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Currency Value, Productivity, and a Currency’s Command over Use-Values

Summary:
In general terms, Modern Monetary Theory (MMT) defines the value of the currency as “what must be done to obtain it”. As MMT authors have noted, this general definition can be interpreted in terms of labor time. A Marxist interpretation, consistent with MMT’s general definition, is to define currency value in terms of socially necessary labor time. Two interpretations seem particularly suitable. A first approach is to define currency value as the reciprocal of the average money wage. This measure indicates the amount of labor-power that must be supplied in exchange for a unit of the currency and, on average, the amount of socially necessary labor that is performed in exchange for the currency unit. A second approach is to define currency value as the reciprocal of the monetary

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In general terms, Modern Monetary Theory (MMT) defines the value of the currency as “what must be done to obtain it”. As MMT authors have noted, this general definition can be interpreted in terms of labor time. A Marxist interpretation, consistent with MMT’s general definition, is to define currency value in terms of socially necessary labor time. Two interpretations seem particularly suitable. A first approach is to define currency value as the reciprocal of the average money wage. This measure indicates the amount of labor-power that must be supplied in exchange for a unit of the currency and, on average, the amount of socially necessary labor that is performed in exchange for the currency unit. A second approach is to define currency value as the reciprocal of the monetary expression of labor time (MELT). This measure indicates the amount of socially necessary labor represented in a currency unit and therefore the amount of abstract labor represented in a currency-unit’s worth of any commodity, including labor-power, which under capitalism is treated as a commodity. The two definitions are closely and simply connected. They are also closely connected to other macro measures such as the price level and average productivity.

 
Meaning of currency value under the two interpretations

To distinguish the two alternative conceptions of currency value, let zw denote currency value when defined as the reciprocal of the average money wage and let z denote currency value when defined as the reciprocal of the MELT. Currency value, under either interpretation, is measured in hours of socially necessary labor per unit of the currency. Taking the dollar to be the currency unit, a currency value of x hours per dollar says that x hours of socially necessary labor are in some sense equivalent to a dollar. The precise sense in which an amount of labor time and the currency unit are equivalent depends on the specific interpretation of currency value adopted.

Currency value as zw. According to Marx, the average money wage paid for an hour of simple labor-power or its equivalent will, as a tendency, be at the level necessary for the cultural reproduction of workers’ labor-power. Let w represent the average money wage actually paid and w* the level to which it tends. Under the first interpretation of currency value, currency value is 1/w, which in Marx’s theory tends to 1/w*.

One relevance of currency value under this interpretation is that it gives a measure of how difficult it is to obtain use-values of a particular nominal value. To know that the average price of a basket of consumer goods is currently P and that this average price has risen over the past year by p percent tells us that the goods have risen in price but does not tell us whether these goods have become easier or more difficult to obtain. But if we also know that the average money wage has risen by x percent over the same time period, it will be clear whether the goods are easier or harder to acquire simply by comparing the price rise to the fall in currency value (equivalent to the rise in money wages) in percentage terms. The decline in currency value means that the currency unit is easier to obtain; the price inflation means that more currency units are needed to purchase the goods. If 1/w falls proportionately more than P rises, the goods actually become easier to obtain, despite the higher price level.

Currency value as z. If the MELT is denoted m, currency value under the second interpretation is 1/m. The MELT indicates the amount of nominal monetary value that is generated in an hour of the labor process. Partly, this monetary value is created directly through labor (the expenditure of labor-power) and partly it is transferred from materials, plant and equipment that are the result of earlier production periods. Conversely, the reciprocal of the MELT, or currency value under the second interpretation, indicates the amount of labor that is currently required to generate (through both value creation and value transference) one currency unit of commodity value.

The MELT is the conversion factor between money and labor time. Multiplying labor-time values by the MELT gives monetary values. Dividing monetary values by the MELT gives labor-time values. Since currency value under the second definition is the reciprocal of the MELT, this measure of currency value likewise can be used to switch between labor-time and monetary values.

 
Three levels of macroeconomic analysis

Many variables of interest in macroeconomics can be viewed on three levels or in three dimensions. Marx, especially, gave strong consideration to all three levels and their interconnections.

