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A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular – the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.

The authors consider a dynamic emission-reduction technology investment decision-making problem for an emission-dependent dyadic supply chain consists of a manufacturer and a retailer under subsidy policy for carbon emission reduction. The consumers are assumed to prefer to low-carbon products and formulate a supply chain optimal control problem.

The authors adopt differential game to analyze investment strategies of cost subsidy coefficient with respect to vertical incentive of a manufacturer and a retailer. A comparison analysis under four different decision-making situations, including decentralized decision-making, centralized decision-making, maximizing social welfare, is obtained.

The results show that the economic benefit and environmental pressure have a win–win performance in centralized decision-making. In four different game models, equilibrium strategies, profits and social welfare show changing diversity and have a consistent development trend as time goes on.

The authors estimate the demand function is a linear function in this paper. According to the consumers’ preference to low-carbon products, consumer’s awareness meets the law of diminishing marginal utility like advertising goodwill accumulation. The carbon-sensitive coefficient might be a quadratic expression, which will complicate the problem and be consistent with reality.

It captures that there is a necessity to strengthen cooperation and exchange of carbon emission technology among the enterprises by simulation of different decision-makings when government granted cost subsidy.

The results provide significant guidelines for the supply chain to make decision-makings of emission-reduction technology investment and relevant government departments to determine emission subsidies costs.

An endogenous subsidies coefficient is produced by the social welfare function. Distinguished from previous study, it also considered the influences of carbon emission trade policy and consumer preference.

This paper aims at examining the possibility of constructing an Arrow‐social welfare function (SWF) in an Islamic community, that is abide by the Islamic tradition (i.e. the Shari'ah), where the domain of the individuals is defined in the context of Islamic framework. This domain is defined by the Shari'ah, where part of that domain is constrained, such that those actions that lie in the wajib (i.e. obligatory) or haram (i.e. prohibited), where the individual has no choice, must be thoroughly explored with respect to such a welfare function to consistency with the Shari'ah. Individual choice functions only within that segment of the domain that Islamic law leaves to the individual; the individual makes choices concerning actions in which they will not lose any praise or reward if they do or do not act one way or another. My concern in this regard will be the Mubah (i.e. permissible) range of the individual domain. In the process of examining the possibility of constructing an Arrow form (SWF) in an Islamic community, I have added a new Axiom to those suggested by Arrow (1951, pp.22–31). Kenneth J. Arrow, in his book Social Choice and Individuals Values (1951), has argued that five requirements of ‘fairness’ must characterize an acceptable social welfare function. He finds that these are inconsistent with each other. In fact, no welfare function exists that will satisfy all of those conditions simultaneously. As laid out by Arrow, these five conditions are, respectively: (1) universal domain; (2) positive association of individuals' values; (3) independence of irrelevant alternatives; (4) citizens' sovereignty; (5) nondictatorship. These conditions, characterized by Arrow as “seemingly innocuous” together rule out the possibility of deriving a complete and consistent (SWF) (Luce and Raiffa, 1957, p.328). The new axiom which I will refer to as Islamically imposed axiom such that, in the process of formulating an Arrow form social welfare function, it is important to be consistent with the Shari'ah. The Islamically imposed condition will thus guarantee the consistency with the Shari'ah in the process of formulating a social welfare function. This axiom implies that to maintain consistency the following must hold: When ti, (which refers to actions that individuals must do) is an element of the choice set (xi, ti), ti will always be chosen over xi (which refers to the feasible set of alternatives that individuals can choose from), and when tio is an element of the choice set (which refers to actions that individuals must not do), it will never be chosen. I came to the conclusion that when the choice set contains alternatives that the individual must do (wajib) or must not do (haram), the former will be chosen and the latter will never be chosen. Thus, for the general case, Arrow's negative results follow. If these elements are not in the choice set (i.e. all elements in the choice set belongs to Mubah activities), then Arrow's results follow in a straightforward fashion.

According to Kolm (1998, p. 3), social ethics addresses the question ‘what should be done in society?’ The topic of justice constitutes a very large part of social ethics although other virtues are also important. Kolm distinguishes between macro-justice and micro-justice. For the former, Kolm proposes ‘a combination of the three rationales of rights and duties about capacities: process-freedom, partial income equalisation by efficient means, and the satisfaction of basic needs and the alleviation of deep suffering’. Sen (1992, pp. ix, 21–22, 150) argues that ‘a common characteristic of virtually all the approaches to the ethics of social arrangements that have stood the test of time is to want equality of something – something that has an important place in the particular theory’. For example, even libertarian thinkers such as Nozick who are perceived as being anti-egalitarian place importance on people having liberty and hence that equality of liberties is important. Sen's own capability approach ‘has something to offer both to the evaluation of well-being and to the assessment of freedom’.