On equilibrium in resource markets with scale economies and stochastic prices

In this paper, I show the existence and the characteristics of equilibrium in a non-renewable resource market where extraction costs are non-convex and market price is subject to stochastic shocks, an empirically relevant setting. In my model firms may be motivated to hold inventories to facilitate production smoothing, which allows them to continue producing at a smooth pace at any instant when extraction ceases, e.g. when reserves are exhausted. This aspect of the model then supports a competitive equilibrium in the presence of non-convex costs. Casual empirical evidence is provided that supports the central features of my model for a variety of non-renewable resources, lending credence to the explanation for equilibrium I propose.     

Flattening the carbon extraction path in unilateral cost-effective action

Internalizing the global negative externality of carbon emissions requires the flattening of the extraction path of world fossil energy resources (=world carbon emissions). We consider governments with sign-unconstrained emission taxes at their disposal and seeking to prevent world emissions from exceeding some binding aggregate emission ceiling in the medium term. Such a ceiling policy can be carried out either in full cooperation or by a sub-global climate coalition. Unilateral action has to cope with carbon leakage and high costs, which makes a strong case for choosing a policy that implements the ceiling in a cost-effective way. In a two-country, two-period general equilibrium model with a non-renewable fossil-energy resource, we characterize the unilateral cost-effective ceiling policy and compare it with its fully cooperative counterpart. We show that with full cooperation there exists a cost-effective ceiling policy in which only first-period emissions are taxed at a rate that is uniform across countries. In contrast, the cost-effective ceiling policy of a sub-global climate coalition is characterized by emission regulation in both periods. The share of the total stock of energy resources owned by the sub-global climate coalition turns out to be a decisive determinant of the sign and magnitude of unilateral cost-effective taxes.     

Set-up costs and the existence of competitive equilibrium when extraction capacity is limited

Although set-up costs are prevalent and substantial in natural resource extraction, it is known that a Walrasian competitive equilibrium cannot exist in simple extraction models with set-up costs. This paper demonstrates that this result is sensitive to the assumption of unlimited extraction capacity and derives sufficient conditions for existence. An equilibrium exists if extraction is limited such that each firm earns sufficient surplus to cover its set-up costs or if firms choose extraction capacity subject to non-increasing returns. The resulting competitive equilibrium price either grows at the rate of interest when total extraction is below industry capacity or is constant when industry capacity is fully utilized. In the equilibrium, identical deposits are opened simultaneously, and set-up costs for new deposits are incurred when the industry has excess capacity rather than when capacity is fully utilized.     

Extraction capacity and the optimal order of extraction

The least-cost-first extraction rule for deposits with different extraction costs previously has been shown to be invalid in general equilibrium. This paper demonstrates that this rule also does not hold in partial equilibrium when extraction capacity is limited. Necessary and sufficient conditions for several surprising extraction orders are presented. If extraction from a high-cost resource is constrained, it may be optimal to begin extraction from a high-cost deposit (or backstop) strictly before extracting from a lower-cost deposit. If extraction from a low-cost resource is limited, it may be optimal to exhaust a high-cost deposit strictly before the low-cost deposit is exhausted or to abandon extraction temporarily from a high-cost deposit and then to exhaust it later. The analysis demonstrates how extraction constraints affect the order of extraction and shows that certain cost reversals are caused by limited extraction capacity rather than by the general equilibrium definition of extraction costs.     

Trade, technology, and the environment: Does access to technology promote environmental regulation?

Focusing specifically on regulation of coal-fired power plants, we examine how technological innovation by early adopters influences the timing of new environmental regulation in non-innovating countries. We build a general equilibrium model of an open economy to identify the political-economy determinants of regulation. With a newly created dataset of SO₂ and NO_x regulations for coal-fired power plants and a patent-based measure of the technology frontier, we estimate the determinants of environmental regulation diffusion. Our findings support the hypothesis that international economic integration eases access to environmentally friendly technologies and leads to earlier adoption, ceteris paribus, of regulation in non-innovating countries. However, we also find evidence that domestic trade protection promotes earlier adoption allowing shifts of regulatory costs to domestic consumers. Furthermore, international market power permits large countries to shift costs to foreign consumers. Other political economy factors, such as the quality of domestic coal, are also important determinants.     

