OPTIMAL REGIONAL GROWTH MODELS: MULTIPLE OBJECTIVES, SINGULAR CONTROLS, AND SUFFICIENCY CONDITIONS

ABSTRACT We develop a generalized Harrod-Domar type of model for optimal regional growth which allows determination of the optimal allocation of regional public investments and which considers multiple growth objectives, as well as both normal and singular fiscal instruments. This general model is shown to include most of the previous optimal regional growth models as special cases. Necessary conditions for some special cases of the general model are analyzed in detail, and decision rules associated with derived optimal regional growth policies are articulated. These special cases verify that singular controls do exist in certain instances, and that they must be considered for the complete specification of optimal regional growth policies; this is significant because singular controls have not been previously analyzed in the literature. We conclude the paper with a discussion of sufficiency conditions for optimal regional growth models which is more general than that given by previous authors.     

THE PALEOLITHIC CAVE ART OF VASCO-CANTABRIAN SPAIN

Summary. This article explores the relationship between cave art and Upper Paleolithic archeology in northern Spain (and extreme southwestern France). Among the 83 known art sanctuaries, only three can probably be terminus ante quem dated to the early Upper Paleolithic (c. 35,000-20,000 BP). Other types of evidence (virtual absence of ornaments and mobile art objects before the Solutrean, stylistic similarities between works of late Upper Paleolithic mobile art and parietal art, overwhelming association of Solutrean and/or Magdalenian cultural deposits with art sanctuaries) clearly suggest that most of the cave art was done in the period between c. 20,000-10,000 BP. Cave art sanctuaries are distributed in non-random fashion. The clusters of sanctuaries usually correspond with dense clusters of habitation sites. The clusters are separated by substantial geographical gaps. These chronological and geographical facts coincide with contemporaneous subsistence intensification, all of which tends to support the hypothesis of increased territorialism in the late Last Glacial.     

Glacial Stratigraphy of the Upper Mersey Valley,Tasmania

The upper Mersey Valley was glaciated on three occasions during the Pleistocene. The youngest, Rowallan Claciation, probably commenced after 28000 years B.P. The maximum ice limit was attained before 13500 years B.P., and retreat occurred before 10000years B.P. Deposits associated with Rowallan Glaciation are weakly weathered chemically. They overlie moderately weathered deposits that were formed during the Arm Glaciation, which is inferred from relative dating data to have occurred before the Last Interglacial Stage. North of the deposits and ice limits of the Arm Glaciation extremely weathered tills and rhythmites occur. They were formed by ice of the Croesus Glaciation which is inferred to be of Early Pleistocene age or older.