On 'rusting' money: Silvio Gesell's Schwundgeld reconsidered. Part I: The short run

Rehme, Günther Article On 'rusting' money: Silvio Gesell's Schwundgeld reconsidered. Part I: The short run Review of Economic Analysis (REA) Provided in Cooperation with: International Centre for Economic Analysis (ICEA), Waterloo, Ontario Suggested Citation: Rehme, Günther (2024) : On 'rusting' money: Silvio Gesell's Schwundgeld reconsidered. Part I: The short run, Review of Economic Analysis (REA), ISSN 1973-3909, International Centre for Economic Analysis (ICEA), Waterloo (Ontario), Vol. 16, Iss. 2, pp. 91-131, https://doi.org/10.15353/rea.v16i2.4942 This Version is available at: https://hdl.handle.net/10419/328162 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ Review of Economic Analysis 16 (2024) 91-131 1973-3909/2024091 91 www.RofEA.org On 'Rusting' Money: Silvio Gesell's Schwundgeld Reconsidered Part I: The Short Run GÜNTHER REHME† Technische Universität Darmstadt  Silvio Gesell hypothesized that money depreciation is economically and socially beneficial, an idea that have often been contended. Here I analyze the spirit of his claims in a Sidrauski model in which households additionally have a 'love of wealth'motive. The analysis is presented in two parts, one focusing on the short and the other one on the long run. In the first part of this work, these features provide micro-foundations for analyzing Gesell's claim in the short run. Contrary to some claims it is shown Gesell's conjectures may indeed be valid in a demand-determined, short-run equilibrium and why money depreciation overcomes the zero lower bound on nominal interest rates. These results are checked against the recent demonetization episode in India and essentially found to be true. Hence, Gesell's hypotheses can be verified for a plausible, short-run environment and may be relevant for current economic, especially, monetary policies. Keywords: Economic Performance, Depreciating Money, Zero Lower Bound, Demonetization, Love of Wealth JEL Classifications: E1, E5, O4 † Professor Rehme passed away last year. The paper is published as it was originally submitted, subject to conversion to the Review’s format..  I am indebted to Ingo Barens and Thomas Fischer for their valuable help and insightful comments. I have also benefitted from discussions with Parantab Basu, Christian Berker, Volker Caspari, Christiane Clemens, Alex Cukierman, Soumya Datta, Hartmut Egger, Sabine Eschenhof-Kammer, Christian Gelleri, Rafael Gerke, Chetan Ghate, Charles Goodhart, Marcus Miller, Werner Onken, Uwe Sunde and from feedback at U Bayreuth, LMU Munich, the 5th International Conference on South Asian Economic Development (SAED), South Asian University (SAU), New Delhi, India, the 5th HenU/INFER Workshop on Applied Macroeconomics, Kaifeng, Henan, China, the 50th Anniversary "Money, Macro and Finance" (MMF) conference at the London School of Economics (LSE), London, United Kingdom, the 10th RCEA "Money-Macro-Finance" Conference in Waterloo, Ontario, Canada, the 15th Annual Conference on Economic Growth and Development, New Delhi, India, in 2019, and the 65th Münden Talks "Proudhon, Gesell, Keynes and Negative Interest Rates", Wuppertal, Germany, in 2021. The usual disclaimer shields them all. © 2024 Günther Rehme. Licensed under the Creative Commons Attribution-Noncommercial 4.0 Licence (http://creativecommons.org/licenses/by-nc/4.0/). Available at http://rofea.org. Review of Economic Analysis 16 (2024) 91-131 92 www.RofEA.org 1 Introduction "Money is the football of economic life." 1 In his main piece of work "The Natural Economic Order" Silvio Gesell, a German merchant and intellectual, developed various insightful arguments to improve the workings of an economy. It was first published in Bern in 1916 and received praise from economists such as Keynes (1936) in his "General Theory of Employment, Money and Interest", ch. 23, and Fisher (1932) in his "Booms and Depressions". In this paper, I reconsider his idea of Schwundgeld (demurrage) and its consequences on economic performance. I analyze whether the spirit of his key conjectures can be justified in a relatively parsimonious, modern theoretical framework. One reason is that Gesell's claims have often been contended by arguing that they cannot be corroborated by 'state-of-the-art' theory. Although Gesell (1920), p. 78, acknowledges that money is "the football of economic life"and thus (probably) being a key driver of, and essential for, any modern economy, he cautions us by arguing;"Only money that goes out of date like a newspaper, rots like potatoes, rusts like iron, evaporates like ether, is capable of standing the test as an instrument for the exchange of potatoes, newspapers, iron and ether. For such money is not preferred to goods either by the purchaser or the seller. We then part with our goods for money only because we need the money as a means of exchange, not because we expect an advantage from possession of the money." (p. 121) According to him placing money and commodities on equal 'physical' footing requires that money depreciates, just as normal goods do due to the wear and tear in usage or storage. In particular, he argued the face value of (paper) money depreciates at a certain percentage over a particular period. To regain the previous face value of the money (note) used, people would have to buy stamps to make up for the depreciation the monetary authority would decree for the money note. 2 1 Silvio Gesell (1920) The Natural Economic Order. 2 Consider his example for the American currency: "This $100 note (bill) is shown as it will appear during the week August 4th-11th, thirty-one ten-cent stamps ($3.10) having been attached to it by its various holders on the dated spaces provided for the purpose, one stamp for each week since the beginning of the year. In the course of the year 52 ten-cent stamps ($5.20) must be attached to the $100 note, or in other words it depreciates 5.2% annually at the expense of its holders." Gesell (1920), p. 121/2. REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 93 www.RofEA.org The introduction of such a monetary arrangement would then influence the economy in ways about which he formed, among others, the following four hypotheses. 