economic stability—is likely to be common to business enterprises and ultimate wealth-holders. With these interpretations of the variables, equation 8 , with w excluded, can be regarded as symbolizing the business demand for money and, as it stands, symbolizing aggregate demand for money, although with even more serious qualifications about the ambiguities introduced by aggregation.
Emphasis on the role of money as a component of wealth is important because of the variables to which it directs attention. It is important also for its implications about the process of adjustment to a difference between actual and desired stocks of money. Any such discrepancy is a disturbance in a balance sheet. As such it can be corrected in either of two ways: The Keynesian liquidity-preference analysis stressed the first and, in its most rigid form, only one specific rearrangement: The earlier quantity theory stressed the second to the almost complete exclusion of the first.
The reformulation enforces consideration of both. The process of adjustment is important in particular for its implications about the time that readjustment may be expected to take. Balance-sheet adjustments can in general be expected to take considerable time, especially when they take the form of adjustments through alterations in flows and especially when they concern the money balance, M , whose function is precisely that of serving as a temporary abode of purchasing power, thereby permitting purchases to be separated from sales.
It is plausible that any widespread disturbance in money balances—through, say, an unanticipated increase or decrease in the quantity of money by the actions of monetary authorities—will initially be met by an attempted readjustment of assets and liabilities through purchase or sale.
But such attempted readjustments will alter the prices of assets and liabilities, leading to the spread of the adjustment from one asset or liability to another. Such changes in prices will also alter the relative prices of capital items and the services they yield and so establish incentives to alter flows of receipts and expenditures.
If the monetary change has altered the total nominal value of wealth, not simply its composition, this will introduce an additional reason to change flows. The effect of any monetary disturbance will thus spread in ever-widening ripples, and some of its most important effects may not be manifest for many months after the initial disturbance. Empirical evidence about the relation between changes in the quantity of money and in prices, although it was sufficiently extensive to produce a widespread belief in the quantity theory, has seldom been systematically collated and organized.
Until modern times, money was mostly metallic—copper, brass, silver, gold. The most notable changes in its nominal quantity under such circumstances were produced by sweating and clipping, by governmental edicts changing the nominal values attached to specified physical quantities of the metal, or by great discoveries of new sources of specie.
Economic history is replete with examples of the first two and their coincidence with corresponding changes in nominal prices see Cipolla ; Feavearyear The most important example of the third is the great specie discoveries in the New World in the sixteenth century.
The association between this increase in the quantity of money and the price revolution of the sixteenth and seventeenth centuries has been well documented see Hamilton The nineteenth and early twentieth centuries offer another striking example, despite the much greater development of deposit money and paper money.
The gold discoveries in Australia and the United States in the s were followed by substantial price rises in the s. When the rate of growth of the gold stock slowed down, and especially when country after country shifted from silver to gold Germany in , the Latin Monetary Union in , the Netherlands in or returned to gold the United States in , world prices in terms of gold fell slowly but fairly steadily for about three decades.
New gold discoveries in the s and s, powerfully rein-forced by the development of improved methods of mining and refining, particularly the development of commercially feasible methods of using the cyanide process to extract gold from low-grade ore, reversed the trend.
The world gold stock started to grow at a much more rapid rate, and no additional important countries shifted to gold, so there was no increase in demand from this source. The price trend also reversed itself. From the mids to , world prices in terms of gold rose by 25 to 50 per cent, depending on the index used.
Evidence from great inflations. The most dramatic evidence about the role of the quantity of money comes from periods of great monetary disturbances, and among these the most striking are the periods of extremely rapid price rise, such as the hyperinflations after World War I in Germany, Austria, and Russia, those after World War II in Hungary and Greece, and the rapid rises, if not hyperinflations, in many South American and some other countries both before and after World War II.
These twentieth-century episodes have been rather more systematically studied than earlier ones. The studies demonstrate almost conclusively the critical role of changes in the quantity of money the most important study is Cagan These studies also enable us to sketch with considerable accuracy a rather typical profile of an inflation that follows a period of fairly stable prices.
The inflation often has its start in a period of war, but it need not.
Currency in circulation tended to be used only as one of several media of exchange in illegal market deals and as a supplement to the ration ticket in transactions at authorized prices. Money as ordinarily defined consists of elements paper currency and checking deposits which yield no money income, while nonmonetary liquid assets do yield such income.
Thus, changes in aggregate velocity reflect either changes in the weights of sectors or changes in sector velocities. Acceptance of the quantity theory clearly means that the stock of money is a key variable in policies directed at the control of the level of prices or of money income.