Borrowing, risks and charges in the water industry : a rejoinder to the Cuthberts

In their article* in the June 2006 issue of this Commentary, Jim and Margaret Cuthbert address a number of questions to the Water Industry Commission for Scotland, the industry regulator. These questions reflect the authors' concerns about some regulatory procedures and decisions, concerns that they have expressed earlier elsewhere. The Cuthberts' criticisms can be summarised in the proposition that Scottish Water should be allowed to borrow more money, and thereby be able to lower its current charges to customers

Scaling laws for large numbers of coexisting attracting periodic solutions in the border-collision normal form

A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two dimensions, a codimension-three scenario was described in previous work at which the map has a saddle-type periodic solution and an infinite sequence of stable periodic solutions that limit to a homoclinic orbit of the saddle-type solution. This paper introduces an alternate scenario of the same map at which there is an infinite sequence of stable periodic solutions due to the presence of a repeated unit eigenvalue in the linearization of some iterate of the map. It is shown that this scenario is codimension-four and that the sequence of periodic solutions is unbounded, aligning with eigenvectors corresponding to the unit eigenvalue. Arbitrarily many attracting periodic solutions coexist near either scenario. It is shown that if $K$ denotes the number of attracting periodic solutions, and $\varepsilon$ denotes the distance in parameter space from one of the two scenarios, then in the codimension-three case $\varepsilon$ scales with $\lambda^{-K}$, where $\lambda > 1$ denotes the unstable stability multiplier associated with the saddle-type periodic solution, and in the codimension-four case $\varepsilon$ scales with $K^{-2}$. Since $K^{-2}$ decays significantly slower than $\lambda^{-K}$, large numbers of attracting periodic solutions coexist in open regions of parameter space extending substantially further from the codimension-four scenarios than the codimension-three scenarios.Comment: 37 pages, 5 figures, submitted to: Int. J. Bifurcation Chao

Factor ordering and large-volume dynamics in quantum cosmology

Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be significant even in certain low-curvature regimes, provided that they add up during long cosmic evolution. The analysis of such terms is therefore an important problem to make sure that the theory shows acceptable semiclassical behavior. This paper presents a general search for terms of this type as corrections in effective equations for a k=0 isotropic quantum cosmological model with a free, massless scalar field. Specifically, the question of whether such models can show a collapse by quantum effects is studied, and it turns out that factor-ordering choices in the Hamiltonian constraint are especially relevant in this regard. A systematic analysis of factor-ordering ambiguities in effective equations is therefore developed.Comment: 27 pages, 3 figure

A Note on the Valuation of Ecosystem Services in Production

There has been considerable recent interest in the valuation of ecosystem services. We focus here on the value of such services in the production of market goods. Although the conceptual basis for conducting such exercises is straightforward, the data with which to implement them empirically is generally not available. An upper bound on the value of ecosystem services arises when the production technology exhibits constant returns to scale in ecosystem services and market inputs jointly. There are compelling reasons to suppose that the existence of fixed factors of production would imply that production technologies exhibit decreasing return to scale. Under these circumstances, no general conclusions can be drawn. We show in an illustrative example that a range of outcomes is possible, depending on the substitutability between ecosystem services and other inputs and the scarcity of ecosystem services relative to other factors of production.ecosystem services, returns to scale, elasticity of substitution

Definitions of Biodiversity and Measures of Its Value

The destruction of natural habitats has prompted concerns about the loss of biological diversity. Regrettably, however, there is no consensus among either biologists or economists on the most meaningful measures of biodiversity. Fundamentally different definitions are useful in asking fundamentally different questions. Considerable attention has been given to the value of diversity in search models. A measure of “aggregate variability” is appropriate to such models. Values derived from search models tend to be well behaved; they exhibit diminishing returns in diversity. In contrast, a definition of diversity as “relative abundance” is more appropriate to more complex objective functions. Values derived in these models are not necessarily well behaved. The differences between diversity values arising in search models and those arising from more general objectives are demonstrated. An example shows that “consistency tests” applied to measures of valuation may not be useful when diversity per se is being valued.Biological diversity; biodiversity; diversity index, abundance; search; variability, consistency; contingent valuation; diminishing returns; increasing returns

Codend selection of winter flounder Pseudopleuronectes americanus

Codend selection of winter flounder (Pseudopleuronectes americanus) in 76-127 mm mesh codends was examined from experiments conducted in Long Island Sound during the spring of 1986-87. The results show a slightly larger size at selection than was found in earlier work as indicated by the selection factor, 2.31 in the present study compared with 2.2 and 2.24 from previous studies. Diamond mesh was found to have a length at 50% retention about 1 cm longer (Lso =22.6 cm), and a selection range (3.4 cm) about 1 cm narrower, than square mesh in 102-mm codends. Tow duration varied from 1 to 2 hours using 114-mm diamond mesh. As has been found in previous studies, tow duration and Lso are positively related, with I-hour tows averaging 24.6 cm and 2-hour tows averaging 26.6 cm. The importance of the slope of the selection curve was examined in yield-per-recruit analyses by comparing knife-edge and stepwise recruitment. In all mesh sizes, stepwise recruitment provides a more conservative estimate of yield in the presence of a minimum size limit. Differences in yield estimates between the two models were generally small (1-7%), except in the largest mesh size, 127 mm, where yield is overestimated by 10% when assuming knife-edge recruitment. (PDF file contains 16 pages.