3 Gesell Conjecture 1 (GC1) The introduction of, and, when present, an increase in, the money depreciation rate leads to a higher velocity of money in circulation. "Everyone, of course, tries to avoid the expense of stamping the notes by passing them on - by purchasing something, by paying debts, by engaging labour, or by depositing the notes in the bank, which must at once find borrowers for the money, if necessary by reducing the rate of interest on its loans. In this way, the circulation of money is subjected to pressure." Gesell (1920), p. 123. Gesell Conjecture 2 (GC2) Money depreciation coupled with expansionary monetary policy stimulates aggregate demand and through that output and employment. "In all conceivable circumstances, in fair weather and foul, demand will then exactly equal: - The quantity of money circulated and controlled by the State. Multiplied by: The maximum velocity of circulation possible with the existing commercial organization. What is the effect on economic life? The effect is that we now dominate the fluctuations of the market; that the Currency Office, by issuing and withdrawing money, can tune demand to the needs of the market; that demand is no longer controlled by the holders of money, by the fears of the middle classes, the gambling of speculators or the tone of the Stock Exchange, but that its amount is determined absolutely by the Currency Office. The Currency Office now creates demand, just as the State manufactures postage stamps, or as the workers create supply." Gesell (1920), p. 127. Gesell Conjecture 3 (GC3) A money depreciation rate is welfare enhancing. "The elimination of interest is the natural result of the natural order of things when undisturbed by artificial interference. Everything in the nature of men as in the nature of economic life urges the continual increase of so-called real capital - an increase which continues even after the complete disappearance of interest. The sole disturber of the peace in this natural order we have shown to be the traditional medium of exchange. The unique and characteristic advantages of this medium of exchange permit the arbitrary postponement of demand, without direct loss to its possessor; whereas supply, on account of the physical characteristics of the wares, punishes delay with losses of all 3 More elaborate justifications for Gesell's claims and ideas can be found in the working paper version of this paper; see Rehme (2018), appendix F, and the quotes presented at the end of this paper. Review of Economic Analysis 16 (2024) 91-131 94 www.RofEA.org kinds. In defense of their economic welfare, both the individual and the community have been and are at enmity with interest, and they would long ago have eliminated interest if their power had not been trammeled by money." Gesell (1920), p. 190. Gesell Conjecture 4 (GC4) A money depreciation rate benefits workers relatively more than capital owners. "By the laws of free competition, the manufacturer's profit must be reduced to the level of a technician's salary - an unpleasant result for many manufacturers whose success was mainly due to their commercial ability. With free money, creative power has become unnecessary in commerce, for the difficulties that called for the comparatively rare and therefore richly rewarded commercial talent have disappeared. And someone must benefit from the reduction of the manufacturer's profit. Either goods must become cheaper, or, to put it the other way about, wages must rise. There is no other possibility." Gesell (1920), p. 135. As pointed out above, the present paper complements research that has used modern economic theory to investigate whether the Gesell hypotheses can be replicated in standard model frameworks. One finds that the results of previous research are mixed. For example, Rösl (2006) finds that only the first hypothesis can be derived from Sidrauski (1967), that is, in a money-in-the-utility set-up. He concludes that Gesell neglected an analysis of the long run and any possible effects on capital accumulation so the other three hypotheses turn out to be non-valid in his model. In turn, Menner (2011), for example, uses an elaborate and involved New Monetarist DSGE model to find that "inflation and 'Gesell taxes' maximize steady-state capital stock, output, consumption, investment and welfare at moderate levels. In a recession scenario, a Gesell tax speeds up the recovery in a similar way as a large fiscal stimulus but avoids 'crowding out' of private consumption and investment." Thus, he finds support for the Gesell hypotheses at moderate levels in his business cycle model of the third-generation monetary search models. The present paper uses an alternative micro-founded and simple general equilibrium model to analyze whether the depreciation of money is socially beneficial. Doing this we will abstract from fiscal policy, as Gesell did not consider the interaction of fiscal and monetary policy in detail. 4 4 If one likes, the results here may also interpreted as holding relative to some given and constant fiscal policy operating in the background, and Ricardian Equivalence holds. Furthermore, another word of caution should be mentioned. I will not address the historical and the more recent empirical experiences that, mostly, local experiments using money depreciation have produced. Of course, the most famous one is the Wörgel experiment from 1932 to 1933 which was stopped by the Austrian National Bank in REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 95 www.RofEA.org We follow Gesell and assume that there is homogeneous money that is issued by the state and by law that money is legal tender in transactions. 5 Furthermore, his advocated monetary system is one where fiat (paper) money is irredeemable, and, thus, directly related to (only redeemable by) real goods in the economy. Irredeemability implies that you cannot exchange a banknote back into another banknote or any collateral that might back the face or any other (real) value of the banknote. For instance, in the Euro and the Fed system you can in principle redeem your banknote, but only to get another banknote with an equally denoted face value. This is not possible under the irredeemability of the banknote and plays a role when there is a depreciation of the face or other value of the banknote. On the issue of irredeemability and fiat money see, for example, Buiter (2003). In the paper, the basic Sidrauski framework is changed importantly. Apart from the motive to derive utility from money it is assumed that agents also derive utility from their wealth. 6 People are taken to be rational and are not fooled by money illusion. Thus, the agents only consider real, physical capital as wealth. Here I relate to this more general concept as 'love of wealth' in a dynamic macroeconomic model as in Rehme (2011). These motives are important for deriving nondegenerate short-run relationships between the nominal interest rate and micro-founded consumption (quasi-) IS and LM curves (in a "nominal interest rate and consumption" space). A similar approach based on the 'love of wealth' as a micro-foundation in a dynamic model with a short-run and long-run analysis as in this paper has recently been presented by Michaillat and Saez (2014). In this framework, I analyze two approaches to capture Gesell's ideas, which are presented in two parts of the analysis. The first approach, the present Part I, concentrates on textbook-like short-run, demanddetermined equilibria of the (quasi-, micro-founded) IS-LM-AS-AD variety, which are based on the micro-foundations of optimal behaviour, that is, the demand of the agents. The link to supply is assumed to be Keynes's "principle of effective demand". September 1933. The interested reader will find a plethora of empirical evidence on whether money depreciation and Gesell's ideas in general work or not in the literature. Here the focus is on theory. 5 Thus, the assumption implies that we rule out currency substitution. For an analysis of depreciating money in a complementary currency system see, for example, Godschallk (2012). 