Accounting for the ecosystem services of migratory species: Quantifying migration support and spatial subsidies

Migratory species support ecosystem process and function in multiple areas, establishing ecological linkages between their different habitats. As they travel, migratory species also provide ecosystem services to people in many different locations. Previous research suggests there may be spatial mismatches between locations where humans use services and the ecosystems that produce them. This occurs with migratory species, between the areas that most support the species' population viability - and hence their long-term ability to provide services - and the locations where species provide the most ecosystem services. This paper presents a conceptual framework for estimating how much a particular location supports the provision of ecosystem services in other locations, and for estimating the extent to which local benefits are dependent upon other locations. We also describe a method for estimating the net payment, or subsidy, owed by or to a location that balances benefits received and support provided by locations throughout the migratory range of multiple species. The ability to quantify these spatial subsidies could provide a foundation for the establishment of markets that incentivize cross-jurisdictional cooperative management of migratory species. It could also provide a mechanism for resolving conflicts over the sustainable and equitable allocation of exploited migratory species.     

Social Security, Optimality, and Equilibria in a Stochastic Overlapping Generations Economy

Social security institutions implement intergenerational transfers and distribute risks over time. To compare various social security designs, we study an overlapping generations model with demographic shocks. Production takes place through a neoclassical production function subject to productivity shocks. We give a near characterization of optimal allocations. We study rational expectations equilibria when contributions are mandatory, based on labor and capital income. We also describe the equilibria of an economy with a voluntary pay-as-you-go social security fund, and show that they have a long-run optimality property. An example with Cobb–Douglas production and utility functions illustrates the results.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

The Structure of Sunspot Equilibria: The Role of Multiplicity

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.     

Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

Efficient ecosystem services and naturalness in an ecological/economic model

In an integrated economic/ecological model, the economy benefits from ecosystem services that include: (1) the consumptive use of a harvested species, (2) the non-consumptive use of popular species, and (3) naturalness, i.e., the divergence of the ecosystem’s biodiversity from its natural steady state. The biological component of the model, which is applied to a nine-species Alaskan marine ecosystem, relies on individual optimizing behaviour by plants and animals to establish population dynamics. The biological component is used to define naturalness. By varying harvesting we arrive at different steady-state populations and humans choose from among these steady states. Welfare maximizing levels of the ecosystem services are derived, then it is shown that in the laissez-faire economy overharvesting occurs when the harvesting industry ignores ecosystem services (2) and (3). Lastly, we introduce efficiency restoring taxes and standards that internalize the ecosystem externalities.

Trade,Growth, and Increasing Returns to Infrastructure: The Role of the Sophisticated Monopolist*

Equilibrium in international trade with increasing returns in infrastructure depends on whether the infrastructure provider is “naïve” or sophisticated. A monopolist produces infrastructure under decreasing cost using fixed equipment. Unlike similar work, we derive a unique closed‐economy equilibrium. In a small open economy, with “naïve” infrastructure provider(s), multiple equilibria obtain. The industrial export potential of the economy depends on unexhausted economies of scale, and equilibria are possible where manufactures are exported despite an autarky price higher than the world price. With a sophisticated infrastructure provider, even an open economy has a unique equilibrium, which, at least as long as economies of scale are unexhausted, also involves more industrialization than the “naïve” equilibria. Access to the unlimited world market is necessary for significant industrialization but is not sufficient: one may also require “Schumpeterian” entrepreneurs, monopolists with a panoramic vision of the economy and of their catalytic role in it.     

Pricing the ecosystem and taxing ecosystem services: A general equilibrium approach

In an integrated dynamic general equilibrium model of the economy and the ecosystem humans and other species compete for land and prey biomass. Each submodel exhibits a price-driven competitive allocation mechanism, and the endogenously determined habitat is either openly accessible or privately owned. In both scenarios specific corrective taxes or subsidies are needed to internalize ecosystem externalities. An open access habitat causes additional inefficiencies through diverging prices for biomass and land in both subsystems. Values of all ecosystem components are determined in an efficient steady state clarifying the role and the interplay of ecosystem prices and economic prices.     

Excess supply equilibria

This paper addresses a fundamental problem in economic theory: How can there be equilibria of the economic system where some commodity is in excess supply, yet that commodity's relative price shows no tendency to fall? Of course, the principal example of such a phenomenon is an economy experiencing a prolonged period of involuntary unemployment of the labor force during which there is no significant change in the real wage.In the following pages, I shall describe a two-commodity, general equilibrium model that has a continuum of unemployment equilibria, one for any given unemployment rate. The important feature of this model is that workers establish their wage rates in an attempt to maximize expected utility. The information upon which these wage setting decisions are based is provided by actual labor market transactions.Despite the voluntary nature of the wage setting decision, I shall argue that each equilibrium of this economy exhibits involuntary unemployment in the Keynesian sense. For there will always be another equilibrium with a lower real wage, a higher level of employment, and at which (at least when workers are risk neutral) each worker achieves a higher level of expected utility.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

On the structure of Ramsey equilibrium: Cycles,indeterminacy, and sunspots

Summary We consider a one-sector neoclassical capital accumulation model under borrowing constraints with infinitely-lived heterogeneous households. Under the standard assumptions of strictly concave and time-additive utility functionals and a strictly concave production function we show that perfect foresight equilibria can be non-unique, even locally non-unique (indeterminate), and periodic of arbitrary long periodp. Moreover, we prove that there can exist non-trivial rational expectations (sunspot) equilibria when the agent's expectations about future factor prices depend on extrinsic uncertainty.Remarks made by an anonymous referee were extremely helpful in preparing the final draft of this paper.     

