Suppose that the economy is described by the following aggregate demand and aggregate supply equations

[AD]:yt=15(mtpt)+dt,[AS]:yt=5(ptwt)+st,

where wages are given by

[Wages]:wt=Et1[pt],

and dt and st are uncorrelated i.i.d. random variables with mean 0 and variance 1.

Further, central bank has loss function

Lt=2t+(1/5)(yty)2,

and monetary policy is given by

[Policy]:t=1+2dt+3st,

where 1, 2 and 3 are policy parameters which the central bank chooses to minimize (the expected value of) its loss function.

a. (5 points) Derive the policy rule which minimizes loss function assuming that the central bank is able to credibly commit to a level of inflation. Derive also the corresponding level of expected loss.

b.(5 points) Derive the policy rule which minimizes loss function assuming that the central bank is not able to credibly commit to a level of inflation. Derive also the corresponding level of expected loss