6 This has been done, for example, by Weber (1930) and Pigou (1941) who argue that individuals derive utility from the mere possession of wealth and not simply its expenditure. Later Kurz (1968) provided a thorough analysis of an optimal growth model where wealth features in utility. Furthermore, Zou (1994), Bakshi and Chen (1996) and Carroll (2000) relate to Max Weber and argue that the dependence of utility on wealth captures the "spirit of capitalism". More generally, it captures 'love of wealth' as argued in Rehme (2017). Review of Economic Analysis 16 (2024) 91-131 96 www.RofEA.org The second one, analyzed in Part II, complements the first approach and uses a standard Ramsey-Cass-Koopmans framework for the long run where markets are as-summed to clear at each point in time, and demand always equals supply. The following results are then obtained for the first approach and so for Part I of the analysis. In a short-run, demand-determined equilibrium where the (physical) capital stock, the inflation rate, transfers, and money supply are fixed, but real factor prices are flexible, Gesell's hypotheses GC1 - GC4 are all valid, given the (demand) micro-foundations of the model and given that the micro-foundations feature direct utility derived from money transactions and 'love of wealth', where only physical capital is considered to be the true source of wealth. A key assumption for the derivation of this result is that the marginal productivity theory of distribution does not necessarily hold in the short run. Importantly, when the inflation rate is given, and the Fisher relationship holds, the real interest rate moves in the same direction as the nominal interest rate in any short-run equilibrium. 7 The details for this are presented in the main text. Thus, the real interest rate is determined by other factors than technology in the short run. Gesell's ideas have been important in recent discussions about overcoming the zero lower bound that has played such an important role after the Great Recession. One argument has been to make nominal interest rates negative to combat what is called a "liquidity trap". For good surveys on this, its relation to Gesell's ideas, their relevance for the current economic situation and their historic precursors see, for example, Darity (1995), Ilgmann and Menner (2011) and Svensson and Westermark (2016). In the present paper, it turns out that many different combinations of money depreciation and money supply policies can sustain a "liquidity trap", that is, a situation with a short-run equilibrium, zero nominal interest rate. These monetary policy combinations are shown to have non-negligible effects for distribution, that is, the rewards to labour and capital. In various model variants, Buiter and Panigirtzoglou (2003) and other contributions by W. Buiter have shown that money depreciation may be used to make the short-run equilibrium interest rate negative and pull an economy out of a "liquidity trap". In this paper, I find the same so complementing their results. But the model structure here is quite different and simple. Given the present model's micro-foundations, this result follows straightforwardly and easily. Another application of the model for the short run is the recent episode of demonetization in India where the 500 and 1000 rupee notes (INR) were declared invalid in a surprise move by 7 Notice that the "Fisher relationship" captures that the nominal interest rate is (approximately) the sum of the real interest rate and (expected) inflation. This should not be equated with the "Fisher effect" which states that the real interest rate is independent of the rate of inflation. For this clarification see, for example, Ahmed and Rogers (1996). For textbook models where the real and the nominal interest rate move in the same direction in the short run, see, for example, Blanchard (2017), ch. 6 and 16. REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 97 www.RofEA.org the Indian Prime Minister. In India, cash is by far the most important medium for economic transactions. Overnight this affected 86.9 percent of the value of total currency in circulation. The model predicts that such a demonetization leads to lower consumption, aggregate demand, and lower wages, but higher real interest rates. Thus, the measure does not seem to be good for workers in the short run. These findings are broadly in line with the empirical evidence documented by the Reserve Bank of India's Monetary Policy Department (MPD) (2016). Summarizing these findings for the short run yields that the present model framework is indeed capable of verifying Gesell's claims. In the short-run, demand-determined equilibrium all claims can be ascertained. This may provide a rationale for why the renewed interest in his ideas plays a role in the current economic policy deliberations. The paper is organized as follows. Section 2 presents the model and 3 analyzes the demanddetermined (short-run) equilibrium, an overcoming of the zero lower bound on nominal interest rates and, as an example, applies the model to the recent Indian demonetization episode. Section 4 concludes. 2 The Model To simplify the algebra the model is set in continuous time. For all variables that are continuous functions of time, I use the subscript 𝑡 to denote their dependence on time. Thus, we define ℎ𝑡≡ℎ(𝑡) for some variable ℎ depending on time. Furthermore, the change of a variable ℎ over time, i.e. 𝑑ℎ𝑡 𝑑𝑡, is denoted by ℎ˙𝑡. By assumption, the economy is populated by many, price-taking households. The aggregate resource constraint of the households is given by 𝐶𝑡+𝐾˙𝑡+𝑀˙𝑡 𝑃𝑡+𝜎⋅𝑀𝑡 𝑃𝑡=𝑤𝑡𝑁𝑡+𝑟𝑡𝐾𝑡+𝑋𝑡 (1) where 𝐶𝑡 and 𝐾𝑡 denote aggregate real consumption and the aggregate real capital stock, respectively. 𝑀𝑡 represents the aggregate nominal money holdings and 𝑃𝑡 is the price level. 𝑁𝑡 denotes population and 𝑤𝑡 is the real wage rate. 𝑟𝑡 denotes the real rate of return on capital, net of depreciation of physical capital 𝐾𝑡. The lump-sum (real) transfers of the government that are granted to the households are denoted by 𝑋𝑡. Thus, the right-hand side of the budget constraint (1) captures aggregate income, consisting of total wage (𝑤𝑡𝑁𝑡) and capital income (𝑟𝑡𝐾𝑡) as well as government transfers (𝑋𝑡). The left-hand side, in turn, captures aggregate spending. Income is spent on consumption (𝐶𝑡), investment in new capital (𝐾˙𝑡) and acquisitions of new, real money holdings (𝑀˙𝑡 𝑃𝑡). The aggregate budget constraint in equation (1) corresponds to the conventional set-up of a Sidrauski (1967), money-in-the-utility-function model. The novel feature and, for this paper, Review of Economic Analysis 16 (2024) 91-131 98 www.RofEA.org the crucial difference is the term 𝜎⋅𝑀𝑡 𝑃𝑡. It captures the Gesell tax, that is, the idea of "rusting money". That can be interpreted as a depreciation on the circulating real money holdings of the households and is tantamount to a tax on them. Sometimes it is argued that the Gesell tax is simply another form of an inflation rate that most people also consider a tax on money holdings. But notice that the Gesell tax is directly determined by a political entity such as e.g. a central bank, and not, like the inflation rate (tax), indirectly by the workings of markets. Now consider a representative agent economy, and define per capita consumption 𝑐𝑡, real money balances 𝑚𝑡, as well as the per capita capital stock 𝑘𝑡 and