Efficient allocations of indivisible commodities: theory and application to land allocation problem

Abstract

The experience of land allocations in transition economies indicates a need to design a redistribution mechanism to reallocate farmland efficiently. As a first step towards designing a land redistribution mechanism, we consider the problem of the existence of equilibrium. Convexity and divisibility of commodities are basic assumptions in general equilibrium theory, while we cannot apply these assumptions to land. In Chapter 2, we propose a condition under which a Pareto optimal allocation can be supported by prices when commodities are indivisible. The proof follows the Second Welfare Theorem. We use the concept of equilibrium with transfers, under which there IS some initial endowment such that a particular allocation and a price vector constitute an equilibrium. We demonstrate that there is a threshold level of monetary endowments for each agent such that below that level, equilibrium exists, and above that level, equilibrium does not exist. Our model is more general than previous literature since agents face budget constraints in our model while the existing literature often assumes that budget constraints do not bind. In Chapter 3, we examine the performance of two-sided market mechanisms for redistributing land parcels by conducting experiments. We use the concept of competitive equilibrium, rather than equilibrium with transfers, in this chapter. Using equilibrium with transfers requires the government to have information on individuals' preferences and to be able to implement the wealth transfers. Both are idealistic assumptions. Instead of the redistribution of wealth by the government, we allow agents to obtain loans to purchase land. Under the parameters used in the experiment, competitive equilibrium prices exist. Theoretically speaking, we thus can expect efficient outcomes to emerge as a result of competition. We compare the performance of three alternative mechanisms; direct negotiation, a double auction, and a combinatorial call market. Direct negotiations can be considered a cooperative mechanism and double auctions a noncooperative mechanism. A combinatorial call market was designed to solve complex resource allocation problems, such as the allocation of spectrum, and is known to outperform other mechanisms in one-sided markets. We investigate the problems we face when we extend the study to two-sided markets.