On one level, there are ‘real’ labor-time (or real value) measures, quantified in hours of labor (for Marxists, hours of socially necessary labor). Real value measures based on labor time cannot be obtained by aggregating amounts of heterogeneous concrete labor. The different kinds of concrete labor must first be made commensurable. In reality, this commensurability is achieved socially. Real labor-time measures must reflect the way labor is compared socially (on the basis of what Marx referred to as abstract labor). When diverse concrete labors are paid the same money wage, society in fact behaves – whether knowingly or unknowingly – as if these different concrete labors are in some sense equivalent. Similarly, when one type of concrete labor is paid more than another type, society behaves as if the first type is in some sense equivalent to a multiple of the second type and that both types of labor can be viewed as multiples of some basic kind of social labor. For Marx, complex labor is a multiple of simple labor; similarly, for Keynes, special labor is a multiple of ordinary labor. All this implies the operation of a social process in which different concrete labors are made commensurable by abstracting from their differences and only considering what they have in common as expenditures of socially necessary effort, with complex or special labor in effect converted into equivalent amounts of simple or ordinary labor.

On another level of macroeconomic analysis, there are ‘real’ use-value measures pertaining to physical output and physical wealth. Heterogeneous physical commodities, just like heterogenous concrete labors, cannot be aggregated. In practice, the measure of physical output is a monetary one but deflated by a suitable price index. A comparison of the ‘real’ (i.e., monetary but deflated) output of two different periods is meant to give us an idea of whether physical output has, in some sense, increased or decreased; whether, loosely speaking, we are producing more stuff now than before. Of course, it is a question with no answer if interpreted literally, because the question of whether an output of three fridges and two computers is “more” than an output of two fridges and three computers is not well defined until we specify a common unit of measurement. But once we agree to measure fridges and computers and other goods and services in currency units, the aggregation can proceed on a uniform basis. The choice of a currency unit in which to aggregate is not merely something that economists do arbitrarily but something that has been dictated by society acting in a way that has made these heterogeneous items expressible in currency units. For Marxists, since value is socially necessary labor time, and since commodities are the result of socially necessary labor, commodities are values, and so commensurable. Likewise, because the currency unit represents an amount of socially necessary labor, the currency can express commodity values. This makes it possible to sum up quantities (specifically, monetary quantities) of diverse goods and services to arrive at a single measure (nominal output PQ) which can then be adjusted for movements in the level of prices in an effort to isolate – at least conceptually – the part of nominal output that reflects the physical quantities of goods and services Q rather than the level of prices P.

On a third level of analysis are purely nominal measures, meaning monetary measures that have not been adjusted for movements in prices. Total nominal output, total money wages and total monetary profit are notable examples. Viewed in isolation, a single nominal measure is not very informative. However, unlike real labor-time and real use-value magnitudes, nominal measures are observable and so easier to evaluate. Further, a comparison of nominal measures over time can have strong macroeconomic significance. For example, if nominal income grows less rapidly than nominal private debt, the burden on private debtors is becoming heavier over time, which will hold implications for the sustainability of the current level of private nominal spending.

Importantly, there are key conversion factors that enable us to switch easily between the three levels of macroeconomic analysis. The link between ‘real’ labor-time values and ‘real’ use-value measures is the level of average productivity. The link between ‘real’ use-value measures and nominal values is the price level. And, as already mentioned, the link between ‘real’ labor-time values and nominal values is the MELT (or, equivalently, currency value when interpreted as the reciprocal of the MELT).

 
Behavior of currency value under the first interpretation

When currency value is interpreted as the reciprocal of the average money wage, currency value simply moves inversely to money wages:

Currency Value, Productivity, and a Currency’s Command over Use-Values

A dot indicates a time derivative and g a growth rate. Whatever drives the determination of the average money wage also drives movements in currency value under the first interpretation of currency value.

 
Behavior of currency value under the second interpretation

Under the second interpretation of currency value, both the value of the currency and its reciprocal, the MELT, can be regarded as weighted averages of two components – a lagged component linking money and dead labor and a contemporaneous component linking money and living labor. The weights that apply in these averages are closely connected but distinct. For this reason, it is worth considering the behavior of the MELT before turning to the corresponding behavior of currency value.