transfers 𝑥𝑡 as follows 𝑐𝑡≡𝐶𝑡 𝑁𝑡, 𝑚𝑡≡𝑀𝑡 𝑃𝑡𝑁𝑡, 𝑘𝑡≡𝐾𝑡 𝑁𝑡, and 𝑥𝑡≡𝑋𝑡 𝑁𝑡 Dividing equation (1) by 𝑁𝑡 and using our definitions then yields 𝑐𝑡+𝐾˙𝑡 𝑁𝑡+𝑀˙𝑡 𝑃𝑡𝑁𝑡+𝜎𝑚𝑡=𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡 It is not difficult to verify that 𝐾˙𝑡 𝑁𝑡=𝑘˙𝑡+𝑛𝑡𝑘𝑡 and 𝑀˙𝑡 𝑃𝑡𝑁𝑡=𝑚˙𝑡+𝜋𝑡𝑚𝑡+𝑛𝑡𝑚𝑡 where 𝜋𝑡≡𝑃˙𝑡 𝑃𝑡 represents the rate of inflation and 𝑛𝑡=𝑁˙𝑡 𝑁𝑡 the population growth rate. Then the budget constraint of the representative household is given by 𝑐𝑡+𝑘˙𝑡+𝑛𝑡𝑘𝑡+𝑚˙𝑡+𝜋𝑡𝑚𝑡+𝑛𝑡𝑚𝑡+𝜎𝑚𝑡=𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡. Again, the right-hand side corresponds to the household's income and the left-hand side captures the household's expenditure. Notice that 𝜎𝑚𝑡 can be regarded as an outlay for the household. The longer the household holds real money balances 𝑚𝑡, the more is foregone (a form of expenditure) in terms of real income. For a similar set-up see, for example, Rösl (2006). It captures what is called the Gesell tax. Building on, for example, Blanchard and Fischer (1989), ch. 4.5, and the Rösl setup we now denote real per capita resources by 𝑎𝑡 where 𝑎𝑡≡𝑘𝑡+𝑚𝑡 . Thus, the household has real resources in the form of physical capital and real money balances. It follows that 𝑎˙𝑡=𝑘˙𝑡+𝑚˙𝑡. After collecting terms and rearrangement Appendix B shows that one then obtains 𝑎˙𝑡=[(𝑟𝑡−𝑛𝑡)𝑎𝑡+𝑤𝑡+𝑥𝑡]−[𝑐𝑡+(𝑟𝑡+𝜋𝑡+𝜎)𝑚𝑡] (2) Thus, the change in real per capita resources 𝑎˙𝑡 depends on the household's income from capital and real money balances (𝑟𝑡−𝑛𝑡)𝑎𝑡 , labour income 𝑤𝑡 and transfers 𝑥𝑡 . Consumption then REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 105 www.RofEA.org Figure 1: The LM Curve Result 1 (LM Curve): Based on the household's optimality conditions, equation (14) describes an LM curve in (c, 𝑖 )-space for a given capital stock 𝑘, and fixed money supply 𝑚 and inflation rate 𝜋. It expresses consumption as a function of the nominal interest rate 𝑖=𝑟+𝜋, depending on real money balances 𝑚 and the money depreciation rate 𝜎. It describes equilibrium in the money market. An increase in the Gesell tax 𝜎 or real money balances 𝑚 shifts the LM curve to the right in a (𝑐,𝑖)-space, for a given nominal interest rate Next, we consider equation (11) which, as one should recall, is entirely based on the demand side of the economy, i.e. the households' optimality conditions. In steady-state that equation reduces to (𝛿+𝛽)𝑐=(𝑟+𝜋+𝜎)𝑚−𝑟𝑎+𝜌𝑎 After some manipulation, using the Fisher relationship 𝑖=𝜋+𝑟, can be rearranged to yield; 𝐼𝑆: 𝑐=(1 𝛿+𝛽)[(𝜋+𝜎)(𝑚+𝑘)−(𝑖+𝜎)𝑘+𝜌(𝑚+𝑘)] (15) This equation amounts to a quasi-IS curve that has a negative slope with respect to 𝑖 in a (𝑐,𝑖)− plane. Thus, 𝑑𝑐/𝑑𝑖∣𝐼𝑆<0 . Furthermore, as wealth considerations play a role, i.e. 𝛽>0 , it turns out that the IS schedule also depends on real money balances. That is so because through Review of Economic Analysis 16 (2024) 91-131 106 www.RofEA.org the introduction of preferences for wealth (physical capital) the model also implies a Pigou effect whereby money positively bears on (real) consumption, i.e., 𝑑𝑐/𝑑𝑚∣𝐼𝑆>0. ⬚ 17 Figure 2: The IS Curve The same holds for an increase in the inflation rate 𝜋 , that is, 𝑑𝑐/𝑑𝜋∣𝐼𝑆>0 . One also verifies that 𝑑𝑐/𝑑𝜎∣𝐼𝑆>0. Thus, apart from an increase in real money balances 𝑚, an increase in the Gesell tax (an increase in 𝜎 ) also shifts the IS curve to the right for a given nominal interest rate. Result 2 (IS Curve): Based on the household's optimality conditions, equation (15) describes an IS curve in (𝑐,𝑖)-space for a given capital stock 𝑘, and fixed money supply and inflation rate. It expresses consumption as a function of the nominal interest rate 𝑖=𝑟+𝜋 and depends on real money balances 𝑚 and the money depreciation rate 𝜎. It describes equilibrium in the goods market. The IS curve features a Pigou effect. An increase in real money balances or the inflation rate raises consumption and shifts the IS curve to the right for a given 𝑖. An increase in the Gesell Tax shifts the IS curve to the right in a (𝑐,𝑖)-plane for a given nominal interest rate. 17 Pigou (1943) argues that output and employment can be stimulated by increasing consumption due to a rise in real money balances. Later Patinkin (1948) coined the term for this effect after Arthur Cecil Pigou, one of the teachers of John Maynard Keynes. REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 107 www.RofEA.org 3.1 The short-run, demand-determined equilibrium As is well known from elementary macroeconomics, the intersection of the LM and IS curves describes a short-run, demand-determined equilibrium. From now on let a variable ℎ=ℎ(𝑡) in short-run equilibrium be denoted by ℎ. Then solving equation (14) for the nominal interest rate 𝑖 plus 𝜎, inserting the result into the 𝐼𝑆 equation (15) and rearrangement yields the aggregate (short-run) demand for goods 𝑐. In appendix D it is shown to be given by 𝑐=(𝜋+𝜎+𝜌)⋅𝑚 𝛿 (16) Using equation (14) one verifies that the (short-run) equilibrium nominal interest rate satisfies 𝑖=(𝜋+𝜎+𝜌)[1−(𝑚 𝑘)(𝛽 𝛿)]−𝜎 (17) where the expression in the square bracket is non-negative by assumption. One can calculate the velocity of money as the ratio of 𝑐 to real money balances 𝑚. As both quantities are expressed relative to the price level, the velocity of money (in terms of consumption) in a short-run equilibrium is then given by 𝜈≡𝑐 𝑚=(𝜋+𝜎+𝜌) 𝛿 (18) which is increasing in 𝜎, and captures Gesell's idea that controlling the velocity of money has a direct bearing on aggregate (real) demand. The velocity of money is usually larger than one which I assume to be the case. Assumption 2: The velocity of money, in terms of consumption, is taken to be larger than one, that is, 𝜈>1 and, thus, 𝛿 to be sufficiently smaller than 𝜌+𝜋+𝜎. Thus, the ratio of consumption - or more conventionally GDP - to money aggregates like 𝑀0 (base money) or 𝑀1 is taken to be a value over one. As an example consider the velocity of 𝑀1 in the U.S. between 1960 and today. ⬚ 18 18 Money Velocity: Velocity is a ratio of nominal GDP to a measure of the money supply (M1 or M2). It can be thought of as the rate of turnover in the money supply, that is, the number of times one dollar is used to purchase final goods and services included in GDP. Source: http:// research.stlouisfed.org/fred2/categories/32242 Review of Economic Analysis 16 (2024) 91-131 108 www.RofEA.org Figure 3: Velocity of 𝑀1 in the U.S. Source: http://research.stlouisfed.org/fred2/categories/32242 From the graph, the velocity of 𝑀1 has consistently been larger than one over the period considered. In this model, 𝑀 refers to 𝑀0 (base money). It is well known that the velocity of 𝑀0 is usually higher than the one for 𝑀1 because 𝑀0<𝑀1 . As aggregate consumption corresponds to roughly 60 percent of GDP in most, especially OECD countries, it is safe to say that empirically the ratio of 𝑀0 to aggregate consumption is also larger than one. This holds no matter whether we look at the steady state or shorter periods. Given the expressions for a demand-determined equilibrium various comparative static investigations are then possible. As the paper's focus is on Gesell's conjectures, I concentrate on the effects on the short-run equilibrium if 𝜎 or 𝑚 is changed. For now, assume that the inflation rate is non-negative, that is, 𝜋≥0. From equations (16) and (17) aggregate