Proof of the Invisible Hand: Why the satisficing purchase becomes optimal?

Abstract

The paper develops the systematic analysis of the self-organization mechanisms of the imperfect market under price dispersion by means of the "labor-search-leisure" model. The model proves the fact that the inequality of the marginal values of search, produced by the satisficing decision, ends with the consumption-leisure corner solution where the consumer quits the market without purchase. If the consumer tries to get rid of the disappointment of the search, he exits from the corner and the first offer, which corresponds to his aspiration level, becomes satisficing as well as optimal; it equalizes the marginal values of the search and maximizes the consumption-leisure utility. The match of the satisficing and optimal buying decisions opens the door for a deeper analysis of the self-organization of the imperfect market. If the consumer evaluates correctly his purchasing power and his real wage rate before he starts to work and to search, the unit elasticity of the costs on purchase with respect to consumption automatically makes optimal any quantity purchased for the given time horizon. However, the unit elasticity rule tells nothing about the distribution of labor and search costs; it simply states the fact that this distribution is optimal and it equalizes the marginal costs of search with its marginal benefit. The act of the successful buying proves the fact that the total consumer efforts on the search and the purchase are unit elastic with respect to consumption. It means that the unit elasticity rule is followed by some inner pricing mechanism. This mechanism leads the self-interested producer to make an offer, which provides the automatic optimal consumer's labor-search trade-off and proves in this way the hypothesis of the "invisible hand".