Formulating an objective for an economy

This paper is dedicated to the memory of E.M.L. Beale. Not a small part of Martin Beale's success in developing and solving large-scale mathematical programs is attributed to the care he took in properly formulating his models.Our presentation concerns our efforts to also properly formulate a model. Our model is an economic model used for technology assessment. In order for it to be useful, it is important that the dual variables represent as realistically as possible real world prices. This required us to formulate the model as a time-staged economic equilibrium model. Our main result is a proof that an equilibrium formulation using expected aggregate demand can under certain conditions be replaced by one in which the economy is driven by an aggregate utility or objective function, one that promotes economic growth subject to physical flow constraints. We show that such an objective function always exists except for populations consisting of significantly large classes of people whose consumption patterns differ radically one from another. Assuming that the latter is not the case, this equivalent formulation means that mathematical programming software can be applied to efficiently solve the model. This paper summarizes an extensive paper entitled Deriving a Utilty Function for the U.S. Economy 3]. The main theorems are stated without proof.The authors wish to thank Kenneth Arrow, Gerard Debreu, Robert Dorfman, Dale Jorgenson and Lawrence J. Lau for their helpful comments.Research of this report was partially supported by the National Science Foundation Grants DMS-8420623, SES-8518662 and ECS-8617905; U.S. Department of Energy Grant DE-FG03-87ER25028; Office of Naval Research Contract N0004-85-K-0343, Electric Power Research Institute Contract RP 5006-01, and the Center for Economic Policy Research at Stanford University.