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Chaotic behavior of prices can emerge as a robust result from a very simple and standard price adjustment process. Consider the dynamics of prices adjusting according to supply and demand in economies with increasing returns to scale. Increasing returns in production implies the existence of a globally attracting set of prices, containing a stable disequilibrium price, within which the motion of the system is chaotic. This property holds for any step size in the price adjustment process when consumption and leisure are complementary. We prove that long-run statistical properties of the system's behavior in this set are described by an ergodic measure. Price dynamics drive the system into the globally attracting region, and then chaotic motion takes over. On average according to this measure there is excess supply. We suggest possible empirical implications of our analysis, particularly with respect to the relationship between wages changes and the demand for labor, the “Phillips curve”.

We prove the existence of an optimal growth path in an economy where goods that are not consumed are either invested in next period capital or in R&D with overall non-convex production possibilities, using results of non-linear functional analysis in weighted Lp spaces of Chichilnisky (Journal of Optimization Theory and Applications, 1977, 61, no. 2, 504–520) and (Journal of Mathematical Economics, 1981, 8, 1–14).

A condition oflimited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. Theorem 1 establishes thatlimited arbitrage is necessary and sufficient for the existence of a competitive equilibrium in markets with or without short sales. Limited arbitrage bounds utility arbitrages, the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments (Proposition 2); it is related to but nonetheless different from the no-arbitrage condition used in finance. Theorem 2 establishes that an Arrow — Debreu economy has a competitive equilibrium if and only if every one of its subeconomies withN + 1 traders does, whereN is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the existence of the core [16], to the contractibility of spaces of preferences and to the existence of continuous anonymous social choice rules which respect unanimity [10], [14], [15], [16].

El cambio climático se presta a la economía política. Joseph Henry Vogel ha construido un argumento a favor de llevar a los países ricos en carbono, pero pobres económicamente, a través del cuello de botella de la economía de vaquero y hacia el “comercio en el derecho de emisiones” de los países Anexo I del Protocolo de Kioto. Ecuador sirve como el modelo.

Publisher Summary Short sales can enhance market performance and improve a trader's ability to allocate resources. But increased gains often mean increased risks and thus short sales can also lead to market volatility and increase the risk of widespread default. This chapter explains how volatility and widespread default arise in markets with short sales and shows a practical way to avoid increased volatility and defaults in markets with short sales such as those observed in the US financial crisis of 2008–9. When traders are sufficiently diverse, a market with short sales creates incentives for increasingly long and short trading positions, a situation that can continue unchecked and without limits. In such situations, a market with short sales generally fails to reach equilibrium, trading grows without bounds, leading to volatility and eventually traders default on their contracts. Financial innovation makes things worse because it increases the exposure to default by creating system-wide risks through a cascading effect where default by one trader leads to default by all. The introduction of appropriate graduated reserves can such check volatility and restore the conditions needed for market equilibrium. Graduate reserves are defined as a system whereby the reserves ratio increases with the size or value of the short trade. This means that the relative value to the trader of selling short decreases the larger short sale. In this manner, graduated reserves resolve runaway volatility and default in markets with short sales.

Summary We use growth models with natural resources to study the consequences of a ranking of intertemporal paths, due to Chichilnisky, which places weight on their very long run or limiting characteristics as well as on their characteristics over any finite period. This criterion shows more intertemporal symmetry or egalitarianism than the discounted utilitarian approach, which clearly emphasizes the immediate future at the expense of the long run. In this respect it captures the concenrs of those who argue for sustainability and for a heightened sense of responsibility to the future. In some of the examples that we consider, the long-run characteristics of paths optimal by this criterion are a mixture of those of utilitarian paths and the “green golden rule” (the configuration which maximizes long-run sustainable utility from consumption and environment).

We review the optimal pattern of carbon emission abatements across countries in a simple multi-country world. We model explicitly (with the model in Chichilnisky [4]) the fact that the atmosphere is a public good. Within this framework we establish conditions for it to be necessary for optimality that the marginal cost of abatement be the same in all countries. These condition are quite restrictive, and amount to either ignoring distributional issues between countries or operating within a framework within which lump-sum transfers can be made between countries. These results have implications for the use of tradeable emission permits, which as normally advocated will lead to the equalization of marginal abatement costs across countries. The observation that the atmosphere is a public good implies that we may need to look at a Lindahl equilibrium rather than a Walrasian equilibrium in tradeable permits.

