Final answer:
The correct statement is (b), where a relative expansion of U.S. output leads to a dollar appreciation against the euro, and a European output expansion leads to a dollar depreciation. This is due to the resulting shifts in demand and supply for the respective currencies influenced by investment attractiveness and relative economic performances.
Step-by-step explanation:
The most accurate statement regarding the impact of economic output on currency value is a relative expansion of U.S. output causes a long-run appreciation of the dollar against the euro, while a relative expansion of European output causes a long-run real depreciation of the dollar against the euro. This can be explained by considering how economic conditions affect currency values. When there is an expansion of the U.S. economy, there is typically a higher demand for the dollar because more foreign investors would want to invest in the growing U.S. markets, thus leading to an appreciation of the dollar. Conversely, an expansion in the European economy would result in higher demand for the euro and increased investment opportunities in European markets, which would make the euro more valuable relative to the dollar.
Lower U.S. interest rates make U.S. assets less desirable, decreasing the demand for dollars and consequently causing the dollar to depreciate. Similarly, if a country's inflation rate is high relative to others, it would likely prompt a decrease in demand for that country's currency. A country's ability to pay back its debts, influenced by whether borrowing is for investment or consumption, may affect currency stability and risk of capital flight. All these factors play into how currency exchange rates are determined in the long run.