Pollution control and technological advance: A dynamic model of the firm

The paper extends the static comparison of effluent taxes and effluent standards to a dynamic world in which firms invest resources in improving their abatement technology as well as their production technology. The analysis shows that the two pollution control policies lead to a distinctly different allocation of research and development (R & D) funds between improvement in abatement technology and improvement in production technology. The model also shows that a temporally constant effluent tax leads to an increasing effluent discharge rate for “typical” firms. Other results concern the pattern of output growth and the rate of technological advance.     

Derived decision rules for pollution control in a general equilibrium space economy

This paper attempts to narrow the gap between economic theory and policy inthe field of environmental pollution control by expanding the traditional general equilibrium model to include the kind of spatial detail that is important for describing pollution. This model is then used to derive theorems which provide the basis for the development of spatially differentiated, tax-based decision rules. In spite of the fact that these rules require no information on either damage costs or control costs, they maintain many of the desirable properties of the more conventional informationally intensive tax policies.     

Pollution control in a simplified general-equilibrium model with production externalities

Pollution externalities of the producer-producer type are considered in a positive two-sector model with stationary capital and labor. By assumption, output from the polluting sector can be diverted to pollution abatement. Environmental authorities attempt to control the level of pollution to some minimum “acceptable” standard by requiring polluters to depollute through the mechanism of a uniform tax on production. Following discussion of short-run considerations, the stability of the tax-adjustment scheme is examined and the dynamic nature of growth paths in the economy is explored.     

Household incidence of pollution control policies: A robust welfare analysis using general equilibrium effects

This study assesses the incidence of pollution control policies on households. In contrast to previous studies, we employ an integrated framework combining a multisector general equilibrium model with a stochastic dominance analysis using household-level data. We consider three policy instruments in a domestic emission trading system: (i) an output-based allocation (OBA) of permits; (ii) the use of the proceeds of permit sales to reduce payroll taxes (RPT); (iii) and the use of these proceeds to reduce consumption taxes instead (UCS). The general equilibrium results suggest that the return to capital is more negatively affected than the wage rate in all simulations, since polluting industries are capital intensive. Abstracting from pollution externalities, the dominance analysis suggests that all three policies have a normatively robust negative (positive) impact on welfare (poverty). Formal dominance tests indicate that RPT first-order welfare dominates OBA over all values of household incomes. UCS also first-order poverty dominates RPT for any choice of poverty line below $CAN 18,600, and poverty dominates for any poverty line (and thus welfare dominates) at the second order. Finally, while the three pollution control policies do not have a numerically large impact on inequality (in comparison to the base run), statistical tests indicate that inequality increases significantly more with OBA and RPT than with UCS.     

Experimental study on dynamic equilibrium of headland-bay beaches

A dynamic equilibrium bay (DEB) is an embayment with continuous sediment supply and its shoreline planform can remain stable over a long period of time without erosion or accretion. For coastal conservation of sandy headland-bay beaches (HBB), the concept of using a static equilibrium bay (SEB) is well known, but that for DEB has received little attention. Moreover, an empirical equation for the stability of a DEB is not yet available. Experiments on DEB shape that aim to derive new coefficients in the parabolic bay shape equation (PBSE) for DEB are now being conducted in the laboratory. The work commences from an initial artificial HBB in static equilibrium with sediment supply source from the lee of an upcoast headland. A final equilibrium planform is obtained for the condition with a specific wave obliquity and sediment supply rate until no further shoreline change is found. In order to fit the PBSE for a DEB, a new parameter called SSR (sediment supply ratio) that represents the ratio of sediment supply rate from the source and the potential longshore sediment transport rate is introduced to quantify the balance of sediment to the bay. Alternative C coefficients in the PBSE for DEB, which include wave obliquity and the SSR, are then calculated. These new coefficients for DEB can now be used to evaluate the influence of sediment supply from a riverine source on a DEB and to classify its equilibrium status for planning sediment management strategies in coastal conservation.     

