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Revista Mexicana de Economia y Finanzas, Vol.1, no.2, 2002. ... Moeda. XVI Anais da Associação Nacional de Centros de Pós-Graduação em Economia.
THE VALUE OF LIQUIDITY

LEONARDO FERNANDO CRUZ BASSO Universidade Presbiteriana Mackenzie Rua da Consolação, 896 – 2º andar – Sala 213 Consolação – São Paulo – SP – 01302-907- Brazil Tel: +55 (11) 2114-8597 Fax: +55 (11) 2114-8600 Cel: +55 (11) 9109-4098 AND-mail: [email protected]

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Electronic copy available at: http://ssrn.com/abstract=1083995

ABSTRACT The objective of this article is to examine four theories that consider an explanation and measurement for the value of liquidity. Liquidity will be understood as cash, that is, we are leaving aside assets of lesser degree of liquidity than cash. The article begins with the Keynesian view about the value of liquidity followed by an exploration of the value of currency in accordance with the Marxists, neoclassical economists and classical economists (Ricardians

and

Sraffians).

The message of all models is clear. Liquidity always has a positive value, being differentiated in the measurement of it by the value model underlying the theory. This point of view contrasts with naive proposals on the value of liquidity that only consider the opportunity cost to hold currency, leading to the conclusion that the value of liquidity is null or negative.

Key Words Liquidity, Value of liquidity, Value of money, Own rates of interest, Keynesian Theory of Money, Marxist Theory of Money, Classical (Sraffian Theory of Money), Neoclassical Theory of Money. JEL: A13,B12, B13, B14,B24, D46, D51, E11, E12, E13, E51, F00

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Electronic copy available at: http://ssrn.com/abstract=1083995

The Value of Liquidity Liquidity is one of the most difficult topics in economics. Brealey&Myers (2000) admit at the end of their textbook that there is not yet any satisfactory answer to the value of liquidity (Chapter Thirty Five of the book: What we do and do not know about finance, page 1014). Unlike treasury bonds, currency retention does not spawn interest. On the other hand, currency retention spawns more liquidity than securities. People that maintain currency in their possession believe that the loss of interest is offset by the benefit of retaining currency. In the balance the marginal value of additional liquidity equals the interest rate. Brealey&Myers (2000) rule out two explanations as simplistic: 1- Explanations that rule out the benefit and say that the cost of maintaining currency is the loss of interest. This would imply concluding that cash always exhibits a negative net present value (NPV). 2- The declaration that because the marginal value of liquidity is equal to loss of interest, it does not matter how much cash the company retains. This would imply alleging that currency retention always exhibits null NPV.

They also declare that the marginal currency value (cash) declines with the size (sum) of cash, which is disputable for those that argue that the marginal currency value does not change. Intuitively this can be perceived when a person is of middle class origin and purchases a car. If he or she wins the lottery and can acquire a castle, does the marginal value of each monetary unit applied in the castle afford less pleasure? We would answer in the negative.

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Electronic copy available at: http://ssrn.com/abstract=1083995

Brealey&Myers (2000) indicate another problem with liquidity: that it is a question of degree. A Treasury bond has a lower liquidity level than cash, but it is still a note with high liquidity because it can be sold and transformed into cash easily and almost instantaneously. The obligations of companies have less liquidity than Treasury bonds; trucks are less liquid than the obligations of companies; a specialized machine has less liquidity than trucks, and so on successively. But even specialized machinery can be converted into cash if the owner is willing to accept some advance payment and some cost of sale. Hence the main question is not "how much cash should the company retain?" but "how can it divide its total investment between relatively liquid and relatively illiquid assets?", maintaining everything else constant of course. This is a difficult question to answer. All companies should obviously be prepared to obtain funds on the short term, but as emphasized by Brealey&Myers (2000), we do not have resource to a good theory about the sum of funds considered sufficient or about the speed at which the company should be able to raise these funds. To make the matter even more complicated, we draw attention to the fact that funds can be quickly obtained through loans, with the sale of other securities, or with the sale of assets. A financial manager with an unused credit line of $ 1 million can sleep just as easily as another whose company has $ 1 million in marketable securities. Although they reject simplistic explanations about the value of liquidity, Brealey&Myers (2000) do not present an alternative theory for it. The objective of this article is to examine four theories that consider an explanation and measurement for the value of liquidity. Liquidity will be understood as cash (the famous limited conception of cash, paper currency in the possession of the public, plus demand deposits of the public at commercial banks), that is, we are leaving aside assets with lesser degree of liquidity than cash. Besides this introduction the article also contains a Keynesian view of the value of liquidity in section 2; an exploration of the value of money according to