ACL-1; International audience; Global environmental phenomena like climate change, major extinction events or flutype pandemics can have catastrophic consequences. By properly assessing the outcomes involved – especially those concerning human life – economic theory of choice under uncertainty is expected to help people take the best decision. However, the widely used expected utility theory values life in terms of the low probability of death someone would be willing to accept in order to receive extra payment. Common sense and experimental evidence refute this way of valuing life, and here we provide experimental evidence of people's unwillingness to accept a low probability of death, contrary to expected utility predictions. This work uses new axioms of choice defined by Chichilnisky (2000), especially an axiom that allows extreme responses to extreme events, and the choice criterion that they imply. The implied decision criteria are a combination of expected utility with extreme responses, and seem more consistent with observations.

This chapter presents an application of competitive general equilibrium theory of markets in the spirit of Walras, formalized in the 1950s by K. Arrow and by G. Debreu. In using general equilibrium theory to generate insight into current policy issues, it follows a tradition established by Arrow in his work on welfare economics of medical care (1963), on the organization of economic activity (1969), on the evaluation of public investment (Arrow and Lind, 1970), and in urban development (1970). The intention if to use formalized general equilibrium theory to derive general statements about the economic behavior and interrelations between two groups of countries: industrial and developing countries.The goal is to obtain simple and general results, and for this purpose we consider a styled model with the minimum of characteristics needed for the task: two regions, two produced goods, and two factors of production. Within this simple model, we explore issues of current import, such as export-led policies and the transmission of economic activity between regions.

This paper studies a general equilibrium North-South economy consisting of two countries which produce and trade two goods using two inputs of production. It extends the North-South trade model of Chichilnisky (1981, 1986) by assuming that one input of production is a renewable resource which follows its own physical dynamics. From these dynamics and from optimal extraction behavior we derive explicitly the supply of environmental inputs as a function of their market prices. Therefore this paper fully derives the price dependence of inputs which is postulated exogenously in the original North-South model. All markets for goods and for inputs are free and competitive throughout. We establish that different property regimes lead to different supply functions for environmental resources. When property rights are well defined (as in the North) the supply of environmental inputs is less price responsive than it is when property rights are ill defined (as in the South). Ill defined property rights lead to an apparent ‘abundance’ of environmental resources in the south. We establish that the difference in property rights in two otherwise identical regions (the same technologies, preferences, and endowments) is itself sufficient to explain why the two regions trade. The region with ill defined property rights exports the environmentally intensive good. This leads to overuse of the environment worldwide and to lower market prices of environmentally intensive goods. The difference in property rights of the two regions determines an apparent ‘comparative advantage’ in the export of environmentally intensive goods in the South, even when the two countries are identical and therefore there is no real comparative advantages. The difference in property rights also gives rise to ‘apparent’ gains from trade, even when there are no real gains from trade.

Following Chichilnisky and Chichilnisky-Kalman we establish existence and optimality of competitive equilibrium when commodity spaces are infinite dimensional Sobolov spaces, including Hilbert spaces such as weighted L2 which have L∞, as dense subspaces. We allow general consumption sets with or without lower bounds, thus including securities markets with infinitely many assets and unbounded short sales, and economies with production. We give non-arbitrage conditions on endowments and preferences which suffice for the existence of an equilibrium. Prices are in the same space as commodities. Equilibrium allocations are approximated by allocations in other frequently used spaces such as C(R) and L∞.

This note links two conditions which have generated some interest in the literature and have an important role in proving the existence of an equilibrium, the second welfare theorem and the core equivalence theorem in infinite dimensional commodity spaces: These are thecone condition introduced in Chichilnisky and Kaiman (1980), and theproperness condition in Mas-Colell (1986a), which were studied also in Yannelis and Zame (1986), Aliprantis et al. (1987a, b) and (1989), Aliprantis and Burkinshaw (1988), Mas-Colell (1986b), Chichilnisky and Heal (1984, 1992), and Rustichini and Yannelis (1991) among others. I establish that these two conditions are the same. Indeed, the cone condition coincides also with the assumption of anextremely desirable commodity used in Yannelis and Zame (1986) and Rustichini and Yannelis (1991). The motivation for studying these conditions comes from the same economic application, showing the need to bring within the scope of equilibrium theory commodity spaces whose positive orthants have empty interior, a typical situation in infinite dimensional linear spaces.

