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Liquidity Preference and Loanable Funds : Stock and Flow Analysis

1958; Wiley; Volume: 25; Issue: 100 Linguagem: Inglês

10.1111/ecca.1958.25.100.300

1468-0335

Don Patinkin,

Political Economy and Marxism

Despite Hicks’ demonstration nearly twenty years ago of the equivalence between liquidity-preference and loanable-funds theories of interest, the debate on this issue continues to fill the pages of the journals. Indeed, on this issue the 1950's have seen a revival of the polemics of the 1930's. It is not my purpose here to provide a systematic survey of this revival. Instead I shall restrict myself to two arguments that have been advanced in implicit or explicit rebuttal of Hicks’ demonstration—and will show why they are invalid. The first argument bases itself on the distinction between stock and flow analysis —and will be discussed in Section 1. The second bases itself on the distinction between static and dynamic analysis—and this will be discussed in Section 2.2 The argument of both these sections is carried out on the assumption of full employment ; a generalization—under certain assumptions—to the case of unemployment is presented in Section 3. (a) Consider an economy with n goods, consisting of n-2 commodities (inclusive of services), bonds (perpetuities), and money. In the corresponding system of n excess-demand equations, one of the equations is redundant and can be eliminated—that is, if any n-1 excess-demand equations are satisfied, the remaining one must also be satisfied. This will be called Walras’ Law. (b) It follows that a general-equilibrium analysis of the commodity and bond markets yields exactly the same equilibrium rate of interest as that yielded by an analysis of the commodity and money markets. (a) The following classification system is adopted : A theory which chooses to eliminate the money equation and to determine the rate of interest in the commodity and bond markets is called a “ loanable-funds theory “ ; and one which chooses to eliminate the bond equation and to determine the rate in the commodity and money markets, a “ liquidity-preference theory “. (b) By Proposition 1 (b), the loanable-funds theory is equivalent to the liquidity-preference theory. I have restated Hicks’ argument in this over-elaborate way in order to place in proper perspective the oft-repeated Lerner quip : “ And what kind of an interest theory do we have if we eliminate the equation for peanuts ? “ This is a well taken criticism of part of the foregoing statement. In more dignified terms, Lerner's quip demonstrates the inadequacy and incompleteness of the classificatory system of Proposition 2 (a). It shows that this system does not tell us how to classify a theory which retains both the bond and money equations, and drops instead one of the commodity equations. But the proper inference to be drawn from this fact is not that the whole Hicksian approach is wrong—which is the kind of inference we sometimes find in the literature’—but simply that we should get rid of its classificatory system. In other words, we should dispense with Proposition 2, while retaining Proposition 1. Indeed, a full understanding of Proposition 1 leads to the conclusion that it is meaningless to classify interest theories by the nature of the equation chosen for elimination. For by the very nature of Walras’ Law it can make no difference which of the n equations is so eliminated. Every one of the possible subsets of n-1 equations is equivalent—for each is equivalent to the full set of n equations written in such a way as to make the equational dependence explicit. Hence it is meaningless to attempt to associate these different subsets with different theories. In brief, from this viewpoint there is only one theory of interest—or, for that matter, of any other economic variable : the general-equilibrium theory represented by the full set of n equations. So much for Proposition 2. Let us now turn to Proposition 1. In order to evaluate some recent criticisms of this proposition, it is best to repeat briefly one possible demonstration of it.2 For simplicity—and without affecting the general validity of the demonstration—we can consider the case of an exchange economy operating on Hicksian weeks. Any individual will, at the beginning of any given week, be making plans for his expenditures on and receipts from commodities, for his borrowing and lending activities, and for his money holdings at the end of the week. Let us designate by “ demand for money flow “ the amount of money which the individual plans to receive during the week in these various ways, and by “ supply of money flow,” the amount he plans to spend. Then for any individual the following budget relationships obtain : Obviously, for any given individual, at most one of the items b or 1 can be positive, while the other must be zero—though, of course, both can be zero. The same statement holds for items r and p. where Fd, Fs, D, … are the aggregate counterparts of fd, fs, d, … Now, since we are assuming the economy to be closed and without a government, every perpetuity held by one member of the economy represents a debt outstanding of another. Hence total interest receipts, R, must always equal total interest payments, P - so that the last parenthetical term of (3) must be zero no matter what prices and interest rate prevail in the economy. This is not true for the terms S − D and B − L. Only at the set of prices and interest rate which