Final answer:
An expansionary monetary policy in Japan will lead to lower interest rates and increased output in the US, with an appreciating dollar. Japan's expansionary fiscal policy might initially harm the US trade balance, but it could eventually lead to improvement, especially when considering J-curve effects.
Step-by-step explanation:
When Japan elects a new prime minister who convinces the Bank of Japan to pursue an expansionary monetary policy under a flexible exchange rate regime, it influences the US economy in various ways. This policy will typically lead to a decrease in Japanese interest rates, making US investments more attractive and likely increasing capital flows to the US. This will shift the US IS-LM curve outward, meaning lower interest rates (i.e., from i1 to i2) and higher output (from Y1 to Y2) due to higher investment and net exports. Subsequently, the higher demand for the dollar will appreciate its value, leading to a higher exchange rate (from E1 to E2). The trade balance of the US will be influenced by the changed relative interest rates, the real exchange rate movements, and the changes in domestic income.
In the case of Japan implementing an expansionary fiscal policy, the US may witness different effects. Japanese government spending increases demand for yen, appreciating the Japanese currency, which could lead to the depreciation of the dollar (lower E from E1 to E2). This scenario might increase the US trade balance as exports become relatively cheaper and imports from Japan become more expensive. However, Japanese fiscal expansion might also spur its economic growth, possibly increasing US exports to Japan, further affecting the trade balance positively.
If we assume J-curve effects, the initial impact on the trade balance could be negative due to price effects taking time to adjust, leading to a worsening trade balance before it improves as volume effects dominate over time.