Long-run equilibrium in international assets and goods markets: Why is the law of one price required?

Globalization is a complex phenomenon, best represented by a general framework in which all financial markets and some goods markets adjust quickly, while for the other goods markets prices vary across countries. We consider a two-period financial model. In the first period, agents consume, buy and sell financial assets to diversify their portfolios. In the second period, they spend their endowments and financial gains to purchase consumption goods. We define the concept equilibrium*, in which the total nominal value of trade is balanced and, for any non-negative individualized system of prices, the total nominal value of demand does not exceed the total value of supply. This equilibrium* coincides with the standard concept of equilibrium when the Law of One Price (LOP) is satisfied for any country. In this model, we introduce imperfect international trade. Assuming that Uncovered Interest (rate) Parity (UIP) holds in all financial markets and the LOP does not hold in some goods markets, we prove that an equilibrium* does exist; for markets in which the LOP fails, however, the equilibrium becomes autarkic. This result explains why financial markets and some goods markets are globally integrated, while trade fails in other markets. The world economy is fully globalized only if the LOP holds everywhere.