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the Marxists in section 3; the neoclassical explanation for the value of money in section 4, concluding with the Sraffian view in section 5. The message of all models is clear. Liquidity always has a positive value, being differentiated in the measurement of it by the value theory underlying the model. 2- Keynes and own-rates of interest of assets. According to Keynes (General theory, chapter 17) different types of asset have three attributes in different degrees: a- Some assets produce a yield or output q, measured in terms of themselves, by assisting some process of production or rendering services to a consumer; b- Most assets, except money (currency), suffer wastage or involve some expense through the mere passage of time (regardless of any change in their relative value), whether they are used to produce a yield or not; in other words, they imply carrying cost c, measured in terms of themselves. Intuitively, a person that purchased a flat for the purpose of earning a profit (for retirement, for example) is familiar with the anxiety caused by the carrying costs of this flat when it is not possible to accrue rent; Keynes argues that for the purposes of his explanation (or if you prefer, of his model) the line separating the costs that should be deducted before calculating q and those that should be included in c does not matter. In other words, he is only concerned with the difference, q – c; c- last but not least, the power of disposal over an asset during a period may offer potential convenience or assurance that is not the same for assets of a different nature. There is no result in the form of production at the end of the production period, nevertheless people are willing to pay a price. Keynes calls this price the liquiditypremium (designated l) that people are willing to pay for the potential convenience or

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assurance afforded by the power of owning it (emphasizing that we should exclude the inherent yields or carrying costs thereof).

The discovery that assets in general possess three attributes that confer value, leads Keynes to conclude that the total reward that people expect to enjoy with the ownership of an asset is equal to its yield minus its carrying cost plus its liquidity-premium, i.e., (q – c – l). This expression represents the specific interest rate expected from any asset. A better detailing of the own-rate of interest concept is relevant at this point. According to Keynes the money-rate of interest is the percentage excess of money of a sum of money contracted for forward delivery over what we may call the spot or cash price of the sum thus contracted for forward delivery. He argues that for each category of capital assets there should be a rate similar to that of interest on currency. Since there is a finite and defined quantity of wheat to be delivered a year hence which has the same exchange value today as 100 quarters of wheat for spot delivery: If the former quantity is 105 quarters of wheat we may say that the wheat-rate of interest is 5% per annum and if it is 95 quarters, that it is minus 5% per annum. Thus for every durable commodity we have an own-rate of interest calculated in terms of the actual asset, a wheat-rate of interest, a house-rate of interest, a steel-plant-rate of interest! Keynes emphasizes the difference between spot markets and forward markets that bear a definite relation to the wheat-rate of interest, and that as forward contracts are quoted in currency for forward delivery and not in wheat for spot delivery, and

this difference also

depends on the money-rate of interest. The relation is as follows, using the same example as Keynes:

