In his important book, Basic Principles of Economic Value, Eugen von Böhm-Bawerk develops, among other important concepts, his basic law of prices and includes a footnote that is both intriguing and worthy of exploration.
In the narrative associated with the footnote (p. 119), Böhm-Bawerk develops his law of prices (pp.107-129) by using the now-standard chart showing the subjective values of a group of horse buyers and sellers. Chart 1 (reproduced below), shows that five horses will be bought and sold at a market price somewhere between $210 and $215.
Notice that in the market range of $210 to $215, not all horses are sold since some sellers value their horse more than the established market price (sellers 6, 7, and 8). In the footnote, Böhm-Bawerk reorders the values so that the sellers’ valuations are in descending order similar to the buyers’ set of values (chart 2 below). He then notes that if the buyers and sellers sought out each other in this manner, all available horses would have been sold. This intriguing situation is worthy of further exploration since it is always important to investigate the possibilities of a government helping-hand with regard to the market.
A question arises: If government intervened to coercively pair buyers with sellers in the manner that the chart in the footnote details (chart 2 below) and forced exchanges based solely on the pair at hand’s valuations (e.g. Buyer 1 and Seller 8, Buyer 2 and Seller 7, etc.), ignoring an aggregate market price, would the society of horse buyers and sellers be better off?
First, we have to look at how value is increased through voluntary exchange and then apply that knowledge to the intervention.
Value has a subjective magnitude. Individuals participate in voluntary exchanges if and only if they expect ex ante an increase in subjective value ex post due to the exchange.
Based on the market established in chart 1, Buyer 1 will exchange with Seller 1 at some price between $100 and $300. Regardless of the price, an increase of $200 is recorded to subjective valuations of this two-person society since the buyer values the horse $200 more than the seller; while the buyer and seller simply split the cash based on the agreed upon price.
The pre-exchange valuations show the buyer holding $300 in cash with the seller holding a $100 horse. Should the price have been $200 for the exchange, the buyer now has a $300 horse and $100 in cash while the seller has $200 in cash. This shows a $200 increase in subjective valuation.
Any other price for the horse simply moves cash from one holder’s account to the other; buyer's to seller's, or visa versa. The money price has no effect on the increase in the subjective valuation to the buyer over the seller of the exchanged horse. The money price only affects the decision to exchange or hold, money prices do not change valuations subjective to the individual actors.
The aggregate valuation increase for the larger society as detailed in chart 1 is calculated by summing the valuations of the more-capable buyers – those able to purchase a horse on the market – and subtracting from that total the summed valuations of the associated sellers. In the example, the aggregate increase due to the exchanges is $570.
What would be the aggregate increase to society due to a government intervention that coercively paired buyers with sellers?
Using chart 2, sum the valuations of capable buyers and subtract the sum of the valuations of the associated sellers. In this instance, there are eight buyers and sellers. The result, an increase of $435, shows that the coerced exchange reduced the aggregate subjective valuation gain.
More horses were sold but less value was created. This intervention, like all government interventions, is a net loser.
Moreover, and more importantly, the losses due to the coerced exchanges are not found only in the hypothetical market created by Böhm-Bawerk, the loss of subjective valuation occurs regardless of the make-up of the market. In addition, this can be extended to show that government cannot tax valuation "left on the table"  and increase the aggregate subjective valuation since all government would be doing is reducing cash-holdings through taxation. The subjective valuations remain what they are regardless of the exchange price.
Additionally, if government would then use the cash generated through taxation to subsidize exchanges that would not have occurred naturally in the market, the aggregate net valuation would suffer a loss – just as it did under a coerced exchange – and the cash-holdings would be reduced by the inefficiencies of government.
Based on a superficial analysis, coerced exchanges appear to lead to greater satisfaction. Aren’t more horses traded? Isn’t more cash passed between buyer and seller? The answer is yes to both. However, the unseen is as important as the seen. On the surface, government appears to be a market catalyst for good, while the hidden results proves that interventions lead to a loss of value and cash-holdings.
Governments opt for the seen as their continued power is based on trumpeting their interventions of the obvious; governments then blame the final results, lost values and cash-holdings, on someone or something else altogether.
Yet, this is exactly what government does when it alters the normal actions of individuals through taxation or other coercive forces, such as subsidies, etc. Nothing good results simply because nothing good can result from coerced changes to the free market.
 Valuation “left on the table” is value external to the exchange, viz. the subjective value Buyer 1 assigns to the horse, $300, that is that is greater that the market price, between $210 and $215 in this instance. Some suggest that government should levy a tax of either $90 or $85 respectively so that the value the buyer attributed to the horse is paid in a combination of market price and taxation. The belief is that this combination would capture all value generated by the exchange. As noted above, government simply decreases the aggregate valuation and cash-holdings of society through such interventions.
Jim Fedako [send him mail], a former professional cyclist who lives in Lewis Center, OH, is a member of the Olentangy Local School District and maintains a blog: Anti-Positivist.
note: refer to Mises.org blog posting for chart 2.