Analysis of linear trade models and relation to scale economies

ABSTRACT We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models. In Gomory and Baumol (1), we discussed the equilibria that arise from the classical linear Ricardian model of international trade when the productivity parameters e i,j of the model are allowed to vary, limited only by a maximal productivity constraint, e i,j Յ e i,j max . We plotted each equilibrium as a point in a (Z 1 , U 1 ) diagram, where Z 1 is country 1's share of total world income, , and U 1 is the utility of country 1 at that equilibrium. We had similar diagrams in which we plotted (Z 2 , U 2 ), where Z 2 ϭ 1 Ϫ Z 1 is country 2's share and U 2 is country 2's utility. We showed that in each case the resulting region of equilibria (R 1 for country 1 and R 2 for country 2) could be bounded above by a curve B j (Z 1 ) obtained by solving a very simple linear programming problem for each value of Z 1 . This upper bounding curve has a characteristic hill shape that persists over a wide range of models. Furthermore, as the number of industries in the model increases, we showed that the actual upper boundary of the region rapidly approaches this boundary curve. The economic significance of these results comes from the characteristic hill shape of the region of equilibria. The hill shape implies that there is inherent conflict in international trade, that the best equilibria for one country are poor ones for the other, and that a country is better off with a partly developed trading partner than with a fully developed one. The fundamental mechanism at work is complementary to but different from the mechanisms employed in the analyses of international trade that also have shown the possibility of conflict in Hicks (2), Dornbush et al. (3), and Krugman (4). An excellent summary of the relevant history appears in Grossman and Helpman (5). In this note we complete one component of this analysis by showing that the upper boundary of the region is given exactly by solving a closely related integer programming problem. The relation between the linear programming problem and the integer programming problem is that they are two different relaxations of the economies of scale problem introduced in Gomory (6). We discuss the close connection between the linear family and economies of scale models below. This result enables us to examine models with a small number of products; models in which there is a considerable gap between the boundary given by the linear programming approximation and the actual boundary of the region of equilibria. This includes, for example, the famous model of trade in textiles and wine given by David Ricardo. These small models can and do turn out to have special characteristics, due to their small size, that disappear in all but the most contrived large models. These characteristics cause small models not to exhibit the inherent conflict that is present in almost all large models

The Emergence and Evolution of the Multidimensional Organization

The article discusses multidimensional organizations and the evolution of complex organizations. The six characteristics of multidimensional organizations, disadvantages of the successful organizational structure that is categorized as a multidivisional, multi-unit or M-form, research by the Foundation for Management Studies which suggests that synergies across business divisions can be exploited by the M-form, a team approach to creating economic value, examples of multidimensional firms such as PricewaterhouseCoopers, and a comparison of various organization types including the matrix form are mentioned

Gene content evolution in the arthropods

Arthropods comprise the largest and most diverse phylum on Earth and play vital roles in nearly every ecosystem. Their diversity stems in part from variations on a conserved body plan, resulting from and recorded in adaptive changes in the genome. Dissection of the genomic record of sequence change enables broad questions regarding genome evolution to be addressed, even across hyper-diverse taxa within arthropods. Using 76 whole genome sequences representing 21 orders spanning more than 500 million years of arthropod evolution, we document changes in gene and protein domain content and provide temporal and phylogenetic context for interpreting these innovations. We identify many novel gene families that arose early in the evolution of arthropods and during the diversification of insects into modern orders. We reveal unexpected variation in patterns of DNA methylation across arthropods and examples of gene family and protein domain evolution coincident with the appearance of notable phenotypic and physiological adaptations such as flight, metamorphosis, sociality, and chemoperception. These analyses demonstrate how large-scale comparative genomics can provide broad new insights into the genotype to phenotype map and generate testable hypotheses about the evolution of animal diversity

Longitudinal Molecular Trajectories of Diffuse Glioma in Adults

The evolutionary processes that drive universal therapeutic resistance in adult patients with diffuse glioma remain unclear ¹² . Here we analysed temporally separated DNA-sequencing data and matched clinical annotation from 222 adult patients with glioma. By analysing mutations and copy numbers across the three major subtypes of difuse glioma, we found that driver genes detected at the initial stage of disease were retained at recurrence, whereas there was little evidence of recurrence-specifc gene alterations. Treatment with alkylating agents resulted in a hypermutator phenotype at diferent rates across the glioma subtypes, and hypermutation was not associated with diferences in overall survival. Acquired aneuploidy was frequently detected in recurrent gliomas and was characterized by IDH mutation but without co-deletion of chromosome arms 1p/19q, and further converged with acquired alterations in the cell cycle and poor outcomes. The clonal architecture of each tumour remained similar over time, but the presence of subclonal selection was associated with decreased survival. Finally, there were no differences in the levels of immunoediting between initial and recurrent gliomas. Collectively, our results suggest that the strongest selective pressures occur during early glioma development and that current therapies shape this evolution in a largely stochastic manner

Interpol and the Emergence of Global Policing

This chapter examines global policing as it takes shape through the work of Interpol, the International Criminal Police Organization. Global policing emerges in the legal, political and technological amalgam through which transnational police cooperation is carried out, and includes the police practices inflected and made possible by this phenomenon. Interpol’s role is predominantly in the circulation of information, through which it enters into relationships and provides services that affect aspects of governance, from the local to national, regional and global. The chapter describes this assemblage as a noteworthy experiment in developing what McKeon called a frame for common action. Drawing on Interpol publications, news stories, interviews with staff, and fieldwork at the General Secretariat in Lyon, France, the history, institutional structure, and daily practices are described. Three cases are analyzed, concerning Red Notices, national sovereignty, and terrorism, in order to explore some of the problems arising in Interpol’s political and technical operating arrangements. In conclusion, international and global policing are compared schematically, together with Interpol’s attempts to give institutional and procedural direction to the still-evolving form of global policing

Molecular Profiling Reveals Biologically Discrete Subsets and Pathways of Progression in Diffuse Glioma

Therapy development for adult diffuse glioma is hindered by incomplete knowledge of somatic glioma driving alterations and suboptimal disease classification. We defined the complete set of genes associated with 1,122 diffuse grade II-III-IV gliomas from The Cancer Genome Atlas and used molecular profiles to improve disease classification, identify molecular correlations, and provide insights into the progression from low- to high-grade disease. Whole-genome sequencing data analysis determined that ATRX but not TERT promoter mutations are associated with increased telomere length. Recent advances in glioma classification based on IDH mutation and 1p/19q co-deletion status were recapitulated through analysis of DNA methylation profiles, which identified clinically relevant molecular subsets. A subtype of IDH mutant glioma was associated with DNA demethylation and poor outcome; a group of IDH-wild-type diffuse glioma showed molecular similarity to pilocytic astrocytoma and relatively favorable survival. Understanding of cohesive disease groups may aid improved clinical outcomes