The Greatest Happiness of the MINIMUM Number

I uploaded the manuscript titled "Equal Market Design I: Competitive Market Achieves the Greatest Happiness of the Minimum Number" at SSRN a month ago, which has been downloaded more than 500 times so far! I would like to say big thanks to all of those who kindly red it :)

The main purpose of the paper is to clarify the trade-off between efficiency and equality when redistribution by the third party is infeasible, which has not been documented (at least in a clear manner) in the literature. As a somewhat striking result, we show that the number of agents who engage in trades under market equilibrium must be minimum among all Pareto efficient and individually rational allocations. (provided that Pareto efficiency is modified from the standard definition in order to incorporate our presumption of no possible redistribution.)

While the market equilibrium (an intersection of supply and demand) maximizes total surplus, the sum of the agents' gains from trades measured in monetary value, it inevitably generates the agents who are left-behind from any trades. Moreover, the number of such left-behind agents are maximized through the competitive market. The intuition behind the result can be illustrated by the following figure.

In the figure, the number of successful trades or trade volume is 2. Consequently, 4 agents, 2 buyers and 2 sellers, are left-behind. As I explain in the paper, we can strictly increase the number of (mutually beneficial) trades if alternative buyer-seller matchings are possible. While such allocations reduce total surplus, equality is improved in the sense that more agents can enjoy surplus from trades and less agents become left-behind. That is, there exists a trade-off between efficiency (= total surplus) and equality (= trade volume).

The above finding is not restricted to a specific example; I formally show that there exists a strictly more equal allocation than the competitive equilibrium under very weak assumptions. Therefore, we could essentially say that equilibrium allocations under competitive markets are most unequal (if Pareto efficiency and individual rationality are considered to be least requirements for any sensible allocation). This finding may suggest a potential limitation of market economy even if no market failure is presupposed.

To check the further argument, please click here and download my paper! It is extremely short (the current version has only 8 pages), intuitive, and non-technical. In fact, it is by far the least technical among the papers that I have ever written, but I believe that its message and policy implication are the most significant.

For example, consider a labor market. My finding implies that employment is minimized if the market works competitively. By contrast, some frictions or social mechanisms that prevent the market from being competitive may help to create additional job opportunities. This insight is consistent with the findings in experimental economics in its early literature: decentralized markets typically result in excess quantity. See my blog article "Chamberlin vs. Smith in Roth (1995)" for the detail.


P.S.
I am now trying to extend the model from a homogeneous good market to a general two-sided matching market with monetary transfers. New findings will soon be available!