equilibrates the commodity and bond markets, respectively, will these equal zero. It follows immediately from equation (3) that at this set of prices Fd − Fs must also equal zero, so that the demand and supply for money flows must also be in equilibrium. Alternatively, if the money and commodity markets are in equilibrium, then it follows from (3) that the bond market must be in equilibrium. In this way we have demonstrated Proposition 1 : that it makes no difference for our equilibrium analysis whether we treat the money or bond equation as redundant. Correspondingly, if we insist on classifying theories as “ loanable funds “ or “ liquidity preference “ according to the equation “ dropped “ (though the irrelevance of this classification has been demonstrated above), then we have demonstrated the equivalence of these two theories. The validity of this demonstration has recently been challenged on the grounds that it uses “ demand for money “ and “ supply of money ” in the sense of flows, whereas the Keynesian liquidity preference theory uses them in the sense of stocks—and that these two will not be equal in magnitude “ unless the period of time over which the flows of money expenditures are measured is so defined as to make them equal “.1 Correspondingly, it is claimed, all equation (3) demonstrates is that the demand and supply for money flows must be equal (when the bond and commodity markets are in equilibrium) ; it does not demonstrate this equality for the demand and supply for money stocks. This, however, is a non sequitur. True, the demand for money as a flow is quite different from the demand for money as a stock ; in fact, they do not even have the same dimensions ! Nevertheless, the excess demand for money as a flow is identical with the excess demand for money as a stock. And since for the determination of the rate of interest it is only the system of excess-demand equations which is relevant, the difference between the demand functions is completely immaterial. This conclusion can be readily proven. Indeed, it is the direct implication of the simple accounting identity that the stock at the end of a period must equal the stock at the beginning plus the net inflow during the period. In order to show this let us return to our simple exchange economy and analyze the budget restraint of a representative individual from a slightly different viewpoint. Let md represent the individual's demand for cash balances at the end of the period—that is, his planned holdings of money at that time. Similarly, let m0 represent his initial money holdings—the quantity of money with which he began this week. Then the foregoing accounting identity states : (4) md = m0 + (s − d) + (b − 1) + (r − p), where the three parenthetical terms represent the planned net inflows of cash from commodity, borrowing, and interest transactions, respectively. Transposing m0 and aggregating over all individuals, this becomes the budget restraint for the economy as a whole (5) Md − M0= (S − D) + (B − L) + (R − P). As before, R − P is zero no matter what prices and interest prevail in the economy. We now note that the right-hand side of (5) is identical with the right-hand side of (3). Hence the left-hand sides must also be identical. But the left-hand side is nothing else but the excess demand for money considered as a stock. For M0 is the total amount of money actually existing in the economy—and hence is the aggregate supply of money in the sense of a stock—while Md is the total stock of money demanded. We also note that the excess demand for money as a stock has the dimensions of a flow. For it is the difference between the stock of money at two points of time : the end and beginning of the week, respectively. This is as it should be. For this excess demand can then be properly equated—as in equation (5)—to the flows of money payments during the week. Furthermore, it can readily be shown that this relationship holds even after we drop the simplifying assumption that the quantity of money in existence at the end of the week equals that at the beginning—and permit the existence of a monetary authority which can change the stock of money during the course of the week.1 To summarize, though the flow demand Fd is entirely different from the stock demand Md, and though Fs is different from M0, the excess demands Fd – Fs and Md – M0 are identical. Hence any set of prices and interest which equilibrates the money market when viewed as consisting of flows, must also equilibrate it when viewed as stocks, and vice versa. In so far as equilibrium analysis is concerned, no difference can arise from this difference in viewpoints. All this is capable of a direct, common-sense, and even obvious interpretation. Consider our individual possessed of a certain quantity of money on Monday morning and making his plans then for (among other things) the amount of money he wants to have in his possession next Sunday night. If at a certain set of prices and interest rate he decides to hold a stock of money next Sunday night which is PM dollars greater than his initial stock, then he has by that very fact decided to arrange his purchases and sales during the week so as to provide a net inflow of ΔM dollars. There is no other way of affecting the level of a stock than by affecting the net inflow which accrues to that stock. Hence a decision on a stock implies a consistent decision on the corresponding flow, and vice versa. In other words, an individual can be satisfied with