WELFARE GAINS AND LOSSES IN SUNSPOT EQUILIBRIA*

We study a standard two period exchange economy with one nominal asset. As is well known, there is a continuum of sunspot equilibria around each efficient equilibrium. A sunspot equilibrium is inefficient but some households may gain in sunspot equilibria relative to the efficient equilibrium. We show that a household's equilibrium utility level is either locally maximized or locally minimized at the efficient equilibrium, and derive a condition which identifies whether or not a household's utility is locally minimized or maximized.     

Ecosystem services and dis-services to agriculture

Agricultural ecosystems are actively managed by humans to optimize the provision of food, fiber, and fuel. These ecosystem services from agriculture, classified as provisioning services by the recent Millennium Ecosystem Assessment, depend in turn upon a web of supporting and regulating services as inputs to production (e.g., soil fertility and pollination). Agriculture also receives ecosystem dis-services that reduce productivity or increase production costs (e.g., herbivory and competition for water and nutrients by undesired species). The flows of these services and dis-services directly depend on how agricultural ecosystems are managed and upon the diversity, composition, and functioning of remaining natural ecosystems in the landscape. Managing agricultural landscapes to provide sufficient supporting and regulating ecosystem services and fewer dis-services will require research that is policy-relevant, multidisciplinary and collaborative. This paper focuses on how ecosystem services contribute to agricultural productivity and how ecosystem dis-services detract from it. We first describe the major services and dis-services as well as their key mediators. We then explore the importance of scale and economic externalities for the management of ecosystem service provision to agriculture. Finally, we discuss outstanding issues in regard to improving the management of ecosystem services and dis-services to agriculture.     

Factor-Market Distortions, Dynamic Stability, and Paradoxical Comparative Statics

In the late 1960s and early 1970s there was a strong revival of interest in the role of factor-market distortions in those branches of our subject which rely on the Lerner–Samuelson two-by-two model of production. Among the legacies from that period were several comparative statical propositions which seemed counterintuitive or paradoxical. However, the revival lost momentum when confronted with Neary's observation that the major paradoxes are associated with unstable equilibria and therefore rarely observed. On the other hand, there are now seen to be several errors in Neary's analysis. For example, in the important case of a closed economy (and, by interpretation, in the case of a large open economy) he overlooked the fact that paradoxes can be associated with stable equilibria.     

Harvesting in an integrated general equilibrium model

Harvesting of prey biomass is analyzed in an integrated ecological-economic system whose submodels, a predator–prey ecosystem and a simple economy, are microfounded dynamic general equilibrium models. These submodels are interdependent because the ecosystem responds to harvesting—through the reactions of optimizing individual organisms—by changing the provision of public ecosystem services to consumers. General analytical results are derived regarding the impact of harvesting policies on short-run equilibria of both submodels, on population dynamics, and on stationary states of the integrated model. A key insight is that prey biomass carries a positive ecosystem price which needs to be added as a tax mark-up to the economic price of harvested biomass to attain allocative efficiency. Further information on the dynamics is gained by resorting to numerical analysis of the policy regimes of zero harvesting, laissez-faire harvesting and efficient harvesting.

It “... is a matter of weighing costs and benefits of taking action, whether the action is the “inert” one of leaving resources alone in order to conserve them, or whether it involves exploiting a resource ... for so-called material ends”. Pearce (1976, p. 320)

Helpful comments from an anonymous referee are gratefully acknowledged. Remaining errors are the authors’ sole responsibility.     

On ‘Informationally Robust Equilibria’ for Bimatrix Games

Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked. The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players. The authors would like to thank Marieke Quant for her helpful comments.     

Verifying gross substitutability

Summary. In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability. Received: 21 August 2000; revised version: 28 November 2001     

Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability

This paper develops and analyzes an economic growth model which incorporates environmental quality into the production and utility functions. We solve our model for the balanced growth path and find that a unique low growth equilibrium is attained when environmental quality is given less weight in the utility function. Multiple equilibria exist if environment quality is given greater weight in the utility function. We also perform local stability analysis of our model. We conclude that an economy in which the environmental quality is given relatively less importance by the agents will be caught in low growth, high consumption poverty traps as is the case for many developing countries while other economies can potentially reach a relatively low consumption, high growth steady state if they place greater weight on environmental quality. Finally we look at how the gap between low and high growth equilibria shrinks when individuals place greater weight on environmental quality and how governmental policies can promote growth when societies give less weight to the environment.     

Incomplete Markets, Allocative Efficiency, and the Information Revealed by Prices

We compare rational expectations equilibria with different degrees of information revelation through prices. These equilibria arise in a two-period exchange economy with finitely many states and signals, multiple commodities and incomplete financial markets for nominal assets. We show that there are always equilibria where information is redundant in the sense of being of no value to the uninformed traders. We give conditions under which for a generic set of economies, parametrized by endowments and utilities, there exist open sets of equilibria for which allocative and informational efficiency are independent, with implications for monetary policy. Journal of Economic Literature Classification Numbers: D52, D60, D82, E52.     

The genesis of expectations and of sunspot equilibria

The existence—under certain conditions—of sunspot equilibria in overlapping generations models is a well-known theoretical result, but a lot of research has still to be made to understand whether and how such equilibria may occur as a consequence of a dynamic process. In this paper, we explore a model with individuals having simple utility functions and discover situations in which the dynamic processes of expectations and observed prices do not converge in spite of the existence of static equilibria. In other words, unfounded beliefs do still have a permanent influence on the real economy but induce erratic evolutions.