Free Disposal Assumption Research Articles

Almost tight bounds for online hypergraph matching

In the online hypergraph matching problem, hyperedges of size k over a common ground set arrive online in adversarial order. The goal is to obtain a maximum matching (disjoint set of hyperedges). A naïve greedy algorithm for this problem achieves a competitive ratio of 1k. We show that no (randomized) online algorithm has competitive ratio better than 2+o(1)k. If edges are allowed to be assigned fractionally, we give a deterministic online algorithm with competitive ratio 1−o(1)ln⁡(k) and show that no online algorithm can have competitive ratio strictly better than 1+o(1)ln⁡(k). Lastly, we give a 1−o(1)ln⁡(k) competitive algorithm for the fractional edge-weighted version of the problem under a free disposal assumption.

Truthful fair division without free disposal

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

On some semilattice structures for production technologies

Tracing back from Charnes et al. [9] many approaches have been proposed to extend the DEA production model to non-convex technologies. The FDH method were introduced by Deprins et al. [13] and it only assumes a free disposal assumption of the technology. This paper, continues further an earlier work by Briec and Horvath [7]. Among other things, a new class of semilattice production technologies is introduced. Duality results as well as computational issues are proposed.

An essay on the state of economic science

This work is concerned in the existence problem of equilibria for economies with increasing returns to scale. The consequences of relaxing the free disposal assumption are investigated. It is shown that the free disposal assumption cannot be dropped, not even be relaxed to the assumption of free elimination, without risking that equilibria may fail to exist.

Quota-Induced Discarding in Heterogeneous Fisheries

Individual quota (IQ) programs are a promising and increasingly common means of regulating fisheries. This paper examines how profit maximizing fishers respond to different types of IQ programs in fisheries where many types of fish are harvested simultaneously. This analysis shows that the most common types of individual quota programs can induce discarding, and that individual quota programs that regulate the value of harvests never induce discarding. Since discarded fish have a high mortality rate, “value-based” individual quota programs are superior to their more conventional counterparts in that they waste fewer fish. The disadvantages of value-based quotas are also examined. Results are driven by the fact that the harvest technology examined here does not satisfy a “free-disposal” assumption. Since this free-disposal assumption is ubiquitous in production theory, and not obviously true, the framework developed herein may be useful for analyzing a broad class of problems involving joint production.

From a theorem of Radner

This note, by means of an example, shows the distinction of the monotonicity assumption and the free disposal assumption in the context of differential information. Equilibrium prices could be negative even with monotone preferences.

Existence of equilibria in nonconvex economies without free disposal

In this paper we eliminate the free disposal assumption in a general equilibrium model in which the production sector may exhibit increasing returns to scale or more general types of nonconvexities and where the firms follow general pricing rules. Under standard assumptions in this framework, we state this existence of an equilibrium generalizing the classical results on this model.

The Existence of Equilibrium without Free Disposal in Economies with Transaction Costs and Incomplete Markets

This paper presents a general model of an economy with transaction costs, and proves the existence of a competitive equilibrium using T. C. Bergstrom's procedure to discard the free-disposal assumption. Since economies with incomplete markets are shown to be special cases of economies with transaction costs, this result is used to discuss the conditions for the existence of an equilibrium in economies with incomplete markets. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption

Here we prove, by means of Brouwer's theorem and the concept of a continuous partition of unity, a variant of a result of Debreu (1956) which has a corollary, useful for discarding free disposability, which could not be derived from the initial statement. Applying this theorem to the excess demand correspondence of a pure exchange economy where disposition activities are described by a closed convex cone contained in the negative orthant of R 1 , we show the existence of quasi-equilibrium with or without the free-disposal assumption. We then investigate the conditions under which a quasi-equilibrium is an equilibrium.

A proof of the existence of equilibrium without the free disposal assumption

A proof of the existence of equilibrium without the free disposal assumption

Optimal Capital Accumulation in a Polluted Environment

In The Costs of Economic Growth [8], Dr. Mishan criticizes the importance attached to economic growth by politicians, businessmen, and economists. He contends that these groups generally overlook the spillover effect of the growth process-such as environmental pollution. This is nowhere more apparent than in the modem theories of economic growth (see for example [2]). These theories implicitly assume no wastes are produced by the economic process, or, alternatively (and more likely), that if any wastes are generated they can be disposed of at no cost to the community. It is naive to think that no wastes are produced and fairly obvious that the free disposal assumption of the neoclassical growth model is not satisfied in the real world. Accordingly, any theory of optimal economic growth that does not take into account these spillover effects cannot claim to be complete. This paper will investigate the effects of introducing pollution explicitly into the neoclassical growth model. The model is formulated in Section I. Section II contains the solution, while Section III summarizes the discussion.