Final answer:
According to the purchasing power parity theory, if prices have been rising faster in Japan than in the United States, the exchange rate between the two countries will decrease.
Step-by-step explanation:
According to the purchasing power parity theory, relative price levels play a significant role in determining exchange rates in the long-run.
If prices have been rising faster in Japan than in the United States, we can predict that the exchange rate between Japan and the United States will decrease. This is because the higher inflation rate in Japan would lead to a decrease in the purchasing power of the Japanese yen compared to the US dollar, resulting in a weaker exchange rate for the yen.
Therefore, option 1) The exchange rate between Japan and the United States will decrease is the correct prediction.