THE COSTATE VARIABLE IN A STOCHASTIC RENEWABLE RESOURCE MODEL

ABSTRACT. In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See for example Lyon [1999], Clark [1990, pp. 102 107] and Arrow and Kurz [1970, pp. 35 37]; however, there is little discussion of this variable for stochastic models, even though thecostate variable has similar roles in the two models. In both models the costate variableis a shadow value of the associated state variable, and as such has the role of rationingthe use of the state variable. In addition, as has been shown in Lyon [1999], in natural resource problems the costate variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example to help solidify the results.     

OPTIMAL DISCOUNTING OF BENEFITS FROM CLEANUP AT WASTE SITES

Abstract This paper uses a general equilibrium optimal growth model to discuss the role of optimal discounting of future benefits from cleanup at high‐level toxic waste sites. Cleanup simultaneously generates two streams of benefits. One of these is directly from utility and the other is indirectly from the added productivity of workers. We note that the optimal discount rate is different for these two types of benefits. Along the optimal path, the former are discounted at the rate of time preference and the latter at the market rate of interest. We achieve this by identifying four components of the shadow value of the stock of toxic waste. These are the utility, productivity, cost, and abundance effects. The distinction between discount rates appears to have been overlooked in the literature but has significant implications for environmental cost‐benefit analysis due to the growing interest in applying zero time preference to environmental problems, (like waste cleanup) whose consequences extend many generations into the future. A numerical example is included to illustrate these concepts.     

网络B2B交易如火如荼 汽车电子“渠道”裂变

新兴的网上B2B交易模式已经延伸到汽车电子及汽车用品的渠道领域，据了解，国内首家专营汽车电子出口业务的网上交易平台——主街网（www．bossave．com）今年3月份创建上线以来，目前每月网上交易额急剧成长，并创造了上线第二个月即开始赢利的又一个“互联网神话”。     

Costing minimal-repair replacement policies over finite time horizons

An integral-equation technique is used to evaluate the expectedcost of maintaining a system functioning over the period (O,t] using two minimal-repair replacement policies. These costfunctions provide appropriate criteria to determine T^*, theoptimal scheduled replacement period over this finite time horizon.For both policies, it is shown that significant cost savingscan be achieved by using the T^* values predicted by the newmodels with a finite time horizon rather than those obtainedfrom the established asymptotic formulations. An adaptive finiteminimal-repair replacement policy is also formulated using dynamicprogramming, and the expected cost of this policy is shown tobe only slightly less than that of the best stationary policy.     

THE COSTATE VARIABLE IN NATURAL RESOURCE OPTIMAL CONTROL PROBLEMS

ABSTRACT. In this paper we discuss the role of the costate variable (shadow value) for the resource stock in both nonrenewable and renewable resource problems. We separate the information in this variable into a scarcity and a cost effect. The scarcity effect is the portion of the shadow value that is due just to the scarcity of the resource relative to its demand, while the cost effect is a measure of the impact of the marginal unit upon future extraction costs. It is shown that in the nonrenewable resource, mining, problem both can exist simultaneously, but in the renewable resource, fisheries, model the two effects are mutually exclusive. In our analysis of the fisheries model we develop an expression for the time path of the marginal unit of fish stock. We do this using the theorem of Continuous Dependence on Initial Conditions. This result is then used to generate the conclusion that g(x) is the biological own rate of interest, where g(x) is the growth function for the resource stock, x.     

The velocity autocorrelation function and self-diffusion coefficient of fluids with steeply repulsive potentials

We consider the velocity autocorrelation function, vacf, or C_v(t) and self-diffusion coefficients, D, of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, ? (r) = ?(σ/r)ⁿ. The C_v(t) are calculated numerically by molecular dynamics simulations. Accurate expressions for the short time expansion of C_v(t) to order O(t⁴) for n large are derived for this fluid. We propose novel expressions for C_v (t) that, for n large, spans the transition from the short time regime (expandable in even powers of time) and the longer time exponential-like regime characteristic of hard spheres. Inter alia we introduce relaxation times that characterize the duration of a collision and the decay of the velocity correlation within the mean-collision or Enskog-like relaxation time, T_E.     

NONRENEWABLE RESOURCE EXTRACTIONS WITH A POLLUTION SIDE EFFECT: A COMPARATIVE DYNAMIC ANALYSIS

ABSTRACT. In this paper, we present a nonrenewable resource model including environmental pollution as a state variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The costate variable for the resource stock is decomposed into a scarcity effect and a cost effect; and the costate variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.     

Convolutional architectures for spectrum analysis employing CCD programmable transversal filters

Use of a Programmable analogue transversal filter, implemented as a monolithic charge-coupled device, as a basic signal processing element is presented. The application of such a device in waveform convolution is discussed and architectures which take advantnge of the programmable nature of the device are emphasized. Fourier transform algorithms which demand waveform convolution are shown to be efficiently realized with CCD technology and practical results are presented.     

Thermal conductivity of fluids with steeply repulsive potentials

We consider the thermal conductivity of steeply repulsive inverse power fluids (SRP) in which the particles interact with a pair potential, φ(r) = ε(σ/r)ⁿ. The time correlation function for the heat flux, C_λ(t), and the time average, C_λ(0) are calculated numerically by molecular dynamics simulations, and accurate expressions for these are also derived for the SRP fluid. We show, by molecular dynamics simulations, that close to the hard-sphere limit this time correlation function has the same analytic form as for the shear and pressure correlation functions for the shear and bulk viscosity, i.e. C_λ(t)/C_λ(0) = 1 ?T* (nt*)² + 0((nt*)⁴), where T* = k _B T/ε, is the reduced temperature, k _B is Boltzmann's constant and t* = (ε/σ²)^1/2 t is the reduced time. The thermal conductivity for the limiting case of hard spheres is numerically very close to that given by the traditional Enskog relation. At low densities the normalized relaxation times are typically largest for the thermal conductivity, followed by shear and then bulk viscosity. Close to the maximum fluid density, the latter two increase rapidly with density (especially for the shear) but continue a monotonic decline for the thermal conductivity. This reflects the relative insensitivity of the thermal conductivity to the approach to the fluid-solid phase boundary.