This series of programs solve a Bewley model with production(This abstract was borrowed from another version of this item.)

The last section of this paper presents a rigorous version of Tiebout's theory of local public goods. It is shown that equilibria exist and are Pareto optimal. This rigorous theory follows closely the more rigorous part of Tiebout's work. This rigorous theory makes a number of very special assumptions which make local public goods essentially private. The body of this paper presents a series of examples, which show that if one tries to generalize the rigorous version of Tiebout's theory in a number of interesting directions, then equilibria may no longer exist or may not be Pareto optimal. The conclusion is that Tiebout's idea does not lead to a satisfactory general theory of local public goods. THE GOAL OF THIS PAPER is to point out that Tiebout's notion of equilibrium with local governments does not have the nice properties of general competitive equilibrium, except under very restrictive assumptions. Tiebout [39] suggested that there are competitive forces which tend to make local governments allocate resources in a Pareto optimal fashion. Consumers choose to live in those towns with the mix of taxes and public goods they prefer. Local governments choose this mix so as to attract inhabitants. This idea may seem intriguing, for it suggests that the invisible hand solves an important part of Samuelson's perplexing public goods problem [32]. Tiebout, in fact, makes an argument which is nearly rigorous. I give a rigorous version of his argument at the end of the paper. However in this rigorous version, so many restrictive assumptions are made that public goods become essentially private. In the body of the paper, I give a series of examples with which I try to convince the reader that one is forced to adopt Tiebout's restrictive assumptions. The idea is that if one changes any of his assumptions, then either equilibria may not exist or may not be Pareto optimal. My examples are presented in the context of a general class of Tiebout models. I consider several subclasses, one of which is the special case considered by Tiebout. In each of the subclasses except that considered by Tiebout, I give a counterexample either to the existence of equilibrium or to its Pareto optimality. The subclasses are so chosen that the difficulties they reveal would be shared by any reasonable Tiebout model which differed from his special case. I believe that my examples controvert Tiebout's suggestion [39, last paragraph] that his theory compares favorably with competitive equilibrium theory. Most of the examples in this paper have already appeared in the literature. I cite related work as I go along. What is new here is that I assemble the examples in a unified argument.

We study the properties of the core of large markets. We assume that traders' preferences have certain standard properties, that their preferences belong to a set which is compact with respect to a certain topology, and that there is a bound on their initial endowments. It is then found that if a market contains sufficiently many traders and if there are many traders similar to any one trader, then every core allocation is similar to a price equilibrium in a very strong sense. This fact implies a precise formulation of the following statement: for most large markets, the core decomposes into disjoint clusters of allocations, the allocations in each cluster being very similar. This statement may be interpreted as an explanation of why traders in large markets normally feel that they have little bargaining power.