Working paper (Federal Reserve Bank of Minneapolis. Research Dept.)
We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite dimensional fixed point problem stated in terms of prices and commodities into a finite dimensional Negishi problem involving individual weights in a social value function. By adding a set of artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time zero factor endowments and derivatives of the social value function.
We look for the scale effects on growth predicted by some theories of trade and growth based on dynamic returns to scale at the national or industry level. The increasing returns can arise from learning by doing, investment in human capital, research and development, or development of new products. We find some evidence of a relation between growth rates and the measures of scale implied by the learning by doing theory, especially total manufacturing. With respect to human capital, there is some evidence of a relation between growth rates and per capita measures of inputs into the human capital accumulation process, but little evidence of a relation with the scale of inputs. There is also little evidence that growth rates are related to measures of inputs into R&D. We find, however, that growth rates are related to measures of intra-industry trade, particularly when we control for scale of industry.
We extend the analysis of Kiyotaki and Wright, who study an economy in which the different commodities that serve as media of exchange are determined endogenously. Kiyotaki and Wright consider only symmetric, steady-state, pure-strategy equilibria, and find that for some parameter values no such equilibria exist. We consider mixed-strategy equilibria and dynamic equilibria. We prove that a steady-state equilibrium exists for all parameter values and that the number of steady-state equilibria is generically finite. We also show, however, that there may be a continuum of dynamic equilibria. Further, some dynamic equilibria display cycles.