Final answer:
The correct answer is D. An improvement in investment opportunities in the U.S. would cause the dollar to appreciate against the Euro. This is because such improvements would increase the demand for dollars among investors and decrease the supply of dollars on the foreign exchange market.
Step-by-step explanation:
When investment opportunities in the U.S. improve, it attracts more capital from foreign investors, including those from Europe. For European investors to invest in the U.S., they must exchange their euros for dollars. This increases the demand for the dollar on the foreign exchange market. Consequently, there's a shift in the demand for U.S. dollars to the right from D to D1, and a decrease in the supply of dollars as fewer investors would want to get rid of their dollars. The new equilibrium would be at a higher exchange rate, meaning that the value of the dollar has appreciated relative to the euro.
On the contrary, if interest rates were to fall in the U.S. relative to the rest of the world, we would expect a decrease in the demand for dollars and an increase in the supply of dollars in foreign currency markets, leading to the depreciation of the dollar compared to the euro. However, it's important to note that actual market outcomes can also be influenced by a range of other factors not considered in this simplified scenario.