the level of his planned stock at the end of the week if and only if he is satisfied with his planned net inflow during the week. It should also be clear that though we have above analyzed the bond market in terms of the demand and supply for flows (lending and borrowing), we could just as well have carried out the analysis in terms of the demand and supply for the stocks of perpetuities. In particular, let C0 represent the initial number of perpetuities held by creditors. By the assumption of a closed economy, this is also the number of debtors’ perpetuities outstanding. The creditors’ demand for the stock of perpetuities at the end of the week (Cd) is accordingly (6) Cd = C0 + L, while the supply is (7) Cs = C0 + B. Subtracting (7) from (6) we obtain (8) Cd – Cs = L – B. Thus the excess demand in the bond market considered from the viewpoint of stocks must necessarily equal the excess demand considered from the viewpoint of flows.1 In this way we also see that the choice between the money and bond equations has nothing at all to do with the choice between stock and flow analysis. Either of these equations can be—with equivalent results—analyzed from either analytical viewpoint. At this point I would like to venture the suggestion that all of economic analysis is really concerned with flows and not stocks. For there are two possibilities : either the stock is immutably fixed—and always has been so—in which case there is nothing to analyze ; or the stock is subject to variation—in which case this variation constitutes a flow which can be analyzed as such. This and the preceding discussion should point out the non sequitur in the contention sometimes advanced that only stock analysis is appropriate for those economic goods whose existing stock is very great in comparison with current production. Clearly, the analysis of any such good can be carried out just as well in terms of the flow of current production—though in this analysis the existing stock will obviously be one of the factors that must be taken into consideration. Even the level of the mighty ocean is analyzed in terms of the relatively puny variations in the inflows and outflows of water due to climatic factors. I would also like to conjecture that there have been more errors of omission in connection with stock and flow analysis than errors of commission : more valid propositions which were stillborn because of unnecessary inhibitions about using “ stock “ and “ flow “ in the same sentence, than invalid propositions which went afoul on the improper combination of these terms. In a certain sense this is a very safe— because unverifiable—conjecture : for there is no record of the unuttered propositions. But I do think I am referring here to a real phenomenon. Thus, for example, we sometimes encounter completely unfounded fears about writing functions which depend on both a stock and a flow. The baselessness of such fears is sufficiently established by our simple accounting identity (4) above—which states that the stock at the end of a period equals the stock at the beginning of the period plus the net flow during the period. There is obviously nothing illegitimate about this functional relationship. Similarly, there is no logical reason why we should hesitate to say that a firm's supply of a given commodity during a given period depends on the flow of raw materials purchased during that period as well as on the stock available at the beginning. Nor, finally, should we hesitate to say that the demand function for any given commodity depends on the flow of income during the period in question as well as on the stock of asset holdings at its beginning. Before concluding this part of the paper, I should like to restate its general argument in the following way : Stock analysis, as well as flow analysis, presupposes a period of time : namely the period between the moment at which the individual is making his plans, and the moment for which he is making them. Hence if the periods presupposed by the analyses are the same, the excess-demand function of stock analysis must be identical with that of flow analysis. This proposition holds also in the limiting case where the period is an instantaneous one. Conversely, if the periods presupposed by the two analyses are not the same, then the two excess-demand functions will also generally not be the same. Thus, for example, assume that we are conducting our stock analysis on the basis of a month, and our flow analysis on the basis of the first week of this month. Obviously, there is no reason for the two excess demands described by these two analyses to be equal. And this will be the case even if the stock excess demand should be zero. For even though prices and interest may be such that the individual is planning to hold the same stock of money at the end of the month as at the beginning (i.e., excess demand equal to zero), there is no reason why he might not be planning to have an excess inflow of money during the first week of that month (i.e., an excess demand for money), to be offset in subsequent weeks by corresponding excess outflows (i.e., excess supplies). It should, however, be obvious that the different excess demands in these cases are not the result of any alleged difference between stock and flow analysis as such, but rather the result of our using two different periods of time in our two different analyses. Clearly, these same differences between excess demands would remain even if we were to apply stock analysis—or flow analysis—to both cases.’ All this is the reflection of the simple fact that the prices and interest rate which might equilibrate an economy over a period of a month need not do so over a period of a week—and conversely. It should also be clear from the above that the distinction that is sometimes attempted between “ flow equilibrium “ and “ stock equilibrium “ is an inadvisable one. Once again, if the periods are the same, the existence of one type of equilibrium implies the existence of the other. And if they are not the same, then it is much better to make the required distinction explicitly in terms of the familiar Marshallian “ instantaneous ”, “ short run ”, and “ long run ” ; or the Hicksian “ temporary equilibrium ” and “ equilibrium over time ” ;1 or any other classification which emphasizes that the relevant criteria are the periods of time over which the analysis is carried out. We only confuse the real nature of the issue if we introduce the terms “ stock “ and “ flow “ into a context where they really do not belong. 2. The analysis of the preceding section was restricted to that of static equilibrium. It has, however, sometimes been contended that the difference between liquidity-preference and loanable-funds theories is one that manifests itself only in dynamic analysis. In order to examine the validity of this contention, it will be convenient to sketch out first a graphical technique for dynamic analysis which I have described more fully elsewhere.2 For simplicity, let us continue with our full-employment assumption. Consider an economy with four markets : commodities, labor, bonds, and paper money. Assume that the real demand for each of these goods depends on real income (assumed constant), the rate of interest (r), and the real value of cash balances (M0/p). By assumption, the labor market is always in equilibrium. The analysis of the determination of the equilibrium price level and rate of interest in this model can now be carried out in terms of Figure 1, where CC represents the locus of all combinations of r and p at which the commodity market is in equilibrium, while BB represents the corresponding locus for the bond market. These two curves intersect at the equilibrium point (p0, r0), and divide our diagram into four sectors, designated by roman numerals. At any point in Sectors I–II there exists an excess supply of commodities (denoted by “ C < 0 “) driving the price level downward ; and at any point in Sectors III–IV an excess demand (” C > 0 “) driving them upwards. Similarly, at any point in Sectors II–III there exists an excess demand for bonds (” B > 0 “) driving their price upwards, and thereby driving interest downwards ; while at any point in Sectors IV–I there is an excess supply (” B < 0 “) driving the rate upwards. The directions of these dynamic pressures are indicated by the arrows in Figure 1. Under certain assumptions, it can be shown that this dynamic process is a stable one—but this does not interest us here. Let us now consider the remaining market, that for money. The locus of all combinations of price level and interest rate that equilibrate this market would also yield a positively sloped curve in Figure 1 : for a rise in interest decreases the amount of real cash balances demanded ; hence—in order to maintain equilibrium—there must take place a rise in the price level to decrease the real supply correspondingly.1 By virtue of Walras’ Law we also know that this curve must pass through the point (p0, r0) : for any point which equilibrates the commodity and bond markets must also equilibrate the money market. Can we say anything more about this curve ? The answer is that we can—by examining the same budget restraint (5) with the aid of which we established Walras’ Law. Remembering that the last parenthetical term in this restraint is zero, let us rewrite this restraint as (9) Md – M0 = (Cs − Cd) (Bs – Bd), THE STATE OF EXCESS DEMAND IN THE MONEY MARKET This is shown in greater detail in Figure 2 and its accompanying table, where M O represent states of excess supply and demand for money, respectively. As just explained, the curve MM must pass through Sectors II and IV, in which there is an excess demand for one of the two goods, commodities and bonds, and an excess supply for the other. In Sector II, for example, there is an excess supply of commodities and an excess demand for bonds. If the former is greater than the latter, then—by equation (9)—there exists an excess demand for money ; this is the situation represented by Sector IIa. if the opposite is true, then there is an excess supply of money—as in Sector IIb. If, finally, the excess supply of commodities exactly offsets the excess demand for bonds, then the excess demand for money is zero ; that is, the money market is in equilibrium. This, of course, is the situation at every point on the curve MM itself. A corresponding analysis can be made for Sector IV. When there is an excess supply of money, the rate of interest will fall, and when there is an excess demand, it will rise ; When there is an excess supply of bonds, the rate of interest will rise, and when there is an excess demand, it will fall. Now, there can be no question but that these two statements represent two different theories as to the dynamic behavior of the interest rate. But what must now be emphasized is that this difference does not result from the fact that the propositions refer to two different markets, but from the fact that they imply different