A model system of four species with a unique equilibrium point

A four component model of two competing organisms, each with a specific parasite, has been exercised so as to investigate its equilibria. In addition to the equilibrium to which the model is known to return after moderate disturbance, severe perturbation led to a new steady state which had the appearance of an equilibrium but which was not maintained in the long term. Some discussion of what constitutes equilibrium and of stability of equilibria is presented.     

Production, consumption, and general equilibrium with physical constraints

This paper analyzes the consequences of integrating the conservation laws of mass and energy into the microeconomic models of production, consumption, and general equilibrium. We show that abstract models and especially general equilibrium theory are consistent with these physical constraints, but most applied and environmental economic models are not. We analyze the consequences of physical conservation laws for substitution possibilities and show that these constraints limit the number of independent substitution processes but not the value of the substitution elasticities. Finally, we propose a method for integrating physical constraints into static microeconomic models with a minimum of changes.     

Production externalities and corrective subsidies: A general equilibrium analysis

Several recent attempts have been made to demonstrate that corrective subsidies and taxes do not have symmetric allocation effects. These demonstrations have utilized graphical partial equilibrium analysis. In this paper a general equilibrium model is introduced to show that a standard partial equilibrium result may be incorrect and that subsidies may lead to equilibrium states which are socially preferred to the status quo position.     

Pollution control and inputs to production

The primary concern of this paper is to identify the inputs required for air, water, and solid waste pollution abatement in the United States. Industry level data on pollution abatement expenditures in 1976 are decomposed into expenditures on various intermediate inputs and on two primary inputs—labor and capital. The 1971 input-output table is adjusted to reflect the input needs of pollution abatement technology. This revised direct input coefficients matrix is used to derive the gross output and primary input requirements of the 1971 final bill of goods.     

Open- and closed-loop equilibrium control of trophic chains

If a nearly natural population system is deviated from its equilibrium, an important task of conservation ecology may be to control it back into equilibrium. In the paper a trophic chain is considered, and control systems are obtained by changing certain model parameters into control variables. For the equilibrium control two approaches are proposed. First, for a fixed time interval, local controllability into equilibrium is proved, and applying tools of optimal control, it is also shown how an appropriate open-loop control can be determined that actually controls the system into the equilibrium in given time. Another considered problem is to control the system to a new desired equilibrium. The problem is solved by the construction of a closed-loop control which asymptotically steers the trophic chain into this new equilibrium. In this way, actually, a controlled regime shift is realized.     

A dynamic model of human dispersal in a land-based economy

This paper presents a dynamic state variable model that examines human dispersal in a land-based economy. In humans, like other animals, many individuals disperse during their lifetimes, with extensive variability in the timing and likelihood of dispersal by individuals of different states. The model places human and non-human dispersal in a common framework, specifically by utilizing a cost-benefit approach. As with other animals, individual access to resources likely plays an important role in shaping human dispersal, and the model explores the mechanisms underlying this relationship. Over a series of time steps, individuals must decide whether to stay in their natal area or disperse, given their states (wealth, marital, and inheritance status) and the environmental constraints on dispersal. Costs of dispersal include time and an initial drop in wealth, while the benefit is the potential of the dispersal area to increase wealth. The model determines whether dispersing or staying results in the highest fitness, where fitness is a function of individual wealth and years married. The model shows that dispersal is favorable under a wide range of environmental conditions, but that it also varies predictably according to individual states. Men of middle wealth values disperse under a wider variety of circumstances than poorer or wealthier men. Wealthy men, who are particularly sensitive to the time cost and mortality risk associated with dispersing, appear to adopt a more conservative dispersal strategy than poorer men, who are more sensitive to the wealth cost and wealth growth rate associated with dispersing. Dispersal behavior is also contingent on its effects on an individual's probability of marrying or inheriting wealth. Finally, the model fosters an examination of how the interaction of life events, and their directions of causation, can be studied. Received: 6 May 1998 / Received in revised form: 3 February 1999 / Accepted: 7 February 1999     