demand for goods (in short run-equilibrium) is increased and the short-run equilibrium nominal interest rate falls when the Gesell tax (given real money balances) or real money balances (given money depreciation) rise. Thus, when the inflation rate is non-negative, we have; 𝑑𝑐/𝑑𝜎>0, 𝑑𝑖 /𝑑𝜎<0 and 𝑑𝑐/𝑑𝑚>0, 𝑑𝑖 /𝑑𝑚<0 (19) That means the (negative) nominal (short-run equilibrium) interest rate reaction to a positive change in the Gesell tax (𝜎) is larger in absolute value for the LM shift than the absolute (but positive) shift in the IS curve. This follows because 𝑑𝑖/𝑑𝜎∣𝐼𝑆=𝑚/𝑘 and 𝑑𝑖/𝑑𝜎∣𝐿𝑀=−1, and by the assumption that 𝑚<𝑘. Thus, if the economy's short-run equilibrium is initially at point 𝐴 , an increase in 𝜎 or real money balances will move the LM and the IS curve to the right, to end up at a point like 𝐷 with REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 109 www.RofEA.org a higher 𝑐 and a lower nominal interest rate 𝑖 in the new short-run, demand-determined equilibrium. Proposition 1: Suppose the capital stock, prices, the inflation rate, and the transfers are fixed in the short run. Then an increase in the Gesell Tax 𝜎, for a given nominal money supply, 1. increases the velocity of money 𝜈, and 2. increases short-run, aggregate consumption 𝑐, and 3. implies a lower short-run nominal interest rate 𝑖 in a (quasi-) IS-LM environment in a (𝑐,𝑖)-plane. Figure 4: The Short-Run, Demand-Determined Equilibrium By similar arguments, we also obtain that, for a given 𝜎 and 𝜋≥0, an increase in real money balances, 𝑚 , increases short-run, aggregate consumption, 𝑐 , and implies a lower short-run nominal interest rate, 𝑖. So far we have ignored that the household's budget constraint, that is, equation (2) must also be satisfied. We consequently need that 𝑟⋅𝑘+𝑤+𝑥−𝑐−(𝜋+𝜎)⋅𝑚=0. Review of Economic Analysis 16 (2024) 91-131 110 www.RofEA.org For convenience denote variables that are fixed in the short run by an upper bar. ⬚ 19 Assume that in a demand-determined (short-run) equilibrium the sum of wages and capital income equals output, called 𝑦, which equals aggregate supply. Then 𝑦= 𝑟⋅𝑘‾+𝑤. Given the determination of consumption by the IS-LM apparatus and in light of the budget constraint equation (2) we get 𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾=𝑦(𝑟,𝑤,𝑘‾)=𝑟⋅𝑘‾+𝑤 (20) where the left-hand side denotes aggregate demand (net of fixed and given transfers 𝑥‾) and the right-hand side is a quasi-aggregate supply relationship that depends on the fixed capital stock 𝑘‾, and the factor prices 𝑟 and 𝑤. If the factor prices are taken to vary freely and are not tied to marginal productivity remuneration, but some other exogenous process that is independent of 𝑘, it is indeed possible that the left-hand side of the equation, that is, aggregate demand, called ad, determines the righthand side of the equation. Letting 𝑎𝑑≡𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾ denote aggregate demand, we have in a (short-run) demand-determined equilibrium that 𝑎𝑑(𝜎;𝑚‾,𝜋‾,𝑥‾)≡𝑐+(𝜋‾+𝜎)⋅𝑚‾−𝑥‾=𝑦(𝑟,𝑤;𝑘‾) As a consequence, we can then define the following: Definition 1 Based on the household's optimality conditions in equations (10), (11), and (2), a short-run, demand-determined equilibrium is given when aggregate demand ad (𝜎;𝑚‾,𝜋‾,𝑥‾) equals aggregate output (supply), 𝑦(𝑟,𝑤;𝑘‾) , for a given capital stock, given real money balances and inflation rate. For flexible factor prices 𝑟 and 𝑤, the intersection of IS and LM determines aggregate demand ad (...) and with it output 𝑦(𝑟,𝑤;𝑘‾) so that the equilibrium is demand-determined. Whatever the values of the fixed variables and the parameters may be, the factor prices can equilibrate short-run demand and "supply" in such a world. Notice that we have not invoked the marginal productivity theory of distribution in which case the rewards would ultimately be functions of 𝑘. Instead, here we think of 𝑟 and 𝑤 determined by (e.g. market) forces outside the 19 Recall that the IS-LM apparatus holds for a simultaneous equilibrium in the goods and money market. In that sense a given supply money makes it an exogenous variable for most of the analysis in this part of the paper. REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 111 www.RofEA.org model, but still assume that they equilibrate demand and supply in the way required by the model. If that is the case, ad (⋅) indeed determines "supply" 𝑦(𝑟,𝑤;𝑘‾). ⬚ 20 Proposition 2: Suppose the capital stock, output prices, the inflation rate, the transfers, and the money supply are fixed, but real factor prices are flexible in the short run. Then a shortrun, demand-determined equilibrium, when the inflation rate is non-negative, is characterized by ad (𝜎;𝑚‾,𝜋‾,𝑥‾)=𝑦(𝑟,𝑤;𝑘‾) An increase in the Gesell Tax 𝜎 or real money balances then increases short-run, aggregate demand, ad, and consequently short-run output and supply, 𝑦. The properties easily follow from equation (20). From the proposition, we can also deduce the following. If 𝜎 rises, it follows from Proposition 1 that the (short-run) equilibrium nominal interest rate 𝑖 falls. If the inflation rate is fixed in the short run, then the real interest rate 𝑟 would have to fall. This follows from the Fisher relation 𝑖=𝑟+𝜋. If we assume that the factor prices are free to move in the short run, then Proposition 2 implies that the wage rate 𝑤 must rise when 𝜎 increases. Thus, a higher 𝜎 implies a lower 𝑟, for a given 𝜋‾, and higher 𝑎𝑑 so a higher 𝑦 and a higher 𝑤. Hence, for a given capital stock, labour input and inflation rate, the wage earners would benefit from an increase in the Gesell tax. Corollary 1: For fixed capital, labour input and inflation rate, the wage earners may benefit from an increase in the Gesell tax or real money balances in the short-run, demand-determined equilibrium environment. The capital owners may earn less in such an environment. Of course, that begs the question of the factor prices are really more flexible than output prices, which determine the inflation rate 𝜋. Clearly, this distributional implication may not hold if the inflation rate is not fixed in the short run. Lastly, the welfare implications in the short-run, demand-determined environment are considered. Clearly, if the money supply and capital stock are fixed in the short run, period (short-run) welfare from equation (4) is given by 20 It is interesting to note that there may be many different combinations of w and r that can equilibrate ad and y . Hence, under the assumptions made many different distributional arrangements for the rewards to capital and labour are feasible, and so the income distribution would in general not be determinate. Review of Economic Analysis 16 (2024) 91-131 112 www.RofEA.org 𝜑(𝑐,𝑚‾,𝑘‾)=ln 𝑐+𝛿ln 𝑚‾+ 𝛽ln 𝑘‾ But then one easily verifies that 𝑑𝜑/𝑑𝜎=(𝑑𝑐/𝑑𝜎)/𝑐>0, because 𝑑𝑐/𝑑𝜎>0. Thus, period welfare would rise with an increase in 𝜎. Proposition 3: Suppose the capital stock, the inflation rate, transfers, and money supply are fixed, but real factor prices are flexible in the short run. Then a short-run, demand-determined equilibrium is characterized by period welfare 𝜑(𝑐,𝑚‾,𝑘‾)=ln 𝑐+ 𝛿ln 𝑚‾+ 𝛽ln 𝑘‾ with 𝑑𝜑 𝑑𝜎=𝑑𝑐/𝑑𝜎 𝑐 >0,𝑑𝜑 𝑑𝑚‾=𝑑𝑐/𝑑𝑚‾ 𝑐 +𝛿 𝑚‾>0 that is, period welfare is higher, when the Gesell tax or real money balances are