dynamic behavior in the same market. This can readily be shown with the aid of Figure 2 and its accompanying table. In every sector except IIa and IVa an excess demand for money is accompanied by an excess supply of bonds and vice versa. Hence the direction of the change in interest is the same whether we use Hypothesis (A) or (B). The only difference arises in Sectors IIa and IVa. For example, at point R in the latter, interest will fall according to Hypothesis (A), but will rise according to (B). (This is indicated in the graph by the letters (A) and (B) attached, respectively, to the two vertical and oppositely pointing arrows.) A corresponding statement holds for any point in Sector IIa. Let us now see what this means. Hypothesis (A) states that an excess supply of money drives interest down in the bond market regardless of the state of excess demand there. Hypothesis (B), on the other hand, implies that the effects of an excess supply of money on interest cannot be determined except by examining the concurrent situation in both the bond and commodity markets. In particular, Hypothesis (B) implies that under certain circumstances (and point R is an example) an excess supply of money may be accompanied by such a large excess demand for commodities that individuals will attempt to finance their additional purchases not only by using up all their excess cash, but also by selling part of their bond holdings. In this way, an excess supply of money might be accompanied by an excess supply of bonds and hence by an increase in the rate of interest. Thus the difference between Hypotheses (A) and (B) results from their differing assumptions as to the implications of an excess supply (or demand) in the money market. Correspondingly, this difference would remain even if Hypothesis (B) were replaced—as it can readily be—by an equivalent hypothesis—say, (D)—referring to the money market and postulating explicitly that dynamic behavior for this market which is now implicit in (B). Conversely—and this might be worth noting even if it is a tautology—there would be no difference between Hypotheses (B) and (D)—even though the former refers to the bond market and the latter to the money market. where is the rate of change of the interest rate, K1 and K2 are positive constants, and the simplifying assumption is made that the rate of change is proportionate to the amount of excess demand or supply. That is, an excess demand for money affects both the interest rate and the price level. Clearly, the dynamic system corresponding to Hypotheses (A) and (C) differs in general from that corresponding to (B) and (C). On the other hand, systems (B) and (C), (B) and (D), and (C) and (D) are all equivalent—even though they refer to different markets. Thus the markets in which the dynamic analysis is carried out cannot per se affect the outcome.1 Let us now return to the interpretation of Hypothesis (A) given above and note that it clearly demonstrates its implausibility. For it is difficult to understand why an excess supply of money should drive up the price of bonds even when there exists an excess supply of the latter. But this is precisely what Hypothesis (A) claims to be true for every point in Sector IVa of Figure 2. And a corresponding statement holds—mutatis mutandis—for every point in Sector IIa. At first sight it might appear that an escape from this implausibility can be achieved by adding to Hypothesis (A) the contention that points such as those described by Sectors IIa and IVa do not exist. In other words, we add to Hypothesis (A) the further Hypothesis: (E). The excess supply of money is identical with the excess demand for bonds. It then follows that a point of excess supply (demand) for money is necessarily a point of excess demand (supply) for bonds, and vice versa— so that the difficulty described in the preceding paragraph can never arise. In graphical terms, this means that curves MM and BB coincide in Figure 2 : for any combination of price and interest which makes the excess demand for bonds zero must do the same for the excess demand for money, and vice versa. Thus under Hypothesis (E) Sectors IIa and IVa simply disappear. But this is to jump from the frying pan into the fire. For Hypothesis (E) really implies that the system is not stable : that the automatic functioning of market forces will not bring it to a determinate position of price and interest equilibrium. This can readily be shown in the following way. We know—by virtue of Walras’ Law—that the analysis of Figure 2 can be carried out in terms of any two of the three markets. Now, there is no reason why the two markets so chosen should not be the bond and money markets. Hence—since we are ignoring the commodity market— Figure 2 reduces to Figure 3—where the single curve represents both MM and BB. Assume now that the system is in equilibrium at the point P and that a random disturbance moves it to Q. Clearly, the dynamic pressures which exist in the system (denoted by the arrows) can at best succeed in bringing the system back to the curve BB (or MM)—say, to point T. They cannot assure its return to the original position P. Thus the system is not stable. It is in a state of neutral equilibrium. This same conclusion can be reached—though in a somewhat more complicated way—even if we carry out the analysis in terms of the commodity and bond (or money) market. First we rewrite our budget restraint (9) as (10) Cd − C8= (M0 − Md) − (Bd − Bs), where the first parenthetical