Formalization of Trade Balance Flows in Portfolio Game

Portfolio space (first time published at [1]) enables us to formalize economic activities in bookkeeping framework. In paper [2] author has defined production vector Y and new type of asset A2, that represent human work done during production of one new product. In paper [3] portfolio play was enriched about relative price of money interest rate and also unit labor cost was introduced. Some restriction on fraction demand / supply was introduced. Income constraint was main tool during the proof. In this paper author has defined key vectors of international trade. So vectors of exchange of goods EX (stands for export of goods) and 1M (representing import of goods) were defined. Again vectors specify relative price of one piece of goods or money vis-a-vis another convertible currency. Vector EXR describes exchange of two currencies. Again small letters are used in the case of scalars. These types of variables express the whole real volume ofthese particular foreign trade deals. In this paper author takes into accounts only 3 countries (players) because it on the one hand enables us to introduce flow matrix among countries and on the other hand this little set of indices is easier and shorter for description. Flow matrix represents only flow of goods in real terms. (Dual flows of moneys are not treated here.) This is matrix of scalars and it is used afterwards for formalization of vector flows between particular portfolios. Problem of proper specification of asset Al is again crucial. Here is for the first time required acceptance of Al like means of international payment - it means convertibility and especially usability as reserve currency. Al can be currency of particular state (for example USD) or artificial one (for example pre monetary union EUR). Other countries quote exchange rate of their own currency against AI. After these assumptions Al can also act as settlement currency for clearing between/among countries. Trade can be done through this one or through any other convertible currency. So we distinguish two types of payment procedure. First one is executed directly in Al and second one is calculated in nation currency and then converted into AI. But what really decides is flow of real goods. Surplus or deficit arising from the trade (or better said, trade balance surplus or deficit) will decide about redistribution of Al between considered countries. Chapter 3 highlights some phenomenon that can bring us closer to thinking about exchange rate dynamic and potential risk of turbulence thanks to inappropriate level of fixed exchange rate.