Evaluating predictive errors of a complex environmental model using a general linear model and least square means

A general linear model (GLM) was used to evaluate the deviation of predicted values from expected values for a complex environmental model. For this demonstration, we used the default level interface of the regional mercury cycling model (R-MCM) to simulate epilimnetic total mercury concentrations in Vermont and New Hampshire lakes based on data gathered through the EPAs Regional Environmental Monitoring and Assessment Program (REMAP). The response variable for the GLM was defined as R-MCMs predictive error: the difference between observed mercury concentrations and modeled mercury concentrations in each lake. Least square means of the response variable are used as an estimate of the magnitude and significance of bias, i.e., a statistically discernable trend in predictive errors for a given lake type, e.g., acidic, stratified, or oligotrophic. Using our approach, we determined lake types where significant over-prediction and under-prediction of epilimnetic total mercury concentration was occurring, i.e., regions in parameter space where the model demonstrated significant bias was distinguished from regions where no significant bias existed. This technique is most effective for finding regions of parameter space where bias is significant. Drawing conclusions concerning regions that show no significant bias can be misleading. The significant interaction terms in the GLM demonstrated that addressing this problem using univariate statistical techniques would lead to a loss of important information.     

Pollution control and optimal taxation: A static analysis

This article attempts to contribute to the analysis of identifying an optimum tax for the generation of pollutants when both anti-bads and bads are included in the utility function. Bads and anti-bads are introduced via a technological tradeoff relationship with substitution allowed. It is shown that in some instances in order to know the optimum tax on polluters it may not be important to know the marginal damage function. A brief analysis is undertaken of the tradeoffs between private actions to reduce the effect of pollutants and collective provisions for pollution control. The analysis further demonstrates that under certain circumstances the appropriate tax on polluters can be calculated from observed defensive behavior on the part of receptors.     

Sustained dynamic transience in a Lotka-Volterra competition model system for grassland species

Theoretical approaches, such as the Lotka-Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment of stable states. Managed grassland ecosystems in Northwestern Europe experience structural periodic fluctuations in environmental conditions: the seasons. In addition, periodic disturbances such as cutting are very common. Here we show, using a Lotka-Volterra system applied to grassland species with empirically derived parameters, that seasonal variability can result in a time dependent equilibrium and redirection of displacement processes.Parameter estimates differed between species and - in most cases - between the seasons. As a result, five of the fifteen tested species combinations had different outcomes of species interactions between seasons. This indicates that systems remain in dynamic transience over the year as the equilibrium changes and the species composition of the system follows the equilibrium without ever attaining it. The non-attainment of the steady state enables coexistence of species even if there is competitive exclusion in one of the seasons. For three of the fifteen species combinations, cutting frequency affected the long-term coexistence patterns. Cutting resets the biomass of competing species and favours during regrowth those species that have a high growth rate, which can alter species coexistence in comparison to a Lotka-Volterra model without cutting. The Lotka-Volterra framework with seasonally changing empirical parameters predicts coexistence as a possible outcome of systems that in component seasons are characterised by exclusion, and vice versa.     

Flocking behaviour of passerines: a dynamic model for the non-reproductive season

Summary The behaviour of a small male passerine bird over a typical winter day is studied by a dynamic programming model. The bird can be either unpaired or paired; an unpaired bird can forage in a flock, forage alone or sing to attract a mate. Foraging increases his reserves, while singing reduces them. The optimal policy and the expected behaviour of birds depend both on time and reserves. The model predicts that birds will flock, especially in the morning, if flocking birds find more food (foraging efficiency), and also more flocking can be expected when the predation risk is lower in a flock (antipredator benefit). Where flocking gives lower variance in food intake, with the same mean (reduced variance benefit), birds with low reserves at the end of the day choose to forage alone (high variance option), while otherwise they are risk-averse and forage in a flock. The cost of flocking increases with time in a day and with the probability of mate attraction through singing. Decisions inevitably involve trade-offs. Where flocking results in antipredator benefit, but also lower foraging gain, birds with low reserves forage alone, but birds with high reserves flock. Offprint requests to: A.I. Houston     

