NATURAL RESOURCE EXPLOITATION UNDER COMMON PROPERTY RIGHTS

ABSTRACT. Renewable natural resources such as ground‐water, pastures and fisheries are often governed bycommon propertyrights in which members of a group jointlyown the exclusive use of the resource. We develop a formal model of a common propertycontract based on differential game theory and then use the model to examine (i) the incentives of individual users of the common resource; (ii) the resulting harvest and stock time paths; (iii) the local stabilityof the steady state; and (iv) the steadystate comparative statics. Moreover, we compare the qualitative properties of the common propertyregime to those generated under perfectlydefined private rights and open access. We show how common prop‐ertyownership of natural resources can generate rent and be a second‐best solution when private propertyrights are costly to establish.     

Where do the H atoms reside in PdH x systems?

We present an ab initio density-functional theory study of PdH _x systems. We evaluated the total energy of PdH _x systems with the H atoms occupying interstitial (octahedral and tetrahedral) sites of a Pd supercell, allowing for the relaxation of the coordinates and supercell dimensions. The majority of our calculations were based on supercells consisting of four Pd atoms, and up to four H atoms, covering the range from x = 0.25 to x = 1. In addition some larger calculations are reported. In order to compare the relative stability of systems at different values of x (at fixed pressure and temperature T = P = 0), we computed the enthalpy of formation ΔH _f (x) of the (non)stoichiometric systems. In the regime x = 0 → 1, the ΔH _f (x) decrease in a manner indicative of the existence of attractive interactions between the dissolved H atoms. Ideal-solution theory cannot be applied to this system. Furthermore, we find that tetrahedral occupation is favoured over octahedral occupation at high x, leading to the formation of a zincblende structure at x = 1. A preliminary vibrational analysis of normal modes has been performed. Inclusion of vibrational zero-point energies in a harmonic approximation leads us to conclude, tentatively, that the observed stability of octahedral site occupation is due to more favourable zero-point energies of the H atoms in those sites. The results indicate that a proper understanding of this system must take into account the quantum nature of the dissolved hydrogen.     

THE INTRINSIC QUALITATIVE PROPERTIES OF THE CLASSICAL OPTIMAL STOPPING PROBLEM ARE INVARIANT TO THE FUNCTIONAL FORM OF THE DISCOUNT FUNCTION

Abstract The intrinsic qualitative properties of a generic optimal stopping model are shown to be invariant to the functional form of the discount function. If the discount function is assumed to be a member of particular infinite parametric family—a family that includes the exponential and classical hyperbolic discount functions as special cases—an additional refutable comparative statics result is produced that holds for the entire family. Consequently, if one limits econometric tests of the model to its qualitative properties, one cannot determine the form of the discount function used by the decision maker. It is also shown that the only discount function that yields a time‐consistent stopping rule is the exponential function with a constant rate of discount.