Final answer:
If the Federal Reserve purchases government bonds during a recessionary gap, it is most likely that interest rates will fall and the demand for foreign financial assets will rise, leading to a depreciation of the dollar's exchange rate.
Step-by-step explanation:
The main answer to the student's question regarding the most likely outcome if the United States is experiencing a recessionary gap and the Federal Reserve purchases government bonds would be this: the purchase of government bonds by the Federal Reserve is a form of monetary policy aimed to inject liquidity into the economy, which tends to decrease interest rates. As a result, interest rates will fall, making U.S. financial assets less attractive relative to foreign assets, thus potentially increasing demand for foreign financial assets. When investments flow out of the U.S., the demand for dollars on foreign exchange markets decreases while the supply of dollars increases, which will generally lead to a depreciation of the dollar's exchange rate. Therefore, the most likely outcome is option 3: Interest rates will fall and demand for foreign financial assets will rise, and so the dollar's exchange rate will decrease.