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The goal of this paper is to provide a definition of the concept of sustainability with the level of rigor and clarity of neoclassical theory, based on two axioms that ensure equal treatment of the present and the future introduced by the author. We discuss applications to markets, business strategy and public policy. The approach is anchored on the concept of satisfying the basic needs of the present and the future, defined in the author's work; it is compared with other important contributions to the theory and practice of sustainability.

This paper discusses the challenges and opportunities created for the world by the Kyoto Protocol and the creation in 2005 – based on international law – of its global market for carbon emissions trading. In particular, it discusses the significance of the clean development mechanism (CDM). The projects funded by CDM have already achieved a real impact, they have decreased carbon emissions by the equivalent of 37% of EU emissions. The CDM projects should be expanded and improved. Carbon negative technology is available. Global Thermostat (GT) technology was formed in 2006 to develop and commercialise a unique technology for the direct capture of carbon dioxide from the atmosphere and other sources. It has been successfully tested and demostrated and has the capability of transforming power plants into net carbon sinks. This, together with the Green Power Fund, first proposed by the author in 2009 at Copenhagen COP15 could make a significant difference to the amount of emissions being reduced by involving Latin America, Africa and the Small Island States (relatively low polluters). The green power fund is a private fund of $200 Bn per year for 15 years.

This article provides two axioms that capture the idea of sustainable development, and characterises the welfare criterion that they imply. It presents a formal theory of sustainable development, created by the author (Chichilnisky, 1996a, 1997). The axioms require that neither the present nor the future should play a dictatorial role in society's choices over time. Theorems 1 and 2 show that there exist sustainable preferences which satisfy these axioms and provide a full characterisation. Theorems 3 to 5 study a standard dynamical system representing the growth of a renewable-resource economy, give a 'turnpike' theorem, and exhibit the differences between sustainable optima and the ones according to discounted utilitarianism. (JEL 013)

Energy security, economic development and averting global warming are conflicting objectives in a fossil fuel economy. In the long run, sustainable development requires a shift to renewable energy sources. In the short run it requires swift action (IPCC) and different strategies. The article analyses a negative carbon process to co-produce electricity while reducing carbon concentration in the atmosphere (Jones, 2008, 2009; Chichilnisky, 2008b; Chichilnisky and Eisenberger, 2009; Eisenberger et al., 2009). While providing additional energy the process makes fossil power plants net carbon sinks. The article addresses short and long run challenges with this capability in the context of the economic incentives provided by the carbon market of the UN Kyoto Protocol, created by one of the authors in 1997 (Chichilnisky, 1993, 1996; Chichilnisky and Heal, 1994, 1995; Chichilnisky and Sheeran, 2009; Pagnamenta, 2009). We propose extending Kyoto's clean development mechanism (CDM) in a way that benefits Latin America and Africa (Chichilnisky and Heal, 1999; Chichilnisky, 1996), and analyse the global transition from a fossil to a renewable economy.

This article sets out the importance of the Kyoto Protocol process to be decided at the Copenhagen COP XV Conference of December 2009. It clarifies the latest aspects of the clean development mechanism. It explains in practical terms, the relative negotiating positions adopted by developing and developed countries and possible impacts on world poverty. It presents two proposals that are win-win solutions and modest extensions of existing law. One is a financial mechanism that can help resolve the current impasse between China and the US – a conflict that is reminiscent to the Cold War in the last century. The second is a technological solution that is a small modification of the existing clean development mechanism to allow negative carbon technologies. This would allow poor nations to build power plants that reduce carbon in the atmosphere well beyond what they emit, encouraging economic progress while helping avert global warming risks. The funding can thus come from the Kyoto Protocol process – while increasing export revenues and technological employment in industrial nations – a win-win solution for the world economy. The paper warns about the costs of failure and the importance of the success of the Copenhagen process.