term on the right-hand side represents the excess supply of money, and the second term the excess demand for bonds. But by Hypothesis (E) these are always equal. Hence the right-hand side of (9) is identically zero—which means that the excess demand for commodities is zero no matter what the rate of interest or price level. Thus under the present assumptions the curve CC of Figure 2 becomes blown up until it comprises the entire area of Figure 3. Correspondingly, the “ intersection “ of this counterpart of CC with curve BB (or MM) is the latter curve in its entirety. Thus the indeterminacy of the equilibrium position is again demonstrated.1 Before concluding this section of the paper it might be well to digress on the relationship between the conclusion just reached and Keynesian monetary theory. In particular, at first sight our conclusion seems to invalidate the familiar contention of many Keynesian economists that an excess supply of money creates a corresponding excess demand for bonds. Actually, however, I do not think that these economists had in mind the troublesome identity described in Hypothesis (E). Instead, all they wanted to assume is that there exists an identity with respect to certain kinds of changes. In particular, all they wanted to say is that an excess supply of money generated by an increase in the quantity of money in the system is diverted completely to the bond market and is thus identical with the excess demand thereby generated in that market. This is completely different from saying (as is said in Hypothesis (E) and Figure 3) that an excess supply of money generated by any cause whatsoever is identical with the excess demand for bonds generated by that cause. Indeed, this latter statement contradicts the fundamental Keynesian assumption that an excess supply of money generated by an increase in the rate of interest will be accompanied by a decreased demand for investment goods—a fact which must necessarily also affect the extent of the excess demand for bonds. Thus under this assumption the excess supply of money could not be identical with the excess demand for bonds in the sense of Hypothesis (E). More simply, the aforementioned contention would seem to be intended only as an alternative formulation of the familiar—though usually implicit—Keynesian hypothesis that the real-balance effect manifests itself only in the bond and money markets, but not in the commodity and labor markets. From this it immediately follows that a change in real balances which creates an excess demand in the money market must create an exactly equal excess supply in the bond market. This assumed absence of a real-balance effect in the commodity market may or may not be empirically true : but—unlike Hypothesis (E)—it represents a logically tenable position.1 3.2 All of the preceding argument is based on the validity of Walras’ Law. It is also based on the assumption that a state of full employment exists in the economy. What we must now see is whether Walras’ Law—and hence the preceding argument—continues to be valid even in the case of involuntary unemployment. The reason this generalization is not at all self-evident is that Walras’ Law relates to an economy in which all markets are in equilibrium. In the case of unemployment, on the other hand, there exists a state of excess supply—and hence of continued disequilibrium—in the market for labor. At first sight, then, there would seem to be no place for the operation of Walras’ Law. One way out of this difficulty (there may well be others) is to assume it away by attributing to workers a completely passive behavior pattern according to which they adjust the amount of labor they plan to supply to the amount employers demand at the going wage rate. Hence, by definition, “ equilibrium “ always exists in the labor market. This behavior pattern is akin to that usually postulated by Keynesian theory, according to which—at the minimum wage rate—workers are willing to offer any amount of employment up to the point of full employment. This approach actually dodges the real difficulty. Nevertheless, it may be worth while to see how it enables the establishment of Walras’ Law. This can be conveniently shown by the use of the preceding simplified “ flow of funds “ accounts for an economy without a government. These accounts actually represent the budget restraints of the business and household sectors, respectively. By definition, the two sides of each of these accounts must be equal. With the exception of interest payments—which are by definition predetermined—each of the items in these accounts is an ex ante one reflecting the plans of individuals. The right-hand side of the household account reflects our assumption that wage earners passively expect to receive whatever employers plan to pay ; hence the term Nd appears there as well as on the left-hand side of the business account. A similar statement holds for dividend payments, D. If we now add the two sides of these accounts we obtain (11) Nd + R + D + Id + ∆Mb = Cs + Is + Bs and (12) Nd + R + D = Cd + Bd + ∆Mh. Subtracting (12) from (11) and rearranging terms, we then obtain (13) ∆Mb + ∆mh + = [(Cs + Is) − (Cd + Id)] + [Bs − Bd]. The first set of brackets on the right-hand side of (13) represents the excess supply in the commodity market ; and the second, the excess supply in the bond market. When equilibrium exists in these two markets, each of these bracketed terms equals zero ; hence the left-hand side of (13)—representing