A general two-species competition model with time-varying rates

The classical mathematical model for the behaviour of the populations of two competing biological species has previously been generalized by the author, by assuming that the coefficients of intrinsic growth, self-inhibition and interaction were all functions of time and, for a certain class of the governing differential equations, the exact solutions were obtained: an example was given in which the coefficients were periodic functions. In the differential equations of this model (as well as in the autonomous Lotka-Volterra equations), each of the Malthusian growth-rates was assumed to be diminished by a linear function of the populations of the two species, without there being any rigorous justification for this assumption. We here generalize the differential equations by assuming for these diminution functions general nonlinear forms having time-varying coefficients. The exact solutions are given for four classes of the resulting strongly nonlinear non-autonomous differential equations. Various conclusions about the growth modes of the two populations and their asymptotic behaviour are drawn, both when specific and when arbitrary forms are assumed for the coefficient functions. Cases are examined in which the Competitive Exclusion Principle holds and others in which it does not.     

Application of a coupled ecosystem-chemical equilibrium model, DayCent-Chem, to stream and soil chemistry in a Rocky Mountain watershed

Atmospheric deposition of sulfur and nitrogen species have the potential to acidify terrestrial and aquatic ecosystems, but nitrate and ammonium are also critical nutrients for plant and microbial productivity. Both the ecological response and the hydrochemical response to atmospheric deposition are of interest to regulatory and land management agencies. We developed a non-spatial biogeochemical model to simulate soil and surface water chemistry by linking the daily version of the CENTURY ecosystem model (DayCent) with a low temperature aqueous geochemical model, PHREEQC. The coupled model, DayCent-Chem, simulates the daily dynamics of plant production, soil organic matter, cation exchange, mineral weathering, elution, stream discharge, and solute concentrations in soil water and stream flow. By aerially weighting the contributions of separate bedrock/talus and tundra simulations, the model was able to replicate the measured seasonal and annual stream chemistry for most solutes for Andrews Creek in Loch Vale watershed, Rocky Mountain National Park. Simulated soil chemistry, net primary production, live biomass, and soil organic matter for forest and tundra matched well with measurements. This model is appropriate for accurately describing ecosystem and surface water chemical response to atmospheric deposition and climate change.     

螺旋藻培养与动力学模型

在内循环气升式光生物反应器中,就螺旋藻细胞在不同碳源培养其中的生长行以及藻细胞对光能和碳源的利用特性进行了初步研究,结果表明,向培养体系中通入气体流量1％的CO2,有助于提高经式培养的细胞终浓度和稳定培养体系的PH环境;改进的Lambert-Beer定律可较好地描述细胞浓度及光程对光衰减的综合影响,引入平均光强和平均比消光量概念,探讨了细胞比生长速率与它们之间的关系;藻液中总碳量随细胞浓度的上升呈指数关系减少,藻细胞对碳源的得率系数在批式 不同时期之间存在差异。图12参9     

A dynamic mathematical model for wastewater stabilization ponds

A dynamic mathematical model was developed to predict the effluent quality of facultative wastewater stabilization ponds. For a sound representation of sediment–water column, water column–atmosphere interactions and stratification due to variations in dissolved oxygen concentrations, a two-dimensional hydraulic model was employed considering dispersed flow and diffusion in horizontal and vertical directions, respectively. Resulting partial differential equation system was solved using finite difference methods and matrix manipulation techniques. The model has been calibrated and evaluated on the basis of collected data from a full-scale facultative stabilization pond in Selçuk, Izmir. Variations of COD, NH₄-N, PO₄-P, dissolved oxygen, bacteria and algae concentrations with time and the dimensions of the pond were estimated by using the dynamic model. The model can be used for design of new stabilization ponds and also, for improving the effluent quality of existing ponds.