Real Prices and Ideal Prices - Are Prices Exact?

Are Prices Exact?

Money-prices are numbers, and numbers can be computed with exactitude. This seems to make accounting and economics exact sciences. But in the real world, prices can change quickly, due to innumerable conditions and it may be that prices can only be estimated approximately for budgetary or contractual purposes. In aggregating them, a judgement is made about the meaning of the transactions involved, and boundaries are defined for where they begin and end. Consequently, in calculating price quantities, a value theory of some sort is usually applied, regardless of whether this is made explicit or not. And, typically, this value theory refers to prices which would apply under certain assumed (theoretical) conditions, moving between real prices and ideal prices.

Mathematics professor John Allen Paulos at Temple University states the general problem encountered here clearly:

"A well-known quotation usually attributed to Einstein is “Not everything that can be counted counts, and not everything that counts can be counted.” I’d amend it to a less eloquent, more prosaic statement: unless we know how things are counted, we don’t know if it’s wise to count on the numbers. The problem isn’t with statistical tests themselves but with what we do before and after we run them. First, we count if we can, but counting depends a great deal on previous assumptions about categorization. (...) Second, after we’ve gathered some numbers relating to a phenomenon, we must reasonably aggregate them into some sort of recommendation or ranking. This is not easy. By appropriate choices of criteria, measurement protocols and weights, almost any desired outcome can be reached."

It may of course be that not "almost any desired outcome can be reached" in price calculations, insofar as one would have to deny relevant evidence. Nevertheless it may be that several different outcomes are possible, or that the presence of biases in interpreting price information can make a significant quantitative difference to the result (see further phenomenology (science)). Insofar as economic actors have a vested self-interest in a particular quantitative result, because their income is at stake, then there is the possibility that they will prefer "one sort of calculation" to another, because it yields a financial result that favours their own position. That financial result may be reasonably "credible" or "plausible" for the purpose of trading - if it was way out of kilter, trading partners would reject it - but it could involve a margin of distortion of the true situation. The small discrepancies would ordinarily not matter so much in individual transactions, but if a very large number of transactions is added up, the distortion might represent a substantial income for someone. For example, on 27 June 2012, Barclays Bank was fined $200m by the Commodity Futures Trading Commission, $150m by the United States Department of Justice and £59.5m by the Financial Services Authority for attempted manipulation of the Libor and Euribor rates (see Libor scandal).

In an interview, the late Benoît Mandelbrot cited Louis Bachelier's thesis that prices have only one parameter defining their variability: they "can only go up or down" - and that, then, seems to provide a robust logical foundation for the mathematical modelling of price movements. But this sidesteps the qualitative problem that many different prices can be calculated for the same good, for all kinds of different purposes, using different valuation assumptions or transaction conditions. Bachelier's idea already assumes that we have a standard way to measure prices. Given that standard, one can then perform all kinds of mathematical operations on price distributions. Yet tradeable objects can also be combined and repackaged in numerous different ways, in which case the referent price may not simply go up or down, but instead refers to a different kind of deal. This issue is wellknown to official statisticians and economic historians, because they face the problem that the very objects whose price movements they aim to track change qualitatively across time, which may necessitate adjustments of the classification systems used to provide standard measures. A good example of that is the regimen of the consumer price index, which is periodically revised. But in times of rapid social change, the problem of devising a standard measure may be much more pervasive.