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Let us suppose that the spot price of wheat is 100 pounds per one hundred quarters and that the price of wheat in a forward contract for delivery a year hence is 107 pounds per one hundred quarters and that the money-rate of interest is 5%. What is the wheat-rate of interest? 100 pounds today buy 105 for forward delivery and 105 for forward delivery will buy (105/107) multiplied by one hundred, i.e., 98 quarters on the same terms. In turn 100 pounds today will buy 100 quarters of wheat for spot delivery. Accordingly, 100 quarters of wheat for spot delivery will buy 98 quarters in a forward contract. On a basis of which it is concluded that the wheat-rate of interest is minus 2% per year. Keynes continues by asserting that assets differ and consequently so do their own-rates of interest. The characteristic of a capital asset (a steel plant, for example) or of a consumer good (a car, for example) is that its yields exceed the carrying costs and that the liquidity-premium is negligible. On the other hand, currency exhibits a null yield, an insignificant carrying cost (that of custody) and an exceptional liquidity-premium. Finally, some assets like wheat are branded by a carrying cost that surpasses the yield and exhibit an insignificant liquidity-premium. Having said this, let us designate the yield of the houses as q1, while their carrying cost and liquidity-premium is zero; c2 is the carrying cost of wheat, while its yield and liquiditypremium are null, and the liquidity-premium of the currency as l3, while the other two components are insignificant. This reduces our reasoning to: q1- interest rate of the houses; c2- interest rate of the wheat;

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l3- interest rate of the currency. Heretofore the interest rates were measured in terms of themselves. To determine the relation between the expected yields, Keynes argues that it is necessary to know the variations expected to occur in their relative values during the analysis period. Adopting the currency as measurement standard and assuming that the percentage of valuation (or devaluation) of the houses is a1 and that of wheat is a2, Keynes reduces the three interest rates to rates that can be compared in monetary terms: a1 + q1 = money-rate of interest of the houses; a2 – q2 = money-rate of interest of the wheat; l3 = money-rate of interest of the currency. The decision about which good to produce will depend on which of the three sums is the highest, with the reminder that the money-rate of interest is not determined microeconomically, but depends on the macroeconomic interaction between demand and supply of currency, whereas the supply is controlled (directly or indirectly) by the government in the opinion of Keynes. It will be profitable to produce houses or wheat in so far as the money-rate of interest thereof supplants that of currency. Although not important for our argument here, the crucial difference between currency and other assets is that the supply is fixed and on account of this characteristic, its quantity cannot be increased at will, which is not the case of the other assets. The increase of their supply can bring about a reduction in the own-rate of interest, besides entailing an increase in the carrying costs if we assume that the incremental cost increases with the increase of quantity (although this assumption is not necessary for our argument, i.e., we can assume carrying cost by constant unit). Let us imagine an economic agent that wants to invest 100 reais to produce wheat.

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Each kilo of wheat costs one Real, and the agent buys 100 kilos of wheat. There is a relation here between a monetary unit and a quantity of merchandise, which we should emphasize as Keynes is emphatic in asserting that his theory is a monetary theory of production, turning away from the neoclassic model. At the end of the production process the agent obtains 110 kilos of wheat, i.e., a rate of profit of 10%. This is equivalent to 10 Reais, the money rate of profit. At this point we need to simplify the issue and assume that the money rate of profit (obtained in production) is equal to the interest rate of wheat (obtained in future markets, i.e., in the exchange). In other words, as soon as the producer begins the production process of wheat, he knows the selling price and makes a hedging operation in the forward market. The investment will only make sense to the economic agent if the (long term) interest rate of the currency is lower than 10%. Otherwise it will fail. If the money has been contracted at a short-term interest rate above 10%, the agent will need to renegotiate the bank loan. Going by Keynes´ argument, the interest rate of wheat in terms of itself needs to surpass the money-rate of interest plus the carrying cost. ( a2 higher than l3 + q2). Whenever this happens the agent benefits from maintaining the currency, as it is part of the wheat production process. In other words, considering the benefits minus the costs, the currency in the possession of the producer exhibits a net benefit of a2-l3-q2. This is the value of liquidity for Keynesians. 3- The value of money to Marxists Liquidity is a sum of cash (the limited conception of cash, paper currency in the possession of the public plus demand deposits of the public at commercial banks. Consequently, each unit of liquidity is equivalent to one unit of cash multiplied by the value of this unit. To define the value of liquidity in the Marxist universe let us consider the value of money as conceived by theoretical exponents of this theory. (Hilferding, 1981; Dumenil, 1980; Foley,

