Structural shifts in urban population density gradients: an empirical investigation

This study investigates the structural shifts in urban population density gradients by first using the shifting regression technique of Farley, Hinich, and McGuire to detect the possible change in the structure of an urban area. Secondly, a generalized random coefficient technique is used to simultaneously detect the possible structural change and stochastic behavior of density gradients. Data for 50 United States SMSA's are used to do the empirical analyses.     

The quartiles of the maximum entropy distribution

The quartile points and interquartile range of the maximum entropy (ME) distribution and sample distribution are compared, using expected values for sampling from a standard normal population. For sample sizes n?20 such that the sample quartile points are uniquely defined, the ME quartile points and interquartile range are found to have lower mean-squared error (MSE).     

The Under-Exploitation of Natural Resources: A Model with Overlapping Generations*

It is well known that competitive markets may fail to generate an optimal rate of extraction of a natural resource-stock. The barrier to optimality may be uncertainty about tenure, commonality of property rights in the resource, or uncertainty about the extent of the resource. In all these cases, suboptimality takes the form of over-extraction. We draw attention to an additional source of suboptimality. In an economy with overlapping generations, the resource-stock plays the double role of repository of savings and source of productive inputs. The decline in the supply of the resource-stock may eventually force its price so high that it ceases to perform its second function. Extraction comes to an end even though the resource has a positive marginal productivity in producing consumption goods. This is inefficient, hence suboptimal. This time, however, suboptimality takes the form of under-extraction.     

Utility theory based on rational probabilities

Classical utility theory assumes that a preference order is defined for all mixtures αa+(1?α)b of pure prospects a,b for all real numbers α between 0 and 1. If α is irrational such mixtures are hard to interpret intuitively. We show here how to modify the usual axiomatisations to deal with the case where α is restricted to rational values, or even further to values of the form m/2ⁿ corresponding to mixtures built up from even bets.