Assume that the IS curve is given as $Y=20-2r$ and the MP curve is given as $r=2+0\mathrm{.}5.$

Which of the following statements is true?

A$.$ When inflation is $3\%,$ the goods market equilibrium level of output is $Y=14.$

B$.$ When inflation is $3\%,$ the nominal federal funds rate is $3\mathrm{.}5\%.$

C$.$ The central bank is violating the Taylor principle.

D$.$ The AD curve is given as $Y=16-.$

If the central bank changes the autonomous real interest rate to $r^{}=3,$ what will happen to output if inflation remains constant at $1\%?$

A$.$ Output will decrease from $Y=15$ to $Y=14.$

B$.$ Output will increase from $Y=20$ to $Y=22.$

C$.$ The effects on output cannot be determined.

D$.$ Output will decrease from $Y=15$ to $Y=13.$