the planned net additions to cash balances—must also be zero. That is, equilibrium must then also exist in the money market. Thus Walras’ Law obtains. The excess supply in the commodity market can be written in a more familiar form if instead of Cs + Is we write net national product, Y ; and if instead of Cd and Id we write simply C and I, respectively. The equilibrium condition for the commodity market then becomes the familiar (14) C + I = Y, where C and I represent the consumption and investment functions, respectively. Figure 4 provides a graphical illustration of Walras’ Law under our present assumptions. Here Y represents real national income, and IS and LL are the familiar Hicksian curves representing those combinations of r and Y at which equilibrium prevails in the commodity and money markets, respectively. The third curve—ZZ—represents the equilibrium conditions of the bond market under certain simplifying assumptions. All three curves are drawn as of a fixed price level and quantity of money. By virtue of Walras’ Law, the curve ZZ must pass through the intersection point of IS and LL. With the aid of Figure 4, we can immediately generalize the arguments of Sections 1 and 2 to the present case too. In particular, all of the interrelationships and dynamic implications of the CC, MM, and BB curves of Figure 2 hold also—mutatis mutandis—for the IS, LL, and ZZ curves, respectively, of Figure 4. Correspondingly, the conclusion of Section 2—that the distinction between liquidity-preference and loanable-funds theories can have nothing to do with the distinction between Hypotheses (A) and (B)—holds also for an economy with unemployment. Similarly, Hypothesis (E) would generate the same instability in Figure 4 as in Figure 2 : for the LL and ZZ curves would then coincide, while the IS curve would become blown up until it comprised all the points in the diagram. 4. The general argument of this paper can now be summarized as follows : Differences among the various theories of interest there certainly are. But there is no logical possibility of attributing these differences to the different equations selected for analysis, or to the choice of stock versus flow analysis. On the other hand, it may well be that the intellectual processes of those who formulated these theories (and I am thinking particularly of Keynes) were significantly influenced by the fact that they worked in terms of one set of concepts instead of the other. It may well be that, for example, they were able to achieve certain insights from the money equation that they would not have achieved from the bond equation. This is an important and interesting question for the psychology of intellectual processes. But it clearly has no bearing on the fact that it is logically possible to deduce these insights equivalently from either equation. Thus the search for substantive differences among interest theories along these lines is a sterile one. It may well be that the “ liquidity preference—loanable funds “ controversy was a necessary stage in the working out of new ideas. But we should now recognize it for the confused, transitory stage that it was, and we should accordingly relegate it to that same limbo of intellectual curiosa to which we have already agreed to relegate the even more famous “ savings-investment “ controversy. Like the latter, it is not a chapter in the recent history of economic doctrine of which we should be particularly proud. Correspondingly, the substantive differences which do exist among various interest theories must be traced to other causes. For example, the differences may arise from the different periods of time considered by the various analyses. In this connection it might be emphasized— since it has been misunderstood by Keynesians—that a systematic feature of neoclassical interest theory itself is the difference between short-run and long-run analyses. In the former, for example, an increase in the quantity of money will depress the rate of interest, whereas in the latter it will leave interest invariant.1 Similarly, differences between two theories may flow from the fact that one emphasizes the margin of preference between holding bonds and holding money, while the other neglects this margin. Accordingly, the first theory provides for the permanent effects of shifts in this preference on the rate of interest, while the second does not. This would seem to be one of the fundamental differences between Keynesian and neoclassical theories. The Eliezer Kaplan School of Economics and Social Sciences, The Hebrew University, Jerusalem. Note to page 314 which in turn implies that all the partial derivatives are identical : namely, − Ψ 1( ) Ψ≡ B1( ) − Ψ 2( ) ≡ B2( ), and − Ψ 3 ( ) ≡ Ba( ). Thus (5) is a much more restrictive condition than is not : for the effect of real balances enters through the supply side (represented by the right-hand side of equation (6) ). Note too that the budget restraint implies that (8) ϕ 3( ) + B3( ) + Ψ 3( ) ≡ 0 ; that is, any increase in real balances is entirely expended on the goods of the system. It then follows that if equation (4) holds, it must be true that ϕ 3 ≡ 0 : that is, there is no real balance effect in the commodity market. Conversely, if ϕ 3( ) ≡ 0, then equation (8) implies equation (4). Thus the absence of a real-balance effect in the commodity market is equivalent to the identity between the excess demand for money and the excess supply of bonds for changes generated by the real-balance effect.