The purpose of this note is to clarify and complement several comments on my work [Chichilnisky, 1980, 1982a], which appeared in this Journal: Baigent [1987], Nitzan [1989], and Baigent [1989]. I shall offer two new results. The first result constructs a continuous, anonymous social selection rule that respects unanimity and the proximity of preferences, for a large family of preferences (Theorem 1). This complements the result of Nitzan [1989] and Baigent's [1989] extension of it and is achieved by accepting, as they do, that social outcomes be optimal choices, rather than rankings of all possible choices or social preferences This result is of interest because it appears to contradict the original impossibility theorem of Chichilnisky, which establishes that, for the same family of preferences, social aggregation rules with these properties do not exist (Theorem 2).

We consider the economics of global environmental risks. In this area, we are dealing with risks that are poorly understood, endogenous, collective, and irreversible. In policy terms, the nature and extent of uncertainty about global climate change implies that society's position will be dominated by two questions: What cost is worth incurring to reduce the poorly-understood risk of climate change, or to improve our understanding of the risk? How may existing social institutions, such as insurance contracts and securities markets, be used to provide the most efficient allocation of the risks associated with global climate change?

This two-volume collection brings together critical essays on the economics of climate change, describing advances in the field ranging from the Kyoto Protocol carbon market, to sustainability criteria, international trade, and the management of catastrophic risks.

Climate change lends itself to both political economy and humor. Through the lens of thermodynamics, the payment Ecuador seeks for not drilling in the Yasuní is equitable and efficient.

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he defined them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of risk bearing that follows the axiomatic treatment of Von Neumann and Morgenstern, Milnor, Hernstein, De Groot, and Villegas. The classic expected utility theory embraces normal or frequent risks at the expense of neglecting rare events, even those with important consequences such as catastrophes, causing paradoxical experimental behavior as shown by the author. Kenneth Arrow encouraged the creation of an extension of classic axiomatic theory, and in the early 1990s the author proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and a new form of choice under uncertainty that conforms better to the experimental evidence. Additionally, the introduction of markets with endogenous uncertainty in the early 1990s challenged the foundation of Arrow Debreu's theory of markets. Endogenous uncertainty is generated by the workings of the economy, and breaks down the equivalence between markets with and without uncertainty that prevails in Arrow Debreu's theory. This leads to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008. In 1999 Arrow contributed to the theory of endogenous uncertainty in his work with Frank Hahn.

This collection of essays from leading academics examines the connection between the World Trade Organization (WTO) and human rights issues, a topic which has provoked significant debate, particularly in the decade since the collapsed WTO talks in Seattle in 1999.

We evaluate two risk profiles: (i) global warming risks and (ii) collisions with asteroids that can cause the extinction of our species. The expected values computed for these two risks suggest that no action will be taken to avoid extinction. The result is somewhat counterintuitive, but it is typical of the results of using classic decision theory to evaluate catastrophic risks in the distant future, see the study by Posner (2004). We establish why expected value is insensitive to catastrophic risks see the study by Chichilnisky (1996), and use another criterion to evaluate risk based on axioms for choice under uncertainty that update the classic Von Neumann theory and require equal treatment for rare and frequent events. Optimizing according to the new criterion is shown to be equivalent to optimizing expected utility with a restriction on the worst outcome in the case of a catastrophe. The evaluation obtained from the new criterion seems more intuitively plausible, and suggests a more practical and realistic approach to catastrophic risks: optimizing expected value while minimizing losses in the case of a catastrophe.

Despite almost universal endorsement of human rights and democratic rule, the majority of humankind is currently governed in a repressive militarized manner. Authoritarian rule is especially prevalent throughout the Third World.

We discuss the special role of women in Green Economics. 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. Expectations about women's lower market wages leads to the overutilization 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 breads 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).

