I develop a two-country dynamic stochastic general equilibrium model of the European Union (EU) and use this model throughout the chapters of my dissertation. The model incorporates some realistic features of the European Union members. I calibrate the model and it matches the dvnamics of the data well. In the first chapter I study the need for fiscal policy cooperation between the new EU members (a small country) and the European Economic and Monetary Union (EMU) (a large country). I find that both countries are better off when they do not cooperate their fiscal policies. This result depends on the assumption about the presence of foreign ownership in the smaller country. When there is no foreign ownership in the smaller country, the large economy is indifferent between cooperating and not cooperating but the smaller country still prefers not to cooperate its fiscal policy with the EMU. The new EU members are expected to join the monetary union. In the second chapter I analyze the welfare consequences of different monetary arrangements for the new EU members and investigate whether their participation in the EMU is welfare-improving. Based on households' utility the results show that a flexible exchange rate regime is preferred to a monetary union and a monetary union is preferred to a fixed exchange rate regime. In the third chapter I investigate whether there are welfare gains from fiscal policy cooperation in the EMU. I assume that the EMU consists of countries that are currently its members as well as the countries that will join the EMU in the near future. I find that the incumbent EMU members are better off under fiscal policy cooperation and the new members are as well of under fiscal cooperation as they are in a non-cooperative equilibrium. Under fiscal policy cooperation in my model, all policymakers have the same objective by construction. Therefore, the results in my study differ from some previous findings in the literature.