Feasibility and stability in randomly assembled Lotka-Volterra models

For a Lotka-Volterra model to represent a viable ecosystem it's nontrivial equilibrium must be feasible. If m is the number of species, it is shown that in a set of randomly assembled Lotka-Volterra models, the fraction of models with a feasible equilibrium is some function of m which behaves like 2^?m. Moreover a subset of Lotka-Volterra models, each of which has a feasible equilibrium, has the same stability property as a set of linear models which is assembled randomly in the same manner. This contradicts a recent claim that a Lotka-Volterra model with a feasible equilibrium tends to be stable. Thus for two reasons the probability that a Lotka-Volterra model represents a viable and stable ecosystem decreases rapidly with the number of species. This supports the theme developed by May that stability in model ecosystems decreases with diversity.     

A parsimonious optimal foraging model explaining mortality patterns in Serengeti wildebeest

Based on data collected over 24 years in the Serengeti in Tanzania, Sinclair and Arcese (1995) indicated that the sensitivity of blue wildebeest Connochaetes taurinus to predation risk by lions Panthera leo may cause them to change habitats between open (low risk) and wooded (risky) habitats. They found that, in poor rainfall years, predators kill wildebeest that are in better condition than those that die of natural causes. In good rainfall years, predators kill wildebeest that are in worse condition than those that die of natural causes. Sinclair and Arcese (1995) proposed the “predation-sensitive food” hypothesis. This hypothesis suggests that, as food becomes limiting, animals take greater risks to obtain more food, and some of these animals are killed. I propose a more parsimonious hypothesis based on the marginal value theorem that is consistent with the observations made by Sinclair and Arcese (1995). Wildebeest follow a single decision rule in good and poor rainfall years, viz. move when foraging elsewhere increases your rate of intake of nutritious food. Similarly, predators follow a single decision rule in good and poor rainfall years, viz. take the prey item that maximizes the intake of energy per unit effort expended. This parsimonious model does not require differences in predator sensitivity as required by Sinclair and Arcese's (1995) model. I indicate ways in which my model can be falsified.     

Subgame-perfect cooperative agreements in a dynamic game of climate change

We model climate change as a dynamic game and prove existence of a unique subgame-perfect Nash equilibrium (SPNE) that is also Markov perfect. We interpret this unique SPNE as the business-as-usual (BAU) equilibrium and show that if the countries are not sufficiently symmetric then the familiar trigger strategy equilibria may not be Pareto improvements over the BAU equilibrium and may even lack efficiency properties. We then motivate and introduce a subgame-perfect cooperative agreement as an improvement over the BAU equilibrium in the sense that every country or coalition of countries is better off in every subgame, irrespective of the extent of heterogeneity of the countries. We characterize subgame-perfect cooperative agreements and identify sufficient conditions for their existence. We show that (direct or indirect) transfers between countries to balance the costs and benefits of controlling climate change are a necessity and not a matter of approach.     

Influence of low and decreasing food levels on Daphnia-algal interactions: Numerical experiments with a new dynamic energy budget model

Based on numerical experiments with a new physiologically structured population model we demonstrate that predator physiology under low food and under starving conditions can have substantial implications for population dynamics in predator-prey interactions. We focused on Daphnia-algae interactions as model system and developed a new dynamic energy budget (DEB) model for individual daphnids. This model integrates the κ-rule approach common to net assimilation models into a net-production model, but uses a fixed allocation of net-productive energy in juveniles. The new DEB-model agrees well with the results of life history experiments with Daphnia. Compared to a pure κ-rule model the new allocation scheme leads to significant earlier maturation at low food levels and thus is in better agreement with the data. Incorporation of the new DEB-model into a physiologically structured population model using a box-car elevator technique revealed that the dynamics of Daphnia-algae interactions are highly sensitive to the assumptions on the energy allocation of juveniles under low food conditions. Additionally we show that also other energy allocation rules of our DEB-model concerning decreasing food levels and starving conditions at the individual level have strong implications for Daphnia-algae interactions at the population level. With increasing carrying capacity of algae a stable equilibrium with coexistence of Daphnia occurs and algae shifts to limit cycles. The amplitudes of the limit cycles increase with increasing percentage of sustainable weight loss. If a κ-rule energy allocation is applied to juveniles, the stable equilibrium occurs for a much narrower range of algal carrying capacities, the algal concentration at equilibrium is about 2 times larger, and the range of algae carrying capacities at which daphnids become extinct extends to higher carrying capacities than in the new DEB-model. Because predator-prey dynamics are very sensitive to predator physiology under low food and starving conditions, empirical constraints of predator physiology under these conditions are essential when comparing model results with observations in laboratory experiments or in the field.     