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 the climate change problem requires swift action2 and different strategies. There is no “silver bullet” and a combination of technologies and strategies will be required to meet the Intergovernmental Panel on Climate Change (IPCC) requirements.3 The article develops one example based on ‘negative carbon’ using air capture of carbon dioxide for storage into geological sites and solid materials. When driven by energy produced by carbon-neutral sources (such as Concentrated Solar Power or CSP) this approach can co-produce electricity while reducing carbon concentration in the atmosphere (Jones 2008, 2008b, Chichilnisky 2008, Chichilnisky and Eisenberger, 2009, Chichilnisky and Eisenberger et. al., 2009). While providing additional energy the process makes fossil power plants net carbon sinks, however changing entirely the relationship between the three problems: in the short run it advances energy security and economic development while averting climate change. In the long run, the approach accelerates the transition to renewable sources of energy and is compatible with sustainable development. 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, whose functioning is analyzed. We explore the implications for extending Kyoto’s Clean Development Mechanism (CDM) in a way that benefits most the developing nations in Latin America and Africa, and the global transition from a fossil to a renewable economy.

We extend Bergstrom's 1985 results on nonparametric (NP) estimation in Hilbert spaces to unbounded sample sets. The motivation is to seek the most general possible framework for econometrics, NP estimation with no a priori assumptions on the functional relations nor on the observed data. In seeking the boundaries of the possible, however, we run against a sharp dividing line, which defines anecessary and sufficient conditionfor NP estimation. We identify this condition somewhat surprisingly with a classic statistical assumption on the relative likelihood of bounded and unbounded events (DeGroot, 2004). Other equivalent conditions are found in other fields: decision theory and choice under uncertainty (monotone continuity axiom (Arrow, 1970), insensitivity to rare events (Chichilnisky, 2000), and dynamic growth models (dictatorship of the present; Chichilnisky, 1996). When the crucial condition works, NP estimation can be extended to the sample spaceR+. Otherwise the estimators, which are based on Fourier coefficients, do not converge: the underlying distributions are shown to have “heavy tails” and to contain purely finitely additive measures. Purely finitely additive measures are not constructible, and their existence has been shown to be equivalent to the axiom of choice in mathematics. Statistics and econometrics involving purely finitely additive measures are still open issues, which suggests the current limits of econometrics.

This article studies decisions made under conditions of fear, when a catastrophic outcome is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky 1996, 2000, 2002, 2009). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based functions, is fully consistent with the new type of utility function implied by the new axioms.

« Aucune machine, aucun algorithme, ne pourra jamais être construit pour remplacer les valeurs et les décisions humaines. »

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 the climate change problem requires swift action and different strategies. There is no “silver bullet” and a combination of technologies and strategies will be required to meet the Intergovernmental Panel on Climate Change (IPCC) requirements. The article develops one example based on ‘negative carbon’ using air capture of carbon dioxide for storage into geological sites and solid materials. When driven by energy produced by carbon-neutral sources (such as Concentrated Solar Power or CSP) this approach can co-produce electricity while reducing carbon concentration in the atmosphere (Jones 2008, 2008b, Chichilnisky 2008, Chichilnisky and Eisenberger, 2009, Chichilnisky and Eisenberger et. al., 2009). While providing additional energy the process makes fossil power plants net carbon sinks, however changing entirely the relationship between the three problems: in the short run it advances energy security and economic development while averting climate change. In the long run, the approach accelerates the transition to renewable sources of energy and is compatible with sustainable development. 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, whose functioning is analyzed. We explore the implications for extending Kyoto’s Clean Development Mechanism (CDM) in a way that benefits most the developing nations in Latin America and Africa, and the global transition from a fossil to a renewable economy.

This paper develops a theory of the gender wage gap. In a general equilib- rium model, spouses devide their labor between a formal sector and a home sector. Due to indivisibility eects, productivity of labor in the formal sector is negatively related to labor used in the home; at the same time labor inputs are complementary in home production. We show that initial beliefs about the gender wage gap are self-ful…lling, and a central result is multiplicity of equilibria. Spouses allocate their labor equally, if they expect to earn the same wage rates, which ex post reinforces equal wage rates; whereas they allocate their labor dierently, if they expect to earn dierent wage rates. The latter situation manifests itself in a gender wage gap. By use of numer- ical examples, we show that welfare is highest when spouses allocate labor equally. We relate this …nding to policy recommendations.