The MELT. The MELT of time t can be expressed as a weighted average of the MELT that prevailed at the beginning of the current production period (at the time when inputs entered production) and what can be regarded as the monetary expression of living labor (MELL) that prevails at time t. Letting θ represent a phase of time corresponding to the average length of the production period,

Currency Value, Productivity, and a Currency’s Command over Use-Values

In (2), m is the MELT of time t, m–θ is the MELT of time t–θ and mL is the MELL at time t. The MELT of time t can be interpreted as the hourly rate at which nominal value is generated. It pertains to both ‘dead’ and ‘living’ labor, expressing the rate at which monetary value is generated (both transferred from dead labor and created by living labor). In contrast, the MELT of time t–θ, though it once pertained to both dead and living labor, by time t only pertains to dead labor (since the living labor of time t–θ is now dead). The relevance of this earlier MELT, the start-of-period MELT, is that it links dead labor (constant and variable capital expressed in labor time) to money. For this reason, the start-of-period MELT is also called the ‘input MELT’. The MELL, for its part, relates only to living labor. It is defined as monetary value added $VA divided by total productive employment L measured in hours of simple labor. That is, mL=$VA/L, where $VA=$v+$s, L=v+s, v and s are variable capital and surplus value, respectively, and a $ sign indicates a nominal marxian variable. The MELL is the amount of nominal value created by one hour of socially necessary living labor. Or, to say the same thing in a slightly different way, the MELL is the hourly rate at which nominal value is created.

The weights in (2) depend on λL, the proportion of living labor L in total value TV. Total value is the sum of constant capital c and living labor (or productive employment) L. That is, TV=c+L. Since λL=L/TV, and L/TV and c/TV must sum to one, 1–λL equals c/TP.

Over time, the MELT changes according to

Currency Value, Productivity, and a Currency’s Command over Use-Values

Whenever the MELL differs from the MELT of time t–θ, the MELT is tending toward the MELL at a rate dictated by the proportion of living labor in total value (λL). Typically, the MELL – equal to one plus the markup times the average money wage or, equivalently, average productivity times the price level – will be rising, with the MELT rising toward it.

Currency value as z. Much like the MELT, the currency value of time t can be viewed as a weighted average of two components. One component is the currency value that happened to prevail at an earlier time, z–θ. The currency value of time t–θ represents the amount of labor time currently needed (at time t) to transfer a currency-unit’s worth of value to output from inputs that entered production at time t–θ. The other component is the reciprocal of the MELL. The reciprocal of the MELL, zL, can be thought of as the ‘living labor value of the currency’. It is the amount of social labor currently needed (at time t) to create a currency-unit’s worth of commodity value. As the weighted average of these two components, currency value at time t is the amount of social labor currently required to generate a currency unit’s worth of value through a combination of new value creation and transference of pre-existing value.

Although the expression for z shown below is identical in form to that of the MELT just considered, there is a difference in the weights which here depend upon λ (as opposed to λL). Whereas λL is the quotient of two labor-time measures, λ is the quotient of two purely nominal measures, specifically, monetary value added $VA=$v+$s and nominal total value $TV=$c+$v+$s:

Currency Value, Productivity, and a Currency’s Command over Use-Values

Over time, the value of the currency changes according to

Currency Value, Productivity, and a Currency’s Command over Use-Values

Whenever zL differs from z–θ, the value of the currency is tending toward zL with the strength of this reaction now depending on λ, the share of monetary value added in nominal total value. For a given markup, growth in the average money wage causes zL to decline and currency value to fall toward it, with λ governing the rate of adjustment.

There is a close relationship between λ and λL. Specifically,

Currency Value, Productivity, and a Currency’s Command over Use-Values

Unless z equals zL, λL differs from λ. Conceptually, if we think of the average money wage as being revised periodically through the updating of a subset of employment contracts and suppose the markup roughly stable, then a periodic change in the average money wage will cause zL to change, setting off a process in which z converges on zL while λL and λ converge. In a steady state, z=z–θ, which implies, on the basis of (4), that

Currency Value, Productivity, and a Currency’s Command over Use-Values

Notionally, at any time, the value of the currency will be tending to whatever zL happens to be, but zL itself will be shifting according to the behavior of wages and prices, while the speed of adjustment will change if there is any variation in λ.

