An eastern Enlargement of the EU, from an incumbent country point of view, involves a fiscal burden from extending Union agricultural and cohesion plicies to new members, coupled with potential gains as well as adjustment problems deriving from an extended customs union and a larger single market. Enlargement is controversial, because the net effect is unclear, a priori, and will certainly vary across individual countries. Our two- part contribution tries to do shed light on this controversy. In this first part, we present a general treatment of the likely effects on different incumbent countries, while a subsequent companion paper will take a closer look at the specific case of Austria. The general view of part I, in turn, first focuses on various empirical measures highlighting crucial differences between incumbents, pertaining to the fiscal burden on the one hand, and integration gains on the other. We then argue that a proper evaluation must rely on an explicit welfare criterion, and we use a general model of economic integration in order to identify the principal channels through which aggregate welfare of an incumbent country is affected by an enlargement of the EU. We address traditional effects of trade creation and trade diversion, as well as growth effects arising from an abolition of trade barriers. In addition, we ask how enlargement affects foreign direct investment and labor migration, and what this implies in welfare terms for an invumbent western European country. Taken together, these effects generate a certain presumption of integration gains, which need to be set against the fiscal burden. However, a final judgement requires a case- by-base approach, based on empirical implementations of enriched and parameterized models for specific countries. The companion paper, therefore, uses a suitably specified, calibrated dynamic equilibrium model, in order to take a closer look at the Austrian case.