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1982). A theory for the utilizing the Marxist concept was proposed (Basso,2002) and tested (Basso, Silva e Chang, 2003). The value of money can be conceived by the division of the domestic product of a country by the quantity of hours of work spent on the production of the GDP (PIB in Portuguese). This is a macroeconomic variable and a variation herein means a variation in the value of money. This expression can be written in distinct, yet equivalent ways: M = PIB/HT M = (P. Q)/ HT M = (P . Q)/ (N . HTI) Where M = Marxist value for money; PIB = gross domestic product; HT = hours of work spent on the production of the GDP (we ignored the traditional Marxist distinction between productive and unproductive work – any work that produces surplus is productive) P = price index for the product (Implicit deflator of the gross domestic product); Q = index of quantity for the product (to achieve coherence, when one is determined by the Laspeyres formula, the other should be determined by the Paasche formula); N = number of individuals employed in the generation of the GDP; HTI = hours of individual work, by individual. These expressions should be expressed in terms of growth rates: Mˆ = Pˆ + Qˆ − Hˆ T Mˆ = Pˆ + Qˆ − Nˆ − HTˆI

Mˆ = Pˆ + PRODˆ TRAB

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Mˆ = Pˆ + PRODˆ FIS − HTˆI

Where Pˆ

= variation in the value of money

= variation in the price index;

Qˆ = Nˆ



variation in the index of quantities;

= variation in the number of individuals employed in the production of the GDP;

HTˆI

= variation in the average rate of hours worked by individual;

PRODˆ TRAB = PRODˆ FIS

variation in the productivity of hours worked (quantity of goods by hour worked);

= variation in the physical productivity (goods by working individual)

These expressions have a counter entry (counterpart) in the aggregates of national income. The calculation of wealth produced by a nation in a period of time can be expressed by: I=S+L+A+J+R Where: I + income; S = salaries; L= profits; A = rental; J = interest; R = income from land. The division of the aggregate income (I) by the sum of hours worked to produce it leads to an alternative expression for the value of money: I/ HT = value of money from the perspective of income; S/ HT = salary by hour of work; L/ HT = profit by hour of work; A/ HT = rental by hour of work; J/ HT = interest by hour of work; R/ HT = income from land by hour of work; where HT = hours of work spent on the production of the GDP (we ignored the traditional Marxist distinction between productive and unproductive work – any work that produces surplus is productive). Also knowing that: S (aggregate salary) = s (average salary) multiplied by the number of workers ( NT ); 11

L = rate of profit ( l ) multiplied by the capital utilized to produce it ( K); A = rate of rental ( a )multiplied by the real estate capital to produce it ( KI); J = interest rate (j ) multiplied by the financial capital to produce it ( KF); R = rate of income ( r ) multiplied by the stock of land to produce it ( KT), We can rewrite the expression as: VALUE OF MONEY (perspective of income) = [ (s. NT)/ (NT. hti) ] +[ ( l . K)/ ( NT. hti) ] + [ ( a KI)/ ((NT. hti) ] + [( i.KF)/ (NT. hti)] + [ ( r. KT)/ (NT. hti)], Which can be simplified as: VALUE OF MONEY = salary by hour of work + profit by hour of work multiplied by the intensity of the productive capital (capital by worker) + interest by hour of work multiplied by the intensity of the financial capital (financial capital by worker)+ rental by hour of work multiplied by the intensity of the real estate capital (real estate capital by worker) + income from land by hour of work multiplied by the intensity of the agricultural capital (agricultural capital by worker). The expression can also be expressed in terms of growth rates: Variation in the value of money = variation in the salary-hour + variation in the profit-hour + variation in the rental-hour + variation in the interest-hour + variation in the income-hour + variation in the intensity of the productive capital + variation in the intensity of the financial capital + variation in the intensity of the real estate capital + variation in the intensity of the agricultural capital. One aspect must be clear: neither the variation of prices alone, nor the variation of productivity alone, explain the variation in the value of money. We need to consider all the factors. A positive variation of one, offset by a negative variation in the other, can keep the value of money altered. This value determined macroeconomically is an item of data for an individual company.