 
A currency’s command over use-values

A falling currency value does not necessarily imply a weakening of a currency’s command over use-values. Rather, a falling currency value implies either that workers can obtain the currency unit with less labor (interpretation 1) or that it takes less labor to generate a currency unit’s worth of monetary value (interpretation 2). If, in that time, workers are becoming more productive, it is quite possible for the currency’s command over use-values to remain stable or even strengthen despite a decline in the currency’s value. So long as average productivity is improving, it is actually desirable for currency value to fall over time at a comparable rate. Otherwise, the economy will be prone to deflation and its onerous effects.

Under most circumstances, it is somewhat easier to analyze the currency’s command over final goods and services than it is to analyze its command over all use-values (including fixed and circulating capital).

Command over final goods and services. A measure of a currency’s command over final goods and services can be obtained by multiplying average productivity y by the reciprocal of the MELL. Under the simplifying assumption that all labor is productive, average productivity is the amount of real output (meaning nominal output deflated by a suitable price index and expressed in base-year dollars) produced per hour of socially necessary labor, or $base/hr. The reciprocal of the MELL, equal to the ‘living labor value of the currency’ zL, represents the amount of socially necessary labor that it takes to create a current dollar’s worth of nominal value and so has the dimensions hr/$. Accordingly, the product yzL has dimensions $base/$ and indicates the amount of base-year dollars commanded by a current-year dollar. It is simply the reciprocal of the price level applying to final goods and services:

Currency Value, Productivity, and a Currency’s Command over Use-Values

Here, k is one plus the average pricing markup over money wages, w is the average money wage and P is the price level applying to final output. The third step in (8) makes use of the identity P = kw/y. The product yzL (or, equivalently, the reciprocal of the price level) tells us how much real (final) output a dollar currently commands.

Command over all goods and services. In the simplest scenario where productivity and currency value are held constant for some time, the value of the currency equals the ‘living labor value of the currency’ (that is, z=zL), implying on the basis of (8) that yz=yzL=1/P. In general, though, this is not the case.

As a first step in addressing the general case, the product yz (obtained by multiplying both sides of (4) by y) can be viewed as a weighted average of two components:

Currency Value, Productivity, and a Currency’s Command over Use-Values

The second component, yzL, is already familiar, equal to the reciprocal of the final goods price level (1/P). As just discussed, this measures a current (time t) dollar’s command over final output. The first component, yz–θ, has dimensions base-year dollars per t–θ dollar, or $base/$–θ. The product yz–θ expresses the amount of base-year dollars that were commanded by a dollar at time t–θ. This component reflects a dollar’s command over final output at the earlier time t–θ. This has some relevance to a dollar’s command over use-values at time t, since some final output of t–θ will have entered production as inputs at that time. But it would be more informative to multiply currency value by a different measure of productivity, one that pertained specifically to inputs.

Analytically, a simpler way to approach the general case is to define ‘total productivity’ as real total price T divided by total price TP expressed in hours of socially necessary labor. T is ‘real’ in the sense that it represents nominal total price $TP deflated by an appropriate price index PT that pertains to both inputs (fixed capital and intermediate consumption) and final output. TP, being the sum of dead labor c and living labor L, is a measure of ‘total labor’. Total productivity yT is then real total price divided by total labor:

Currency Value, Productivity, and a Currency’s Command over Use-Values

Real total price is the sum of real constant capital Yc and real net output (or real value added) Y. That is, T= Yc+Y. Real constant capital is equivalent to real capital consumption, which includes both real consumption of fixed capital and real intermediate consumption. Real constant capital is equal to nominal constant capital $c deflated by a suitable price index Pc. Real net output (or real value added) is equivalent to real net domestic product. It is obtained by deflating nominal net output using the price index P pertaining to final goods and services.

