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Inflation gap and exchange rates

How will an increase in inflation gap in the euro zone relative to the inflation gap in the US affect the dollar?

A. Weaken against the Euro in real term

B. Strengthen against the Euro in real term

C. Strengthen against the Euro in nominal term

The model answer says A is the correct choice but I don’t really get it, can some one help me understand this?

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An increase in inflation gap, i.e., an increase in (current inflation - target inflation), would result in central bank increasing policy rate (as per Taylor rule below), resulting in capital inflows into eurozone (as investors want to invest money in region with higher interest rates), and this higher demand for euro would cause euro to strengthen (i.e., dollar to weaken).

Alternatively, an increase in current inflation gap would imply a lower expected future inflation in eurozone (i.e., all else equal, a high CPI is likely to increase by less in the future than a lower CPI), which would imply a weakening of the dollar according to the following equation:

Thank you so much! Now it makes sense, God bless you :)