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This is the value of liquidity to Marxists. On the other hand, the same expressions that were calculated for macroeconomics can be calculated for an individual company, and in actual fact are simpler as they do not involve the problems of aggregation of national accounts. M = PIB/HT M = (P. Q)/ HT M = (P . Q)/ (N . HTI) Where PIB = value added by the company, or equivalently the multiplication of prices by the quantities of final goods of the company (P . Q); HT = hours of work spent on the production of the product of the company; N = number of employees utilized in the production of the company; HTI = individual hours of work (an average value, in the absence of individualized calculations; the average allows us to get rid off individualized calculations). The growth rates that we defined for the economy are applicable to a company: Mˆ = Pˆ + Qˆ − Hˆ T Mˆ = Pˆ + Qˆ − Nˆ − HTˆI Mˆ = Pˆ + PRODˆ − HTˆI

The previous information is also applicable here. The individual value for the company can vary (or remain the same) according to growth rates of the prices and of productivity that compensate one another, requiring an evaluation of what happens to all the factors. Everything that was said about the aggregate of the economy (as concerns the aggregates of income) applies to an individual company, whereas the expression is simplified because the company divides its product between capital and work: VALUE OF MONEY (to the company) = salary by hour of work + profit by hour of work multiplied by the intensity of the productive capital (capital by worker); 13

Variation in the value of money (to the company)= variation in the salary-hour + variation in the profit-hour + variation in the intensity of productive capital.

Whether we regard the situation from the perspective of the product or of income, both expressions define a value of money for the company. This value can be above or below the national average. It can be above or below the sector where the company competes. The comparison between the value of national money (or of the sector where the company competes) defines a liquidity-premium for the company. As we deem it more relevant to evaluate the company in the sector where it competes, the premium should be calculated in relation to the sector. But we do not have relevant arguments if it is alleged that the calculation should be compared to that of the economy as a whole. In other words, the decision to keep cash in the circuit of productive capital (to utilize an expression of Marx’s) proves desirable if the production of a higher value of money for the company than that of the sector where it competes is to be expected. If the company fails, it can still transform the sum of money left over into the goods that it can purchase with this money. The value is never negative.

4- the value of money in the neoclassical model The microeconomic neoclassical model obtains a positive value for cash. (Pindyck, 2006). The theory of consumer behavior is based on three assumptions about preferences: 1 completeness: consumers are capable of comparing all the market baskets and arranging them in order. This arrangement in order is performed considering units of goods, where the prices are not taken into consideration;

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2- transitivity: meaning that if a basket A is preferable to a basket B, which in turn is preferable to a basket C, then A is preferable to C; 3- non-satiety: meaning that more is always better than less, and the consumer is never satiated. These three assumptions are sufficient to build the indifference curves, the locus of points where the consumer is indifferent among different quantities of goods from a given basket. The negative slope of the indifference curves is the measure of its marginal rate of substitution, that is, the quantity of a good that this consumer is willing to forsake to acquire a unit of the other good. Indifference curves can be obtained without the need to talk about money. Money enters the model with the budgetary restriction of the consumer. A budget line indicates all the combinations of a basket of goods that can be acquired with a given income. The slope of the budget line is equal to the ratio of the prices (with the negative sign). Contending that consumers exhibit a satisfaction maximizing behavior, it is shown that the marginal rate of substitution is equal to the relation of prices. We need one more step to arrive at a positive value for money. The marginal rate of substitution is related to the ratio of the marginal utilities of the two goods. Hence prices are also related to marginal utilities. This is an important result as it expresses that the maximization of utility occurs when the budget is allocated when the marginal utility by monetary unit spent is equal for both goods. As far as we are concerned at this point, as the value of money is associated with utility (and marginal utility) it cannot be negative or zero. In the sphere of macroeconomics the neoclassical theory also presents a positive value for money. The value in macroeconomic terms is derived from the quantitative theory of money, which determines the general price level.

