# A Currency’s Command over Real Output in a Nutshell

In principle, a currency’s command over any category of real input or output can be considered in terms of a suitably defined price index. The present focus is on the aggregate level and, in particular, a currency’s command over real final output. Earlier posts explore the topic in greater depth (links below). This is a crib notes version.

A currency’s command over real final output – loosely, the amount of real stuff a currency unit can purchase – will remain stable so long as the average level of prices remains stable. Partly for this reason, price stability is generally regarded as a desirable property of well-functioning economies.

For a given distribution between wage and profit income, price stability requires nominal wages to rise in line with productivity. This maintains a currency unit’s command over real final output while reducing its command over society’s labor time. It might seem counterintuitive, but the latter needs to happen (in a context of rising productivity) if price stability is to be maintained.

Three simple equations help to crystallize the point. Let the price level be represented by P, one plus the average markup over nominal wages k, the average nominal wage w, and average productivity y. Then, by accounting identity,

P = kw/y

This emphasizes that the price level will rise if (one plus) the markup and nominal wage, in combination, rise faster than productivity.

The price level can be related to currency value. In MMT, the value of the currency is defined to be “what must be done to obtain it”. One measure of currency value consistent with this definition is

z = 1/(kw)

The value of the currency, according to this measure z, is the amount of society’s average labor time represented by a currency unit. Like the price level, currency value depends on the markup and nominal wage. But unlike the price level, currency value is independent of productivity (or, at least, not directly affected by it).

For specificity, take the dollar to be the currency unit. One way to gauge a dollar’s command over real output is to multiply currency value by productivity. This works because currency value is measured in hours per current-year dollar whereas productivity is measured in base-year dollars per hour. Accordingly, their product is measured in base-year dollars per current-year dollar. The product of currency value and productivity therefore indicates the amount of base-year dollars (the dollars in which real output is evaluated) that are commanded by a current-year dollar, and so provides an index of a currency’s command over real final output.

Multiplying currency value by productivity also spells out the obvious correspondence between a currency’s command over real output and price stability. Multiplying both sides of the equation for currency value by productivity and making use of the earlier identity for the price level (which enables kw/y to be replaced by P) gives

yz = 1/P

The index of the currency’s command over real final output is nothing other than the reciprocal of the price level. Both a currency’s command over real final output and the price level will remain stable provided movements in the value of the currency are offset by counter movements in productivity.

To summarize the main implication, it is okay that a unit of the currency typically gets easier to come by over time (that currency value tends to decline) if productivity is improving at a comparable rate (to offset the effect on the price level). So long as this is the case, the currency’s command over real final output remains stable.

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