higher in a (short-run) demand-determined equilibrium. The most interesting implication of the propositions for the short run is that Gesell's conjectures are true in the environment developed in this section. Thus, Theorem 1: In a short-run, demand-determined equilibrium where the capital stock, the inflation rate, transfers, and the money supply are fixed, but real factor prices are flexible and the inflation rate is non-negative, Gesell’s hypotheses GC1 – GC4 are all generically valid, given the (demand) micro-foundations in equations (2), (4), (6), (7), (8), and (9), and given that the micro-foundations feature direct utility derived from money and “love of wealth” where physical capital is considered to be the true source of wealth. This result is striking and in contrast to some contributions in the literature. Clearly, the theorem is based on the non-implausible assumptions invoked here. Notice that the theorem is about the short run. However, Gesell’s ideas have occupied the imagination of researchers and policymakers alike in the years right after the Great Recession. It has been and, somehow still, is being felt that money depreciation may be one way out of important crisis problems, in the short and the longer run. 3.2 Liquidity trap and the zero lower bound on nominal interest rates Recently, it has been an important question what monetary policy can accomplish, if the nominal interest rate is at its zero lower bound, that is, if it takes on a value close to zero. As mentioned above there has been renewed interest in Gesell’s ideas. To shed some led onto why REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 113 www.RofEA.org Gesell’s ideas may be relevant in the current situation consider money demand and short-run equilibrium again. ⬚ 21 Money Demand Conditions Consider a situation where the nominal interest rate is at the zero lower bound. Let us again concentrate on equation (7), which describes the optimal choice (demand) of money holdings in the private sector. For simplicity continue to use 𝑚𝑡 to denote real money balances demanded and supplied. Then; 𝛿 𝑧𝑡−𝛽 1−𝑧𝑡−𝜇𝑡⋅𝑎𝑡(𝑟𝑡+𝜋𝑡+𝜎)=0 (7) So far we have concentrated on an interior solution implying that the equation above is satisfied as an equality. Suppose that that is not the case. In particular, suppose that the nominal interest rate is at its zero lower bound with 𝑖𝑡=𝑟𝑡+𝜋𝑡=0. By implication the real interest rate 𝑟𝑡, the inflation rate 𝜋𝑡 or both might in principle be negative. But in the short-run equilibrium, the inflation rate is (exogenously) given by assumption so we take the real interest rate 𝑟𝑡 to adjust when 𝑖𝑡=0. Thus, the real interest rate may be negative. There is, for example, evidence for the U.S. that negative real interest rates are far from unrealistic as is shown e.g. by Eichengreen (2015), Figure 1, which I represent here for convenience. 22 Now, for the ensuing analysis recall that 𝜇𝑡=1/𝑐𝑡 and 𝑎𝑡=𝑘𝑡+𝑚𝑡 where in this section now 𝑚𝑡=𝑚𝑡𝑑. We can then investigate various cases. Case 1: Suppose 𝑖=0,𝜎=0 and 𝛽=0. Then the left-hand side of equation (7) becomes 𝛿 𝑧𝑡> 0 so that 𝑧𝑡→1 is optimal. Given that 𝑚𝑡=𝑧𝑡𝑎𝑡=𝑧𝑡(𝑘𝑡+𝑚𝑡) we need that 𝑚𝑡→∞ for 𝑚𝑡/(𝑘𝑡+𝑚𝑡)→1. Thus, people would demand an infinite amount of money balances and hoard cash. This is the conventional result following the Sidrauski model. The common explanation is that in a situation where the opportunity cost of holding money is nil, people would hold all 21 The following analysis is also interesting for another reason. Gesell advocated a "free money" and "free land" economy. For those the interest rate would eventually have to abolished and any form of credit would be free of interest according to his utopia. 22 More recent evidence for a range of countries can also be found in Desroches and Francis (20062007), Chart B1, and Yi and Zhang (2017), Figure 1. Review of Economic Analysis 16 (2024) 91-131 114 www.RofEA.org their resources in the form of real money balances. That is usually associated with the notion of a “liquidity trap”. 23 Figure 5: Long-Run US Interest Rates Source: Eichengreen (2015), p. 66, Figure 1 Case 2: Suppose 𝑖=0,𝜎=0 and 𝛽>0 . Then equation (7) may yield an interior solution satisfying 𝛿 𝑧𝑡=𝛽 1−𝑧𝑡⇔𝑚𝑡 𝑚𝑡+𝑘𝑡=𝛿 𝛽+𝛿⇔𝑘𝑡 𝑚𝑡=𝛽 𝛿 The important implication here is that 𝑧𝑡<1 is optimal and so the presence of a “love of wealth”-motive (𝛽) makes a liquidity trap less likely. That should be clear from the motive itself. If people value (physical) capital they will not try to get rid of all their capital in order to hoard only cash. 23 The term and concept of a "liquidity trap" was well known by British economists before Keynes's publication of the "General Theory of Employment, Money and Interest", who actually never used the term himself. For details on that and some clarifications on misconceptions in current discourse on the phenomenon of a "liquidity trap" see Barens (2011). REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 121 www.RofEA.org Department (MPD) (2016) concludes that, all in all, the negative effects were "modest" over the short periodfrom November 2016 to February 2017. Importantly, remonetization is running in the opposite direction of demonetization. Thus, we would expect the opposite of the short-run effects captured by Proposition 7. Finally, it ought to be recognized that it is still an unresolved issue whether the policy objective to combat non-legal activities and transactions was successfully achieved by the Indian demonetization episode. 4 Conclusion About one hundred years ago Silvio Gesell argued that money should 'rot' as any other good does. He advocated a monetary system, which he called "Free Money", where fiat (paper) money would be legal tender and irredeemable. He argued that depreciation of such money (cash) in circulation would be stimulative for economic performance and be socially beneficial. In this paper, I question the claim that his ideas for an unconventional monetary policy cannot really be verified in modern economic theory frameworks. To this end I focus on four hypotheses Gesell made and analyze these using standard contemporaneous macroeconomic theory. The following findings of Part I of the analysis are then noteworthy. In a short-run, IS-LM-AS-AD-like demand-determined equilibrium where the (physical) capital stock, the inflation rate, transfers, and money supply are fixed, but real factor prices are flexible, Gesell's hypotheses are all valid, given the (demand) micro-foundations of the model which feature utility directly derived from money and 'love of wealth', and physical capital is taken to be the true source of wealth. This short-run analysis also implies that money depreciation can be a policy option to overcome the zero lower bound problems of nominal interest rates. Furthermore, an interpretation of the economic effects of the recent demonetization episode in India is possible from the model. Hence, in the present model framework, Gesell's claims can be verified for a short-run environment. This may explain why there has been renewed interest in his way of thinking in the present economic, post-Great-Recession situation. One major insight of the analysis of Part I is, therefore, that in the short-run, demand-determined equilibrium all of Gesell's claims can be ascertained. Of course, the analysis faces several caveats. The setup of the model is simple. Alternative utility and production functions might imply more complicated equilibria or the lack thereof. The introduction of fiscal policy may make the results less clean. 