The article explains the origins of the gender pay gap as a Nash equilibrium of a game with incomplete information about women's work at home and in the marketplace based on the earlier results of Chichilnisky (2005, 2008a, 2008b). Expectations about women's lower market wages leads to the over utilisation of women in the household, and this, in turn, leads to lower productivity and lower wages for women in the marketplace. The situation is rational, but (as the prisoner's dilemma) it is generally Pareto inferior. Inequity at home breeds inequity in the marketplace and reciprocally, leading to a persistent gender gap. With learning by doing, at high levels of skill there is a Pareto superior equilibrium where men and women share efforts equally at home and receive the same pay in the marketplace, firms enhance their profits, and there is additionally more welfare at home. Updated Family Law and appropriate contracts can help resolve this Pareto inferior situation as well as increase productivity and economic growth in the economy as a whole (Pyle, 1990).

Catastrophic risks are rare events with major consequences and of great interest to green economics. The article investigates the way economics deals with catastrophic risks. Classic expected utility theory is insensitive to rare events no matter how important these may be, based on the axioms of Von Neumann (1944), Arrow (1971) and DeGroot (1970/2004) that define proximity of observations in terms of 'averages' obliterating outliers. A new axiomatic extension to the theory of choice introduced new axioms that are sensitive to rare events, and characterised the criteria that these imply (Chichilnisky, 1996, 2000, 2002, 2010; Lawuers, 1993). These are expected utility combined with a new term that focuses on extremal events, explaining 'fat tails' and 'outliers'. Continuity based on 'the topology of fear' provides the required sensitivity to rare events (Chichilnisky, 2009c). Experimental evidence for the new axiomatic treatment is in Chanel and Chichilnisky (2009). The results relate to Debreu's (1954) work on Adam Smith's Invisible Hand and Le Doux's (1996) work on the neurological responses to fear.

New physical constraints emerged in the 20th century and are changing the decision criteria used until now. Two optimisation problems are equivalent: (1) maximising discounted utility with a long-run survival constraint and (2) maximising a new type of utility that treats the present and future equally. The latter originates in normative axioms introduced by the author in Chichilnisky (1996a), which capture the essence of sustainable development. The article shows that in the economics of the future, normative and positive goals converge: the axioms representing what we would like merge with what will be observed. The 'weight' given to the long-run future is identified with the marginal utility of an environmental asset along a path that narrowly avoids extinction. No prior welfare criteria satisfy the axioms for sustainable development introduced by Chichilnisky (1996a; 1997). The implied decision criteria have practical implications for new forms of cost-benefit analysis, choices under uncertainty, optimal extraction of renewable resources and the optimisation of investment and trade. These preferences have been tested experimentally (Chanel and Chichilnisky, 2008) and identify the limits of nonparametric econometrics (Chichilnisky, 2009c).

Among the tools of the economic trade, cost-benefit analysis is the most widely used in policy circles. Asking whether there is a role for cost-benefit analysis is like asking whether there is a role for the weatherman. Of course there is.

This paper revisits the aggregation theorem of Chichilnisky (1980), replacing the original smooth topology by the closed convergence topology and responding to several comments (N. Baigent (1984, 1985, 1987, 1989), N. Baigent and P. Huang (1990) and M. LeBreton and J. Uriarte (1990a, b). Theorems 1 and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences PSCO, its subspace of smooth preferences PinfSCOsupS, and a space P1 of smooth (not necessarily convex) preferences with a unique interior critical point (a maximum). The results are proven using both the closed convergence topology and the smooth topology. Because of their contractibility, these spaces satisfy the necessary and sufficient conditions of Chichilnisky and Heal (1983) for aggregation rules satisfying my axioms, which are valid in all topologies. Theorem 4 constructs a family of aggregation rules satisfying my axioms for these three spaces. What these spaces have in common is a unique maximum (or peak). This rather special property makes them contractible, and thus amenable to aggregation. However, these aggregation rules cannot be extended to the whole space of preferences P which is not contractible and therefore does not admit continuous aggregation rules satisfying anonymity and unanimity, Chichilnisky (1980, 1982). The results presented here clarify an erroneous example in LeBreton and Uriarte (1990a, b) and respond to Baigent (1984, 1985, 1987) and Baigent and Huang (1990) on the relative advantages of continuous and discrete approaches to Social Choice.

