The European integration, has established complicated structures of exchanging goods and services, labor, and capital, and the size of these structures is increasing over the time. The main orientation of the study is finding the optimal size of each member has to be shared in this trade structure, and then represents this integration structure in matrices, to find in turn, whether or not these structures are optimal or not, or whether this matrix represent the Pareto-Optimal shares of the trade relationships for the European integration. The study is contributed by setting up a model with some new axioms to analyze the optimality conditions for this matrix, with an appropriate definition of the optimality position. The main aims of the study are evaluating the level of European integration optimality, or any other integration over the world, and examine the impacts of entry of the new member states to this integration, and whether this new entry makes the integration better off or vice versa. The dissertation work found that European Union was not obtaining the optimality position for their relation structure, even before entry of new member states. The study also found that last enlargement adds to the EU gap of not optimization more points.
