Panel discussion: inherent conflict in international trade

Economic development ; International trade

Shares of World Output, Economies of Scale, and Regions Filled with Equilibria

returns to scale ; trade ; economic models

Productivity Differences, World-Market Shares and Conflicting National Interests in Linear Trade Models

Productivity, linear models, international trade

N-Product Natural Monopoly As "Natural Cartel" – On Scale Economies Under Capital Rationing

Production, economic models

National Trade Conflicts Caused by Productivity Changes: The Analysis with Full Proofs

multiple equilibria; linear trade model; trade conflict

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

Antiferromagnetic spintronics

Antiferromagnetic materials are magnetic inside, however, the direction of their ordered microscopic moments alternates between individual atomic sites. The resulting zero net magnetic moment makes magnetism in antiferromagnets invisible on the outside. It also implies that if information was stored in antiferromagnetic moments it would be insensitive to disturbing external magnetic fields, and the antiferromagnetic element would not affect magnetically its neighbors no matter how densely the elements were arranged in a device. The intrinsic high frequencies of antiferromagnetic dynamics represent another property that makes antiferromagnets distinct from ferromagnets. The outstanding question is how to efficiently manipulate and detect the magnetic state of an antiferromagnet. In this article we give an overview of recent works addressing this question. We also review studies looking at merits of antiferromagnetic spintronics from a more general perspective of spin-ransport, magnetization dynamics, and materials research, and give a brief outlook of future research and applications of antiferromagnetic spintronics.Comment: 13 pages, 7 figure