The elderly and students who are citizens of one country in the European Community at the end of 1991 will be able to live in any other EC nation if they wish, it was decided Wednesday. The decision by the 12 EC nations gives jobless nationals in the European Community the same rights as wage-earners. An elderly citizen who has dreamed of retiring in sunnier southern climates will be able to obtain a five-year, renewable residency permit in the EC country of his choice. The retiree must show only proof of health insurance and that he or she will not burden the adopted nation's social security system. And a student who can show proof of registration at a university or college in another EC nation as well as sufficient income will receive a one-year renewable residency permit. Those who are unemployed by choice and do not classify as being either elderly or a student will have to prove they have sufficient income not to need assistance from the social security system in their new country. The 12 EC members are Belgium, Denmark, France, West Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, the United Kingdom, Spain and Portugal. In 1992, the nations will drop trade barriers among themselves to create a unified Euromarket. In Brussels Wednesday the 18 nations of Western Europe's two trading blocs began talks to pave the way for the so-called European Economic Space. The move would bring the six nations of the European Free Trade Association _ Austria, Finland, Iceland, Norway, Sweden and Switzerland _ closer to the European Community. Frans Andriessen, an EC commissioner, said he hoped broad agreement would be reached near the end of this year and be fully implemented on Jan. 1, 1993, when the EC's single market comes into force.