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Market values are not additive, according to Edward Fullbrook, essentially because demand curves are downward sloping. This assertion appears to challenge not so much economics as accountancy. When the government assesses your estate for death duties it adds up the various assets at their current price and is not inhibited by the thought that if some asset were doubled in quantity, its price would decline. It does seem that different issues are being conflated in Fullbrook’s fascinating book.
Let us agree with one of the central contentions of the book that – values are essentially relative. Since prices are determined in market exchange the price of a good, and therefore the value of any given quantity of it, is determined only in relation to that of other goods. No single good can serve as a numeraire and this leads to the conclusion that Aggregate Market Value (AMV) is the only solid basis for value calculations and the value of a good or collection of goods can be expressed as a fraction of AMV. These fractions are, however, additive at any point in time – as the Inland Revenue will insist.
The difficulty comes when we seek to make comparisons across time with change in either prices or quantities (however the latter are measured). If there were some substance whose quantity was always equal to AMV, sub-quantities of it could correspond to any fraction of AMV and therefore represent the value of any good. No single good, however, could play the role of an ideal numeraire, inter-temporally, if subject to the usual law of demand. People try to use money but we know the length of the yardstick fluctuates as a function of money supply.
Relativity leads straight back to the problem of index-numbers. Simply to illustrate, and at the risk of trivialisation, consider a two-good economy with a single relative price, which is subject to the law of demand. We have ten apples and ten pears and we suppose they exchange at an equal price. AMV is therefore 20 whether measured in apples or pears, each of which constitute half of AMV. Now another pear tree is discovered and the number of pears rises to 12. Fullbrook makes play of the fact that price may fall faster than quantity rises when prices are inelastic. So let’s suppose the price moves so two pears are now needed to buy an apple. Does this mean AMV has fallen or that we cannot measure it?
In state two if we measure AMV on the apple standard, it has indeed fallen from 20 to 16. Measured on the pear standard, however it has increased from 20 to 32! In either state the value of apples and pears is additive but how do we compare the two states? If we are interested in quantity comparisons we can apply the prices of state one to both states. This gives a rise in AMV from 20 to 22. |Or we can make the comparison using the prices of state two, which means AMV has risen from 15 to 16. Different price bases give different results but both imply an increase in AMV. In a two-good world without money there is no such thing as inflation since there is only one price and what it does to the apple standard is perfectly offset by the pear standard. A pure inflation refers to a change in prices relative to something basic like labour time (the wage unit) or some synthetic numeraire like money. Define an arbitrary standard and you can define inflation.
This all makes perfectly clear the treacherous nature of value comparisons across different states of the world, with respect to time or space which separates markets. It also raises awkward questions about time aggregation. The value of production in a given day is meaningful (you can aggregate additively across the hours) but the value of annual production is more dubious and may require the use of indexation.
In the presence of relativity, we know measurements depend on your situation. You have to freeze a price set to measure quantities and different price sets will give different answers. The answers are numerical, i.e. cardinal not simply ordinal, but they are conditional and not unique. This makes the testing of hypotheses about economic growth or inflation complicated, requiring more careful attention to data than is often afforded. It is unclear, however, just how Boolean algebra is supposed to help. It is a powerful tool but what concrete question would it elucidate?
We must beware of the trap of essentialism. The point is not to define AMV in abstract but to consider what questions we want to ask about the real world and what definitions best serve the purpose at hand.
According to the “Timeline Of 20th And 21st Century Wars” by The Imperial War Museum (https://www.iwm.org.uk/) “Conflict took place in every year of the 20th Century; the world was free from the violence caused by war for only very short periods of time. It has been estimated that 187 million people died as a result of war from 1900 to the present. The actual number is likely far higher.”
There is no such thing as linear growth in the political economic history of our era. Much of what has been projected and perceived as civilization, technological advances and wealth creativity, has buried the truth in the theories of selective pretension constructed by those groomed with well healed financial rewards to clear the path with a selective retention and reboot the system over and over to start again.
This was a great outline of the truth; but the names have been erased to protect the truth-line from the ruthless self perpetuating status quo.
After reading Schlaudt’s article, my first thought was: how refreshing! Here’s one academic who can think critically and precisely. Most academic work nowadays are so ill thought out, with casually introducing categories that rely on informal language rather than on properly defined terms arising from proper research.
Anyhow, given that in his response Fullbrook does not engage with any of Schlaudt’s questions, rather leaving answers to readers, I understand the following comments might be helpful.
1. On the second paragraph, about “price formation meet[ing] the requirements of proper measurement” I refer to footnote 31 in Varoufakis and Arnsperger (2009): Debreu was always clear in his mind that out-of-equilibrium formalism is impossible. So much so that he, in fact, also rejected stability analysis: “(W)hen you are out of equilibrium, in economics you cannot assume that every commodity has a unique price because that is already an equilibrium determination.”
2. On ‘empiricism’ versus ‘constructivism’ – very good point. Some academics’ obsession with framing arguments within given categories is not always productive. Depending on context, as is the case, the critique may require one’s positioning outside strict categories of thought.
3. Utility being infamous (p.111), so must demand also be, no? I refer to the famous Sonnenschein-Mantel-Debreu theorem.
4. On the law of demand as a causal relationship: very good question. If one is arguing that economic reality has an irreducible macro dimension, then as a logical consequence, quantity and price determination must occur in tandem.
5. Given point 4, the answer on the existence of the Law of Demand is now straightforward: indeed, heterodox economics remains burdened with too much neoclassical heritage. Properly advancing a ‘methodological revolution’ (p.113) is way overdue.
6. On question 2 about ‘depend on’: as I see it, quantity and price should be defined in algebraic dual spaces. No causality, neither up-down nor down-up.
7. On Boolean algebra and the ontology of commodities: if we should discard the concept of ‘demand’, then on the same vein shouldn’t question the concept of ‘market’? Indeed, a market is already some sort of artificial partitioning of the whole economic environment. Isn’t ‘market’ too much of a neoclassical heritage?
8. Further on Boolean algebra: yes, I agree, we need intersections. That’s required in order to construct ‘markets’ or hopefully something better conceived that will play the role currently played by markets.
Fullbrook’s and Schlaudt’s discussion is fascinating, particularly because most economists are aware that the conceptual framework that they use to address their questions of interest is full of logical shortcomings. Yet, they seem unable to break free of old concepts such as utility and demand functions. To me, this is an example of that that Lakatos would call a ‘degenerate research programme’. I will in due course approach Schlaudt directly and hope that we may then continue this conversation.