Is there really a green paradox?

In the absence of a CO₂ tax, the anticipation of a cheaper renewable backstop increases current emissions of CO₂. Since the date at which renewables are phased in is brought forward and more generally future emissions of CO₂ will decrease, the effect on global warming is unclear. Green welfare falls if the backstop is relatively expensive and full exhaustion of fossil fuels is optimal, but may increase if the backstop is sufficiently cheap relative to the cost of extracting the last drop of fossil fuels plus marginal global warming damages as then it is attractive to leave more fossil fuels unexploited and thus limit CO₂ emissions. We establish these results by analyzing depletion of non-renewable fossil fuels followed by a switch to a clean renewable backstop, paying attention to timing of the switch and the amount of fossil fuels remaining unexploited. We also discuss the potential for limit pricing when the non-renewable resource is owned by a monopolist. Finally, we show that if backstops are already used and more backstops become economically viable as the price of fossil fuels rises, a lower cost of the backstop will either postpone fossil fuel exhaustion or leave more fossil fuel in situ, thus boosting green welfare. However, if a market economy does not internalize global warming externalities and renewables have not kicked in yet, full exhaustion of fossil fuel will occur in finite time and a backstop subsidy always curbs green welfare.     

Is there really a green paradox?

In the absence of a CO₂ tax, the anticipation of a cheaper renewable backstop increases current emissions of CO₂. Since the date at which renewables are phased in is brought forward and more generally future emissions of CO₂ will decrease, the effect on global warming is unclear. Green welfare falls if the backstop is relatively expensive and full exhaustion of fossil fuels is optimal, but may increase if the backstop is sufficiently cheap relative to the cost of extracting the last drop of fossil fuels plus marginal global warming damages as then it is attractive to leave more fossil fuels unexploited and thus limit CO₂ emissions. We establish these results by analyzing depletion of non-renewable fossil fuels followed by a switch to a clean renewable backstop, paying attention to timing of the switch and the amount of fossil fuels remaining unexploited. We also discuss the potential for limit pricing when the non-renewable resource is owned by a monopolist. Finally, we show that if backstops are already used and more backstops become economically viable as the price of fossil fuels rises, a lower cost of the backstop will either postpone fossil fuel exhaustion or leave more fossil fuel in situ, thus boosting green welfare. However, if a market economy does not internalize global warming externalities and renewables have not kicked in yet, full exhaustion of fossil fuel will occur in finite time and a backstop subsidy always curbs green welfare.     

The demand for site-specific recreational activities: A characteristics approach

A model of constrained utility maximizing behavior is developed to explain how a representative individual allocates his ski days among alternative sites. The physical characteristics of the ski areas and the individual's skiing ability are explicit arguments in the utility function; the budget allocation is given along with the parametric costs to ski (including travel costs, entrance fees, equipment costs, and the opportunity cost of his time). Shares (a site's share being the proportion of ski days that the individual spends at that site) are derived and assumed multinomially distributed, a stochastic specification which maintains the inherent properties of the shares. Maximum likelihood estimation confirms the basic hypothesis that costs, ability, and characteristics all are important determinants of the sites' shares. The model explains a large proportion of the skier's allocation of ski days. A multinomial logit model of skier behavior is also developed and maximum likelihood estimates of its parameters are obtained. Examination of the summary statistics from my model and the logit model indicates that my model predicts the skier's choice of sites better than the logit model.     

