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Theorem 1 provides proof of the existence of a pseudo-equilibrium. Theorem 2 shows that the pseudo-equilibrium manifold differs significantly from the structure of equilibria in economies with complete markets. It contends that the manifold omega of global pseudo-equilibria is a fiber bundle with the topological structure of a one- or two-fold covering space of G(super k,n), the space of k planes in R(super n), where k is the number of assets in the economy and n the number of states of uncertainty. The pseudo-equilibrium manifold omega is demonstrated as not contractible with incomplete markets, in contrast with complete markets where it is always contractible.

A simple price adjustment process can be employed to derive a robust result from a chaotic behavior of prices. This can be demonstrated in the price adjustment dynamics of returns-to-scale economies. The long-term statistical characteristics of such as system's behavior can be described via an ergodic measure.

An analysis of competitive equilibrium is presented. The analysis focuses on the development of such equilibrium in Sobolev spaces and removes the condition of bounds on short sales. The assumption of consumption sets with or without lowerbounds allows the inclusion of securities markets with extended asset range andshort sales. It is shown that pricing enters the same market space as commodities.

The article focuses on green capitalism, an economic system that values natural resources and addresses both equity and efficiency using carbon negative technology. Topics include requirement of creation of global limits or property rights for the use of atmosphere, biodiversity and bodies of water , the building blocks for green capitalism as well as practical examples to put these principles into practice, and building of carbon negative power plants for developing nations.

Byline: Graciela Chichilnisky 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)

Byline: Graciela Chichilnisky, Peter Eisenberger 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.

Byline: Graciela Chichilnisky 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.

Byline: Graciela Chichilnisky 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).

Byline: Graciela Chichilnisky 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.

Byline: Graciela Chichilnisky 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).