suppose the current price level is 149.2 and one year ago the price level was 14

Question

suppose the current price level is 149.2 and one year ago the price level was 146.7. Output is currently 12,892.5 and potential output is 13,743.5 (both in billions of 2005 dollars).

a. what value of the federal funds rate would the Fed choose if it follows the Taylor rule?

b. suppose that one year later, the price level has declined by 0.4%, output has declined by 1.6%, and potential output has increased 2.0%. In this new situation, what value of the Federal funds rate would the Fed choose if it follows the Taylor rule?

Explanation / Answer

i= r* + pi + 0.5 (pi-pi*) + 0.5 ( y-y*)

Where:
i = Federal funds rate
r* = real federal funds rate (usually 2%)
pi = rate of inflation
p* = target inflation rate
Y = logarithm of real output
y* = logarithm of potential output

Y=log(12,892.5)=4.11

y*=log(13,743.5)=4.13

pi=(149.2-146.7/149.2)*100=1.67

Target inflation set by fed is usually 2% so p*=2

r*=2

substituting the above values in the taylor equation gives

i=2+1.67+0.5*(1.67-2)+0.5*(4.11-4.13)=3.5%

b)

Now pi= -0.4

output=(100-1.6/100)*12,892.5=12686.22

Y=log(12686.22)=4.1

potential output=1.02*13,743.5=140183.7

Y*=log(140183.7)=4.146

substituting the above values in the taylor equation gives

i=2-0.4+0.5*(-0.4-2)+0.5*(4.1-4.146)=0.37%

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