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Force of Invisible Hand, Labor, and Just Price: Basic Principles of Sorting and Matching Under Wage and Price Dispersion

If the consumer realistically evaluates the efficiency of his efforts on labor and search, the purchase any quantity demanded will be optimal. Under equilibrium price dispersion suboptimal satisfying purchases represent corner solutions. A buyer who does not claim the optimal purchase either leaves the market or buys optimally. The invisible hand stops the buyer’s search in time and at the place where and when the purchase price allocates his time optimally between labor, search, and leisure and thereby maximizes the utility of his consumption-leisure choice. The producer does not know how much time the consumer has spent on search and what is his willingness to pay. But it is enough for him to know the quantity demanded in order to accurately determine not only the price but also the meeting point. His working time is divided between the actual production and services, for example, the delivery of goods, which saves the consumer's leisure time. A virtual frontier of production possibilities arises where the manufacturer optimally sells goods and leisure to the consumer. Any point on the frontier represents the trade-off between the time spent on search by the consumer and the time spent by producer on the delivery. Sorting sellers and buyers by their industry and diligence, local markets segment the production opportunity frontier. The force of the invisible hand, i.e., the rate of mutual interest, is increasing with seller’s productivity and buyer’s wage rate. The matching occurs at the just price level, which provides the market equilibrium. This price optimizes the distribution of the buyer's time between labor, search, and leisure, and the seller’s time between production and delivery; it equates the producer’s marginal costs with his average cost and maximizes the buyer's consumption-leisure utility. In every local market, a just price also equates the seller’s markup with the actual buyer’s purchasing power. The concept of just price proposed in this article is consistent with both the theory of marginal utility and the labor theory of value.The transformation of producer’s time into consumer’s leisure time discovers the rate of their mutual interest or their gravitation, where its force is directly proportional to the product of quantity supplied and quantity demanded, and inversely proportional to the product of times the parties to the transaction have spent on it.