'Love of wealth' was captured by a constant. This begs the question of how changes over time in the 'love of wealth' may bear on the optimal paths. These and other extensions of the model are left for further research. Review of Economic Analysis 16 (2024) 91-131 122 www.RofEA.org Appendix A Absolute and relative wealth Suppose the relative wealth of an individual 𝑖 is given by; 𝑥𝑖=𝑘𝑖 ∑ 𝑘𝑗 The relative wealth is the (absolute) level of wealth 𝑘𝑖 in relation (relative) to total wealth (wealth of all people). If that individual's preferences are 𝑢𝑖(𝑐𝑖,𝑥𝑖), then consumption 𝑐𝑖 and relative wealth 𝑥𝑖 would matter for person 𝑖 's welfare. If there are many people, 𝑗=1,…𝑁 where 𝑖∈[1,𝑁] with 𝑁 very large, the effect of changes of 𝑘𝑖 by individual 𝑖 has no discernible bearing on total wealth ∑𝑘𝑗 where the summation is from 1 to 𝑁. ⬚ 29 If the utility function of individual 𝑖 is logarithmic, 𝑢𝑖=ln 𝑐𝑖+𝛾ln 𝑥𝑖=ln 𝑐𝑖+𝛾ln 𝑘𝑖−𝛾ln ∑ 𝑘𝑗 then the decisions of individual 𝑖 about 𝑐𝑖 and 𝑘𝑖 would not have an effect on 𝛾ln ∑𝑘𝑗 which would be a datum for individual 𝑖. That follows from the assumption that there are many people. Those arguments justify what is mentioned in the text. B Derivation of equation (2) The steps leading to this equation are 𝑐𝑡+(𝑘˙𝑡+𝑚˙𝑡)+(𝑛𝑡𝑘𝑘+𝑛𝑡𝑚𝑡)+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑘𝑡+𝑥𝑡 𝑐𝑡+𝑎˙𝑡+𝑎𝑡𝑛𝑡+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑘𝑡+𝑟𝑡𝑚𝑡−𝑟𝑡𝑚𝑡+𝑥𝑡 𝑐𝑡+𝑎˙𝑡+𝑎𝑡𝑛𝑡+𝜋𝑡𝑚𝑡+𝜎𝑚𝑡 =𝑤𝑡+𝑟𝑡𝑎𝑡−𝑟𝑡𝑚𝑡+𝑥𝑡 and so 𝑎˙𝑡=𝑤𝑡+𝑟𝑡𝑎𝑡+𝑥𝑡−𝑎𝑡𝑛𝑡−(𝑟𝑡+𝜋𝑡+𝜎)𝑚𝑡−𝑐𝑡. Rearrangement yields equation (2) . 29 This is almost always assumed in this literature. See, for example, Corneo and Jeanne (2001b). REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 123 www.RofEA.org C Derivation of equation (15) From (𝛿+𝛽)𝑐=(𝑟+𝜋+𝜎)𝑚−𝑟𝑎+𝜌𝑎 one gets that (𝛿+ 𝛽)𝑐 =(𝑟− 𝑟)𝑚+ (𝜋+ 𝜎)𝑚− 𝑟𝑘+𝜌(𝑚+𝑘) =(𝜋+ 𝜎)𝑚− 𝑟𝑘+(𝜋+𝜎)𝑘−(𝜋+𝜎)𝑘+𝜌(𝑚+𝑘) =(𝜋+ 𝜎)(𝑚+ 𝑘)− (𝑟+ 𝜋+ 𝜎)𝑘+𝜌(𝑚+ 𝑘) which becomes equation (15) by the Fisher relationship 𝑖=𝜋+𝑟. D Derivation of equation (16) From equation (14) we get 𝑐[𝛿/𝑚−𝛽/𝑘]=𝑖+𝜎. Substituting this in equation (15) implies 𝑐(𝛿+ 𝛽) =[(𝜋+ 𝜎)(𝑚+ 𝑘) −𝑐[𝛿/𝑚− 𝛽/𝑘]𝑘+ 𝜌(𝑚+𝑘)] =(𝜌+𝜋+ 𝜎)(𝑚+ 𝑘) − 𝑐[𝛿(𝑘/𝑚) − 𝛽] 𝑐[(𝛿+ 𝛽) + 𝛿(𝑘/𝑚) −𝛽] =(𝜌+ 𝜋+ 𝜎)(𝑚+ 𝑘) 𝑐[𝛿+ 𝛿(𝑘/𝑚)] =(𝜌+ 𝜋+ 𝜎)(𝑚+ 𝑘) 𝑐𝛿[𝑚+𝑘 𝑚] =(𝜌+𝜋+ 𝜎)(𝑚+ 𝑘) Rearrangement then yields equation (16), that is, the expression for 𝑐. To obtain the expression for 𝑖ˆ substitute the last expression for 𝑐𝑡 in equation (14) to get; (𝜋+𝜎+𝜌)⋅𝑚 𝛿=(𝑖+𝜎)[𝛿 𝑚−𝛽 𝑘]−1 (𝜋+ 𝜎+ 𝜌)⋅ 𝑚 𝛿⋅[𝛿 𝑚−𝛽 𝑘]=(𝑖+𝜎) From this equation (17) and so the expression for 𝑖 follows in a straightforward way. E The zero lower bound on nominal interest rates In short-run equilibrium the nominal interest rate is at the zero lower bound, 𝑖=0, when; (𝜋+𝜎+𝜌)((1−(𝑚 𝑘)(𝛽 𝛿))=𝜎 The total differential of equation (21) with respect to 𝜎 and 𝑚 yields Review of Economic Analysis 16 (2024) 91-131 124 www.RofEA.org (1−(𝑚 𝑘)(𝛽 𝛿))𝑑𝜎−(𝜋+𝜎+𝜌)(1 𝑘)(𝛽 𝛿)𝑑𝑚=𝑑𝜎 which can be simplified to; −𝑑𝜎 𝜎(𝜎 𝜋+𝜌+𝜎)=𝑑𝑚 𝑚 or 𝑑𝜎 𝜎=−(𝜋+𝜌+𝜎 𝜎)𝑑𝑚 𝑚 This relationship upholds 𝑖ˆ=0 when one of the policy instruments is changed. Thus, a onepercent increase in one instrument requires a corresponding percentage decrease in the other one. Now recall 𝑐∣𝜎=0,𝑖=0=(𝜋‾+𝜌)⋅𝑘 𝛽=(𝜋‾+𝜌)⋅𝑚0 𝛿 and 𝑐∣𝜎>0,𝑖=0=𝑚1⋅𝜎[𝛿−𝑚1 𝑘⋅𝛽]−1 where the indexation 𝑚𝑖,𝑖=0,1 expresses the fact that 𝑚 will be lower when 𝜎>0, that is, 𝑚1<𝑚0. I want to check whether 𝑐∣𝜎=0,𝑖=0⋛𝑐∣𝜎>0,𝑖=0. To this end let us suppose 𝑐∣𝜎=0,𝑖=0≤ 𝑐∣𝜎>0,𝑖=0. Then (𝜋‾+𝜌)𝑘 𝛽≤𝑚1⋅𝜎[𝛿−𝑚1 𝑘⋅𝛽]−1, where, of course, 𝑘=𝑘‾. Then rearrangement implies; (𝜋‾+𝜌)𝑘 𝛽⋅[𝛿−𝑚1 𝑘⋅𝛽] ≤𝑚1⋅𝜎 (𝑘 𝑚1)(𝛿 𝛽) ≤𝜋+𝜌+𝜎 𝜋+𝜌 . This inequality also holds when one takes logarithms. Thus, the claim would have to be that; ln 𝑘− ln 𝑚1+ln (𝛿 𝛽)≤ln (𝜋+𝜌+ 𝜎) − ln (𝜋+ 𝜌) Taking the total differential of this expression yields that −𝑑𝑚1 𝑚1≤𝑑𝜎 (𝜋+𝜌+𝜎)=𝑑𝜎 𝜎(𝜎 𝜋+𝜌+𝜎) REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 125 www.RofEA.org would have to hold. But as can be ascertained from above, both sides of this inequality are equal when 𝑖=0 is upheld. Hence, the introduction of money depreciation coupled with a lower money stock when 𝑖=0 does not bear on consumption in equilibrium when the economy's interest rate is at the zero lower bounds. This is the argument presented in the main text. F Quotes 30 • "The material part of the money has for economic life about the same importance that the leather of a football has for the players. The players do not concern themselves with the material of the ball, or with its ownership. Whether it is battered or dirty, new or old, matters little; so long as it can be seen, kicked or handled the game can proceed. It is the same with money. Our aim in life is an unceasing, restless struggle to possess it, not because we need the ball itself, the money-material, but because we know that others will strive to regain possession of it, and to do so must make sacrifices. In football, the sacrifices are hard knocks, in economic life they are wares, that is the only difference. Lovers of epigram may find pleasure in the following: Money is the football of economic life." (Gesell (1920), p. 78. • "Money requires the State, without a State money is not possible; indeed the foundation of the State may be said to date from the introduction of money. Money is the most natural and the most powerful cement of nations. The Roman Empire was held together more by the Roman currency than by the Roman legions. When the gold and silver mines became exhausted, and coins could no longer be struck, the Roman Empire fell asunder." (Gesell (1920), p. 81. • (*“Usually when a German wants anything he also wants the opposite.", Bismarck. (Gesell (1920), p. 82.) • "This revenue of the currency administration is an accidental by-product of the reform and is comparatively insignificant. The disposal of this revenue will be specially provided for by law. (*For other methods of applying the principle of Free-Money see page 245.) p.124" • "In all conceivable circumstances, in fair weather and foul, demand will then exactly equal: - The quantity of money circulated and controlled by the State. Multiplied by: The maximum velocity of circulation possible with the existing commercial organization. What is the effect on economic life? The effect is that 30 These quotes may or may not be included in a published version. Review of Economic Analysis 16 (2024) 91-131 126 www.RofEA.org we now dominate the fluctuations of the market; that the Currency Office, by issuing and withdrawing money, is able to tune demand to the needs of the market; that demand is no longer controlled by the holders of money, by the fears of the middle classes, the gambling of speculators or the tone of the Stock Exchange, but that its amount is determined absolutely by the Currency Office. The Currency Office now creates demand, just as the State manufactures postage stamps, or as the workers create supply. When prices fall, the Currency Office creates money and puts it in circulation. And this money is demand, materialized demand. When prices rise the Currency Office