Asis Kumar Banerjee

Fuzzy choice functions, revealed preference and rationality

Abstract This paper investigates the conditions under which a fuzzy-set-valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions. Attention is confined to the case where the domain of the choice function consists of all (crisp) finite subsets of the universal set of alternatives. Two sets of weak and strong axioms of fuzzy revealed preference (WAFRP and SAFRP) are stated. In both cases it turns out that WAFRP is not equivalent to SAFRP and that SAFRP does not characterise rationality. In the special case where every set of avialable alternatives has at least one element which is unambiguously chosen, WAFRP is equivalent to SAFRP but SAFRP still does not characterise rationality. A fuzzy congruence condition, stronger than SAFRP, is proposed and is shown to be necessary and sufficient for rationality.

Fuzzy preferences and Arrow-type problems in social choice

There are alternative ways of decomposing a given fuzzy weak preference relation into its antisymmetric and symmetric components. In this paper I have provided support to one among these alternative specifications. It is shown that on this specification the fuzzy analogue of the General Possibility Theorem is valid even when the transitivity restrictions on the individual and the social preference relations are relatively weak. In the special case where the individual preference relations are exact but the social preference relation is permitted to be fuzzy it is possible to distinguish between different degrees of power of the dictator. This power increases with the strength of the transitivity requirement.

A note on a property of maximal sets and choice in the absence of universal comparability

Abstract We show that, given a reflexive and transitive (but not necessarily connected) binary weak preference relation R , the maximal set generated by R coincides with the union of the choice sets generated by all possible orderings that are compatible with R . The property is of interest in assessing the intuitive significance of the maximal set for the choice of an agent whose preferences do not satisfy connectedness.

Credit-Product Interlinkage and Captive Markets in Backward Agriculture: A Theoretical Analysis

This paper builds a model of fragmented duopsony in backward agriculture following Basu and Bell (1991) in which the purchasers (traders) have captive markets each but compete in a contested market. We focus on the formation of captive markets through trader-farmer interlinkage in the form of interlinked credit-product contracts (ICPCs). ICPC (or the formation of captive markets) is not an entry-preventive strategy in the model. Its motive is to push the farmers to their reservation income level. However, the captive and the contested markets are linked by the requirement that the reservation income of a captive farmer has to equal the income of a farmer in the contested market. In general, in our model strategic considerations determine the extent of use of ICPCs rather than explaining their existence. (In a special case, however, they do explain existence.) We also show that a credit subsidy policy will reduce the size of the captive market, improve the welfare of the farmers and raise the agricultural productivity of the economy while the effects of a price subsidy policy will be ambiguous.

Choice between opportunity sets: A characterization of welfarist behaviour

Abstract Welfarist behaviour in choosing between opportunity sets is defined in a number of alternative ways. Under the condition of consistent behaviour these definitions are shown to be equivalent. Two conditions involving revealed preference relations are proposed and shown to constitute a characterization of welfarist behaviour.