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 archaeology of radiocarbon accelerator dating

Accelerator mass spectrometry (AMS) allows radiocarbon dating to be carried out by direct counting of¹⁴C atoms, rather than the conventional counting of radioactive disintegrations. The result is that samples up to 1000 times smaller can be handled. The approach was tested in principle by 1977 and for archaeological operation by 1983. More than 2000 samples per year are now being dated worldwide. The machines can now operate to about ± 80 years or better. Dates older than 40,000 years have not yet been achieved, but the ability to use small samples has already had considerable impact on dating the period 10,000–30,000 years ago. Bone is an ideal material for the new technique, since amino acids can normally be isolated and purified from gram-size samples. Studies of the origins of domestication are aided by the dating of individual grains and seeds. Because small samples can be mobile in the soil, careful sample selection strategies and procedures are required. The full impact of the technique can be assessed only through the rapid and comprehensive publication of archaeological results.