The benefit of obligate versus facultative strategies in a shrimp–goby mutualism

Obligate mutualists are predicted to benefit more from mutualism than facultative mutualists and harbor traits that help derive this extra benefit. I tested these predictions with a shrimp–goby mutualism. Individual shrimp (Alpheus floridanus) construct burrows that are shared with individual gobiid fishes that warn shrimp when emergence from burrows is unsafe. The benefit to gobies is refuge from predation. I compared predator avoidance performance of obligate (Nes longus) and facultative (Ctenogobius saepepallens) shrimp-associated gobies with access to a shell, a shrimp burrow, or no shelter. The two gobies performed similarly with shells and no shelter, but N. longus outperformed C. saepepallens with shrimp burrows. Thus, N. longus benefits more from mutualism than C. saepepallens. Also, N. longus has four behavioral traits that likely allow it to benefit from mutualism more than does C. saepepallens: (1) diving into the nearest shrimp burrow when confronted with predators, (2) long flight initiation distance, (3) long time-until-re-emergence after taking refuge, and (4) remaining close to shelter. The latter three likely come with a cost to foraging or mate acquisition as they limit searching range outside the burrow and detract from time spent outside burrows. Thus, N. longus likely harbors traits that allow it to deal with these costs. I discuss a framework for determining whether traits crucial to obligate association with shrimp (both for reaping benefits and dealing with costs) are pre-adaptations or are created through coevolution with shrimp.     

A general bioeconomic simulation model for annual-crop marine fisheries

A generalized bioeconomic simulation model of annual-crop marine fisheries is described and its use in marine fisheries management is demonstrated. The biological submodel represents the recruitment of new organisms into the fishery, the movement of organisms from one fishing area to another and from one depth to another, the growth of organisms and the mortality of organisms resulting both from natural causes and from fishing. The economic submodel represents the fishing effort exerted on each resource species, the monetary costs of fishing, the value of the harvest and the rent (or excess profits) to the fishery.Basic dynamics of the model results from changes in the number of organisms in the fishery over time, which can be summarized as a set of difference equations of the general form ΔN/Δt = R + I ? E ? M ? F where ΔN/Δt is the net change in number of organisms in the fishery over time, R is recruitment, I is immigration, E is emigration, M is natural mortality and F is fishing mortality. R is a driving variable, whereas I, E, M and F are functions of the state of the system at any given point in time. The model can be run in a deterministic or stochastic mode. Values for parameters affecting rates of recruitment, movement, growth, natural mortality and fishing mortality can be selected from uniform, triangular or normal distributions.Use of the model within a fisheries-management framework is demonstrated by evaluating several management alternatives for the pink shrimp (Penaeus duorarum) fishery on the Tortugas grounds in the Gulf of Mexico. Steps involved in use of the model, including parameterization, validation, sensitivity analysis and stochastic simulations of management policies, are explained.     

Asymmetric contests at the nest

Hatching asynchrony of nestling birds leads to weight asymmetries, which in turn affect the nestlings’ relative success when competing for feedings brought to the nest. We present a game theoretic model that predicts how weight asymmetry influences the nestlings’ energy on securing feedings, thus determining the caloric value remaining for weight gain as well as the distribution of feedings obtained. The model has a unique Evolutionary Stable Strategy (ESS) profile, in which nestlings in more asymmetric nests exhibit less aggression and hence achieve larger weight gain per feeding. The impetus for this model was data from a long-term study of Arabian babblers (Turdoides squamiceps) that showed a surprising negative correlation between the number of feedings that a nest received and the overall weight gain in the nest. This finding is, however, entirely consistent with our model—in more symmetric nests, the individuals fight more and are consequently hungrier and beg for additional food, are fed more, but still gain less weight due to the higher energetic costs of fighting. The model provides a fundamental explanation also for related findings in other species, in which chicks in asynchronous broods were found to be heavier than those from synchronous broods. In addition, it supports the sibling rivalry hypothesis by which brood asynchrony may diminish aggressive interactions among nestlings, leading to more efficient use of resources.     

A model approach to evaluate the effect of temperature and food concentration on individual life-history and population dynamics of Daphnia

We present a model framework for the simulation of growth and reproduction of Daphnia at varying conditions of food concentration and temperature. The core of our framework consists of an individual level model that simulates allocation of assimilated carbon into somatic growth, maintenance costs, and reproduction on the basis of a closed carbon budget. A fixed percentage of assimilated carbon is allocated into somatic growth and maintenance costs. Special physiological adaptations in energy acquisition and usage allow realistic model performance even at very low food concentrations close to minimal food requirements. All model parameters are based on physiological measures taken from the literature. Model outputs were thoroughly validated on data from a life-table experiment with Daphnia galeata. For the first time, a successful model validation was performed at such low food concentrations. The escalator boxcar train (EBT) was used to integrate this individual level model into a stage-structured population model. In advance to previous applications of the EBT to Daphnia we included an additional clutch compartment into the model structure that accounts for the characteristic time delay between egg deposition and hatching in cladocerans. By linking two levels of biological organisation, this model approach represents a comprehensive framework for studying Daphnia both at laboratory conditions and in the field. We compared outputs of our stage-structured model with predictions by two other models having analogous parameterisation: (i) another individual level Daphnia model (Kooijman–Metz model) and (ii) a classical unstructured population model. In contrast to our Daphnia model, the Kooijman–Metz model lacks the structure to account for the optimisation of energy acquisition and maintenance requirements by individual daphnids. The unstructured population model showed different patterns of population dynamics that were not in concordance with typical patterns observed in the field. Thus, we conclude our model provides a comprehensive tool for the simulation of growth and reproduction of Daphnia and corresponding population dynamics.     

