Why imports increase if higher relative inflation? I'm reviewing a previous AP Macroeconomics exam and I saw the following question:


  The United States and South Korea are trading partners, and the United
  States has a zero current account balance. Assume now that the
  inflation rate in the United States decreases relative to the
  inflation rate in South Korea.


Based on the decrease in the inflation rate in the United States, will United States exports to South Korea
increase or decrease? 

The answer is that US exports to South Korea will increase.

But my intuition says the opposite. If South Korea has high relative inflation, their currency will not be worth as much compared to the U.S. dollar, so it will depreciate. Thus, the South Korean currency cannot buy as much from the U.S. and will thus not be able to import as much, so I would think exports from the U.S. would decrease to South Korea. Why is my intuition wrong?
At first, U.S. exports increase because US exports become cheaper due to the low inflation rate. Inflation itself only influences the exchange rate indirectly through its effect on supply and demand for currency. That effect goes through trade. For that to happen, trade must first take place and so US exports must first increase. 

So at first the exchange rate doesn't adjust at all (no difference in supply/demand of the currencies just yet). US goods become cheaper so they're exported more. As US exports increase the demand for dollars by South Korea increases. This will later on lead to the south korean currency to depreciate and for US exporte to go down again (if the Marshall Lerner condition is fulfilled).