I study connected manifolds and prove that a proper mapf:M→Mis globally invertible when it has a nonvanishing Jacobian and the fundamental group π1(M) is finite. This includes finite and infinite dimensional manifolds. Reciprocally, if π1(M) is infinite, there exist locally invertible maps that are not globally invertible. The results provide simple conditions for unique solutions to systems of simultaneous equations and for unique market equilibrium. Under standard desirability conditions, it is shown that a competitive market has a unique equilibrium if its reduced excess demand has a nonvanishing Jacobian. The applications are sharpest in markets with limited arbitrage and strictly convex preferences: a nonvanishing Jacobian ensures the existence of a unique equilibrium in finite or infinite dimensions, even when the excess demand is not defined for some prices, and with or without short sales.

This paper studies maps which are invariant under the action of the symmetry group Sk. The problem originates in social choice theory: there are k individuals each with a space of preferences X, and a social choice map ?:Xk ? X which is anonymous i.e. invariant under the action of a group of symmetries. Theorem 1 proves that a full range map ?:Xk ? X exists which is invariant under the action of Sk only if, for all i=1, the elements of the homotopy group ?i(X) have orders relatively prime with k. Theorem 2 derives a similar results for actions of subgroups of the group Sk. Theorem 3 proves necessary and sufficient condition for a parafinite CW complex X to admit full range invariant maps for any prime number k:X must be contractible.

The paper proposes two axioms that capture the idea of sustainable development and derives the welfare criterion that they imply. The axioms require that neither the present nor the future should play a dictatorial role.

The theory of social choice introduced in [5, 6] is robust: it is completely independent of the choice of topology on spaces of preferences. This theory has been fruitful in linking diverse forms of resource allocation: it has been shown [17] that contractibility is necessary and sufficient for solving the social choice paradox; this condition is equivalent [11] to another — limited arbitrage — which is necessary and sufficient for the existence of a competitive equilibrium and the core of an economy [13, 14, 15, 16, 17]. The space of monotone preferences is contractible; as shown already in [6, 17] such spaces admit social choice rules. However, monotone preferences are of little interest in social choice theory because the essence of the social choice problem, such as Condorcet triples, rules out monotonicity.

This paper analyses both the basic assumptions and the results of the better known and widely used global models - specifically, the UN world model, the RIO (Reshaping the International Order) model and the Bariloche model - in relation to basic needs and to North-South interdependence. The rationale of the exercise is that these very assumptions underlie various development strategies and give legitimacy to competing claims on the world's resources. Even if some of the findings of the analysis are critical of the suitability of a particular model for the study of the questions posed, they serve a useful purpose in that they suggest what strategies and structures built into the model do not work. The paper ends by summarizing the conclusions and indicating their implications for policy as well as for further modelling work.

Unlike discounting and the damage function, the social welfare function has not received so much attention in the debate on climate economics. An important challenge has been to combine efficiency and equity considerations in a single social welfare framework. The Chichilnisky criterion is one way to resolve this. We consider its implementation in the climate-economy model Dynamic Integrated Climate-Economy (DICE), and compare results for different damage functions, namely the standard one in DICE and the one proposed by Weitzman implying potential large climate damages at high temperature increases. We calculate optimal climate policy for different parameter settings and compare the results with those under the green golden rule (only final utility matters) and classical utilitarianism (no discounting). Optimal emission abatement trajectories turn out to be very different between standard discounted utilitarianism, classical utilitarianism and Chichilnisky specifications. The results are very sensitive to the damage function, the climate sensitivity parameter and especially the “Chichilnisky weight” given to utility of generations in the far future. We discuss conditions and reasons for preferring either classical utilitarianism or the Chichilnisky criterion, and conclude that a critical factor is the time horizon used in climate policy analysis. Adopting sustainable preferences as formalized by the Chichilnisky criterion in climate policy analysis has the advantage that the very long-term implications of greenhouse gases in the atmosphere on the environment and human welfare are not downplayed.