Environmental Constituent Interest, Green Electricity Policies, and Legislative Voting

Research in political economy has traditionally sought to disentangle the effects of legislative ideology and constituent interest in explaining policy decisions. Frequently, proxy variables are used to measure constituent interest. However, these measures do not adequately reflect true constituent interest, which is based upon the costs and benefits of the policies under consideration, incorporating the scope of the policies. Using Haiku, a detailed model of the US electricity sector, and TAF, an integrated assessment model of pollution pathways and valuation, I construct economic measures of constituent interest at the state level as well as for federal policy. I then use these measures to analyze state adoption of more stringent green electricity policies and congressional roll-call voting on federal environmental policy. Previous studies that use proxy measures of constituent interest typically find that the legislator ideology matters more, while my study shows that both ideology and constituent interest are significant factors.     

Thin versus Thick CO2 Market

The idea that trading is more costly the thinner the market is is common in most studies of market exchange with frictions. Surprisingly, this element is lacking from previous attempts to allow for frictions in pollution permit markets. This paper considers a CO₂ cap-and-trade model where trading costs develop endogenously as a function of the market size. The pre-trade allocation of permits determines whether the market size can be strongly influenced by expectations that have a role because of adjustment costs. The pre-trade allocation also sets preconditions for endogenously vanishing trading costs and thus has nonstandard effects on long-run trading levels and market allocations.     

Do lower electricity storage costs reduce greenhouse gas emissions?

In the electricity sector, innovation in large-scale storage is anticipated to reduce costs and improve performance. The effect on greenhouse gas emissions of lower storage costs depends on the interactions between storage and the entire grid. The literature has disagreed on the role of storage in reducing emissions. In this paper we present a stylized model, which suggests that the effect of storage costs on emissions depends on the supply responsiveness of both fossil and renewable generators. Under common conditions in the United States, lower storage costs are more likely to reduce emissions when wind investment responds to equilibrium electricity prices and when solar investment does not. Simulations of a computational model of grid investment and operation confirm these intuitions. Moreover, because of its effect on coal and natural gas–fired supply responsiveness, introducing a carbon dioxide emissions price may increase the likelihood that lower storage costs reduce emissions.     

Time budgets and foraging in a Malagasy primate: do sex differences reflect reproductive condition and female dominance?

Female mammals commonly employ behavioral tactics of modulating activity levels and foraging behavior to counter the energetic burden of reproduction; these behavioral changes are reflected as intersexual differences. Traditional views of Malagasy primates posit that high reproductive costs select for female dominance which guarantees to energetically stressed females priority of resource access. I tested predictions regarding reproductive influences on sex differences in time budgets and foraging behavior using two groups of Milne-Edwards' sifaka (Propithecus diadema edwardsi) in southeastern Madagascar. Compared to males, females increased neither feeding nor resting time during gestation or lactation. Sex differences were essentially absent in all foraging time variables examined (time, duration, rate). In contrast, dietary composition diverged between the sexes in some months. The possibility that females selected particular food items to boost nutrient and energetic intake to meet increased requirements during reproduction must be further clarified with nutritional analyses. Sex differences in plant part choices coincided with lactation in one of the two study groups. Thus, the timing of sex differences in feeding patterns of P. d. edwardsi only partially supports the prediction that sex differences are most pronounced during the period of greatest female energetic demand. A comparative review indicated no tight association between female dominance and sex differences in foraging among Malagasy primates. Traditional female dominance theory falls short of explaining the observed patterns. The results of my study coupled with recent evidence suggest that non-behavioral tactics involving energy conservation and storage require further attention as mechanisms by which female lemurs cope with reproductive costs. Received: 12 June 1998 / Accepted after revision: 10 October 1998