The research agenda is divided into the following topics: (1) perfect competition in large assignment models; (2) efficiency properties of competitive equilibrium with innovation; and (3) specialization and division of labor and monetary exchange. The first part involves extending the basic model assigning a finite number of individuals to a finite number of positions to one in which the number of individuals and positions are infinite and represented by a continuum. The second part consists of modeling the innovation problem as a two-tiered assignment problem in which the allocation of resources, including the commodities available for sale, is influenced by occupational choices. The third part examines the trade-off between the technological advantages of assignments exhibiting specialization and division of labor and the disadvantages of such assignments in terms of the demands that this places on the technology of exchange. Research on all three topics is potentially extremely important. In the first topic the proposed work could lead to a new way of conceptualizing competition that would capture as special cases such criteria as non manipulability of prices and the appropriation of agents' marginal contributions. The assignment model has a rich history as a laboratory for the development of important new theories such as linear programming and core theory. Past work by the investigator and his collaborators suggests that their study of the uniqueness of equilibrium prices in large assignment models could provide another new, powerful analytical tool for economic theory. The second and third parts should provide new insights into such fundamental questions as: how are new commodities introduced? why are markets incomplete? how does specialization and the division of labor depend on the exchange process, or transaction technology?