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5-The value of money to Sraffians Marx’s presentation (1998) at the beginning of Capital about the circuit of productive capital, where the production process starts with a quantity of money M and ends with a quantity of money M, became famous'. Marx’s argument for this issue is that all goods enter and leave the production process with the same value (whereas most of them transfer their value when they are "destroyed" in the production process, except for one, the workforce that has the capacity to create more value than the amount that the capitalist pays for them). In Marx’s conception, profit stems from surplus production, which is appropriated by capitalists as they have control over the product of a resource (production factor) called workforce. Marx was sufficiently emphatic for us to perceive that the explanation for value creation should exclude the opportunistic behavior (with a strong presence in transaction cost economics), as value creation should be explained with goods being purchased at their value. Marxist economics makes a clear distinction between heat (quantity of work) and monetary price. The distinction does not exist to neoclassicists and we can talk about opportunity cost. The opportunistic behavior exacerbates the problem of appropriation of value, which occurs in the exchange, but does not explain the production of value. We do not need to have a theory of explanation of profit (i.e., value creation) as a work surplus appropriated by capitalists. Let us imagine a landowner that produces corn. To produce corn this landowner utilizes ten kilos of seed as a raw material and pays a laborer ten kilos of seed (subsistence salary determined socially). At the end of the process this owner harvests and sells 40 kilos of seed. The gross production of value was 40 kilos whereas 10 are “destroyed” in the production process (raw material), and 30 net kilos are left over for distribution between profits and salaries. In this case it boils down to “selling” to oneself 30 kilos of which 10 are utilized in production, 10 for own consumption and 10 to pay the worker.

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This landowner “produced” a surplus of 20 kilos which is his profit and consequently his appropriation of value creation. How is cash introduced in the model? To Sraffians (Sraffa,1960)(and we would also say to Ricardians (Ricardo)) value is calculated by establishing a good as currency (rice for example) and expressing a relationship between a monetary unit and a portion of rice (say a kilo). Any other value can be determined by the ratio of exchange between two products. For example, let us imagine that a kilo of rice can be exchanged for two kilos of corn. In this case the value of liquidity, expressed in terms of corn, is two kilos of corn. Although there is relativity in the sum of goods purchased, one thing is clear: quantities express positive values, which express a positive value for liquidity. In this model we can have two different conceptions for value creation. The ratio of exchange between currency and another good can be interpreted as a marginal rate of substitution between the currency (rice) and the other asset (corn). This ratio of exchange can be explained by the theory of utility-value. We can also move in the direction of a Marxist conception, introducing a theory of labor values to explain the ratio of exchange. What should be clear is that regardless of the theory of value supporting the ratio of exchange among goods in this model, the value of money is never negative.

Conclusion We present four theoretical streams that explain the value of money. In all of them the value is not negative. At any moment in time the value of liquidity for an individual is translated as the quantity of goods that this person can purchase with the sum of cash (synonym for its liquidity).