Applying these definitions, total productivity can be expressed as a weighted average of the narrower productivity measures applying to constant capital and value added. Starting from the definition of total productivity,

Currency Value, Productivity, and a Currency’s Command over Use-Values

Here, c/TP and L/TP are the weights 1–λL and λL encountered earlier, while Y/L is average productivity y. The remaining fraction Yc/c can be thought of as the productivity of dead labor, or yc. It is the real amount of fixed and circulating capital consumed per hour of dead labor. Total productivity can therefore be expressed as

Currency Value, Productivity, and a Currency’s Command over Use-Values

The notion of total productivity can be employed to simplify the analysis of a currency’s command over use-values. By identity,

Currency Value, Productivity, and a Currency’s Command over Use-Values

Rearranging,

Currency Value, Productivity, and a Currency’s Command over Use-Values

In this way, a currency’s command over all use-values (taking into account both inputs and final output) can be measured as the reciprocal of a suitable price index.

 
Price indices and a currency’s command over different kinds of use-values

In principle, a currency’s command over any category of use-value will correspond to the reciprocal of an appropriately devised price index. Just as 1/PT (equal to yTz) indicates a currency’s command over all use-values (accounting for both inputs and final output) and 1/P (equal to yzL) indicates a currency’s command over final goods and services, a currency’s command over consumed inputs can be viewed in terms of a price index that reflects the productivity of dead labor, yc, and the currency value that prevailed at the time inputs entered production, z–θ:

Currency Value, Productivity, and a Currency’s Command over Use-Values

The second step in (15) makes use of the assumption that constant capital enters production at time t–θ, which means that nominal constant capital $c is the product of the MELT of that time and constant capital expressed in labor time; that is, $c=m–θc. Since z is defined as the reciprocal of the MELT, $c=c/z–θ, implying z–θ=c/$c.

In theory, the price indices that apply to inputs, final output and all use-values are in a definite relationship with each other. Specifically, the total price index PT (or its reciprocal) can be viewed as a weighted average of the narrower price indices Pc and P (or their reciprocals).

Starting from the definition of the total price index,

Currency Value, Productivity, and a Currency’s Command over Use-Values

Noting that $c=PcYc and $VA=PY,

Currency Value, Productivity, and a Currency’s Command over Use-Values

The weights in this expression, Yc/T and Y/T, are related to λ and λL encountered earlier. But the weights in (17) are determined not by nominal magnitudes as in the case of λ, nor by labor-time magnitudes as in the case of λL, but by real (i.e., price-deflated) use-value magnitudes. Sticking with a similar notation for the weights, we can let

Currency Value, Productivity, and a Currency’s Command over Use-Values

so that 1–λY and λY are, respectively, the shares of real constant capital and real value added in real total price. Substituting into (17) gives

Currency Value, Productivity, and a Currency’s Command over Use-Values

This expression clarifies the relationship between the three price indices. However, as has been observed, a currency’s command over use-values is most easily represented by the reciprocals of the various price indices. Working once more with the total price index, this time with its reciprocal,

Currency Value, Productivity, and a Currency’s Command over Use-Values

Here, $c/$TP and $VA/$TP are the weights 1–λ and λ that depend upon nominal magnitudes. Noting that Yc/$c=1/Pc and Y/$VA=1/P,

Currency Value, Productivity, and a Currency’s Command over Use-Values

In expressing a currency’s command over all use-values, the currency’s command over consumed inputs and its command over final output are weighted in a way that reflects the share of monetary value added in nominal total price.

 
Summary of basic definitions and their meaning

Various definitions have been utilized throughout the discussion. These are summarized below, along with a brief recap of their meaning. Apart from the first definition, which concerns currency value interpreted as the reciprocal of the average money wage, the summary mostly deals with currency value interpreted as the reciprocal of the MELT. This is due to the added complications that this choice would introduce.

Currency Value, Productivity, and a Currency’s Command over Use-Values

Also at time t,

Currency Value, Productivity, and a Currency’s Command over Use-Values

When currency value is defined as the reciprocal of the MELT, multiplying the currency’s value by a suitable measure of productivity quantifies a currency’s command over use-values. Specifically,

Currency Value, Productivity, and a Currency’s Command over Use-Values

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