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When the Fed lower the interest rate, there will be a rise in GDP and thus a decline in unemployment, which in turn cause the inflation to go up according to the Phillips curve. But Fisher’s equation tells me that real interest rate = interest rate - inflation. So if real interest rate does not change, an increase in interest rate should also cause a increase in inflation, a contradiction.

Any help or comment is appreciated.

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Hint:

If you're keeping real interest rates constant in the second scenario, you should keep real interest rates constant in the first scenario.

If you do this, lowering the nominal interest rate will decrease inflation off the bat (by the Fischer's equation) by the same amount as the change in nominal interest rates.

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  • $\begingroup$ But then why does real interest rate lowers when Fed lower nomial interest rate? $\endgroup$
    – Kun
    Oct 19, 2015 at 18:40
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    $\begingroup$ I was mainly saying that if you hold real interest rate constant in one scenario then you must hold it constant in the other one to avoid the contradiction you found. Another solution to this problem is if you allow real interest rate change if the nominal interest rate increases (similarly to what we see when the Fed lowers nominal interest rates, which you pointed out) $\endgroup$
    – DornerA
    Oct 19, 2015 at 18:44

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