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We should emphasize that the value of this liquidity depends on the economic theory that lies behind this liquidity. To the Sraffians (and we would also say to the Ricardians) value is calculated establishing a good as a currency (say rice) and expressing the ratio between a monetary unit and a portion of rice (a kilo, for example). Any other value can be determined by the ratio of exchange between two products. For example, let us imagine that a kilo of rice can be exchanged for two kilos of beans. In this case the value of liquidity, expressed in terms of beans is two kilos of beans. Although there is relativity in the sum of goods purchased, one thing is clear: quantities express positive values, which express a positive value for liquidity. The Marxists go even further than this, asking what makes the comparison of disparate quantities possible, arguing that there are quantities of work behind all production (simple and complex work which, although representing the reality of the production process where human capital is essential, makes the analysis more complex, the reason why we left over (complex labor) in this analysis (discussion). The macroeconomic relation can be established between the production of a country (the gross domestic product) and the hours of work spent to produce this product. This relation establishes a sum of dollars by hour of work. Once again, as hours of work are not negative quantities, the value of liquidity cannot be negative, as it represents a portion of cash. An interesting issue arises at this point: I can calculate the value of money for a given company, simply dividing the value added by this company by the hours of work required to produce it. For a company with considerable operational efficiency, this value can be higher than that found for a country. In other words, the value added by hour of work for a particular company can be higher than the value of money for a nation. Does this mean that the value of liquidity for a given company can be defined regardless of the value of national currency, in the Marxist conception? The answer is no, because the

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macroeconomic relation (the value of money to a country) is determined by the sum (interaction) of values of moneys for individual firms. There is no incompatibility between the microeconomic and macroeconomic universes. Finally, to today’s hegemonic economic school of thought, the marginalist theory, the relationship between a quantity of cash (liquidity for its owner) and a sum of goods that this quantity of cash can buy is established by the utility of the commodities. Since utilities can decrease, but are never negative, the value of liquidity cannot be negative. This entire discussion of ours is based on a point in time, i.e., the instant value of liquidity, which cannot be negative. What needs to be explored in a future article is how the various economic schools deal with the variation of the value of money (liquidity) over time.

Bibliographical References BASSO, Leonardo Fernando Cruz. An Alternative Theory for Exchange Rate Determination. Revista Mexicana de Economia y Finanzas, Vol.1, no.2, 2002. BASSO, Leonardo Fernando Cruz. Hilderfing e o Problema da Conceituação do Valor da Moeda. XVI Anais da Associação Nacional de Centros de Pós-Graduação em Economia (ANPEC). Belo Horizonte, December 1988. Basso, Leonardo Cruz, da Silva, Roseli and Chen Chang, Susana, "A Marxist Theory for Exchange Rate Determination: An Empirical Investigations" (October 8, 2003). Universidade Presbiteriana Mackenzie Economics Working Paper. Available at SSRN: http://ssrn.com/abstract=457020 or DOI: 10.2139/ssrn.457020 BREALEY, Richard A.; Myers, Stewart C. Principles of Corporate Finance, sixth edition; Irwin McGraw-Hill, New York, 2000. DUMENIL, G. (1980). De la Valeur aux Prix de Production, Econômica, Paris.

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FOLEY, D. (1982). The Value of Money, the Value of Labor Power and the Marxian Transformation Problem. Review or Radical Political Economy. Summer. HILFERDING, Rudolf. Finance Capital. Routledges & Kegan Paul, London, 1981. KEYNES, J.M (1964). The General Theory of Employment, Interest and Money. Harbinger Books, United States. MARX, Karl (1998). O Capital, Volume I. Editora Civilização Brasileira, 16th Edition, Rio de Janeiro. PINDYCK, Roberto S., RUBINFELD; Daniel L. MICROECONOMIA. 6.Ed. trad. PRADO, Eleutério; GUIMARÃES, Thelma. São Paulo: Pearson Prentice Hall, 2006. RICARDO, D. (1821) on the Principles of Political Economy and Taxation. In the Works and Correspondence of David Ricardo. Vol. 1. ed. P. Sraffa, Cambridge: Cambridge University Press, 1951. SRAFFA, P. (1960) Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press. MODIGLIANI, Franco; MILLER, Merton H. The cost of capital, corporation finance, and the theory of investment. American Economic Review, v. 48, p. 655–669, 1958. Ricardo, D. (1821) On the principles of political economy and taxation. In the works and correspondence of David Ricardo. Vol. 1. ed. P. Sraffa, Cambridge: Cambridge University Press, 1951. Sraffa, P. (1960) Production of commodities by means of commodities. Cambridge: Cambridge University Press.

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