Economic Equilibrium and Optimal Economic Planning

Summary

^*This chapter is devoted to mathematical economics. We start with the static model of an exchange economy with a measure space of agents (an abstract device to model perfect competition). We introduce the notions of core allocation and of Walras allocations. We show that in the context of perfect competition, the two sets coincide and they are nonempty (existence result). Then we pass to dynamic models and deal with discrete-time infinite horizon multisector growth models. We deal with both discounted and undiscounted model. For the latter, we introduce the optimality notion of “weak maximality”. We prove existence theorems and we establish weak and strong “turnpike theorems”. Turnpike programs are important because every optimal program eventually moves close to a turnpike one. Moreover, they are easier to compute and are relatively insensitive to the optimality criterion. Subsequently, we conduct an analogous study for models with uncertainty (nonstationary discounted and stationary undiscounted). Then we consider continuous-time models and finally we investigate the “expected utility hypothesis (EUH), the main hypothesis in the theory of decision making.