destroys money, and what it destroys is demand. Thus, the Currency Office controls the tone of the market, and this means that we have at last overcome economic crises and unemployment. Without our consent, the price level can neither rise nor fall. Every movement up or down is a manifestation of the will of the Currency Office, for which it can be made responsible. Demand as an arbitrary act of the holders of money was bound to cause fluctuations in prices, periodic stagnation, unemployment, and fraud. Free-Money makes the price level dependent on the will of the Currency Office which uses its power, in accordance with the purpose of money, to prevent fluctuations. Confronted with the new money everyone will be forced to conclude that the traditional custom of storing up reserves of money must be abandoned since reserve money steadily depreciates. The new money, therefore, automatically dissolves all money hoards, those of the careful householder, of the merchant and of the usurer in ambush for his prey." p. 127. • "Under Free-Money, when sales slacken and prices decline, the explanation is no longer given that too much work has been done, that there has been overproduction. We now say that there is a shortage of money, of demand. Whereupon the National Currency Office puts more money in circulation: and since money is now simply embodied demand, this forces prices up to their proper level. We work and bring our wares to market - that is supply. The National Currency Office then considers this supply and puts a corresponding quantity of money on the market - that is demand. Demand and supply are now products of labour. There is now no trace of arbitrary action, desires, hopes, changing prospects, or speculation, left in demand. We order just the amount of demand that we require, and just this amount is created. Our production, the supply of goods, is the order for demand, and the National Currency Office executes the order." p. 134 REHME Silvio Gesell's Schwundgeld Reconsidered, Part 1 127 www.RofEA.org • "And Heaven help the controller of the Currency office if he neglects to do his duty! He cannot now, like the administration of the old Banks of Issue, entrench himself behind platitudes about having to satisfy "the needs of commerce". The duties imposed on the National Currency Office are sharply defined and the weapons with which we have equipped it are powerful. The German mark, formerly a vague, indefinite thing, has now become a fixed quantity, and for this quantity, the officials of the Currency Office are held responsible. We are no longer the sport of financiers, bankers, and adventurers; we are no longer reduced to waiting in helpless resignation, until, as the phrase used to be, "the state of the market" has been created and improved. We now control demand; for money, the supply of which is in our power, is demand - a fact which cannot be too often repeated or too strongly emphasized. We can now see, grasp and measure demand - just as we can see, grasp and measure supply. Much produce - much money; less produce - less money. That is the rule of the National Currency Office, an astonishingly simple one!" p. 134 • "Many of those who have learned to separate money from gold, who have renounced the heresy of "intrinsic value" and convinced themselves of the importance of stable prices will now be inclined to argue as follows: Why not simply manufacture paper-money and bring it into circulation as soon as supply has overtaken demand or, in other words, when prices begin to fall? And conversely: Why not withdraw paper money from circulation and burn it when demand begins to exceed supply, that is, when prices begin to rise? This is merely a question of quantity: a lithographic press and a fireplace put it in your power to adapt demand (money) so exactly to supply (the wares) that prices remain constant." p. 111 • "Freemoney is not redeemed by the Currency Office. Money will always be needed and used, so why should it ever be redeemed? The Currency Office is, however, bound to adapt the issue of money to the needs of the market in such a manner that the general level of prices remains stable. The Currency Office will therefore issue more money when the prices of goods tend to fall, and withdraw money when prices tend to rise; for general prices are exclusively determined by the amount of money offered for the existing stock of goods. And the nature of Free-Money ensures that all the money issued by the Currency Office is immediately offered in exchange for goods." p. 123 • "The masses of paper money hoarded by private individuals (all private fortunes would finally have assumed that form) might any day have been set in motion Review of Economic Analysis 16 (2024) 91-131 128 www.RofEA.org by some trivial event, and this money, being only redeemable in the market in exchange for goods, would suddenly have become an enormous mass of demand which the State would have been powerless to control by means of the bonds and long-term bills. " p. 156 • "The sale of the currency stamps creates a regular annual revenue for the Currency Office. This revenue of the currency administration is an accidental by-product of the reform and is comparatively insignificant. The disposal of this revenue will be specially provided for by law." p. 124 • "The money reform deprives the Banks of Issue of the privilege of issuing banknotes. Their place is taken by the National Currency Office which is entrusted with the task of satisfying the daily demand for money. • The National Currency Office does not carry on banking business of any kind. It does not buy or sell bills of exchange, it does not classify business firms as first, second and third rate. • To put free money in circulation all public treasuries are instructed to exchange, when requested to do so, the old national metal money or paper money for free money; one dollar (franc, or shilling) of free money being given for one dollar (franc, or shilling) of the old money. • Anyone not consenting to this exchange may keep his gold. No one will compel him to exchange it; there will be no legal pressure; no force will be employed. The public is merely warned that after the lapse of a certain term (1,2 or 3 months), the metal money will be only metal and no longer money. If by that time anyone still possesses metal money he is free to sell it for Free Money to a dealer in precious metals, but he must bargain about the price. The only form of money recognised by the State will be free money. Gold, for the State, will be a mere commodity like wood, copper, silver, straw, paper or fish oil. And just as today taxes cannot be paid in wood, silver or straw, so gold will not be available for the purpose of paying taxes after expiration of the term for exchange." p. 124. • "With Supplementary Free-Money the legal depreciation is compensated in each transaction by a supplementary payment by the holder of the note, as at present in many countries with the purchase tax (sales tax). Theoretically, the principle of free money could be applied by a continuous regular inflation of prices of 5% annually, with, to protect creditors, a corresponding modification of longterm money contracts. 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