Policymaking is much easier when the state of the economy is easly observable than when there is uncertainty about how the economy is doing, as this porblem illustrates. Suppose that the economy is either in an expansion or a recession. Suppose that in an expansion, monetary policy ideally set the interest rate on federal funds (loans between banks) at 6 percent, whereas if the economy is in a recession, the federal funds rate is ideally set at 2 percent. If monetary policymarkers know the state of the economy when they set policy, then policymaking is easy set the fed funds rate at 6% when in expansion and at 2% when in recession. Suppose, however, that policymakers cannot easily observe the current state of the economy. They know only what the state of the economy was three months ago. Suppose that if the economy was in an expansion three months ago, there is a 90% chance the economy is still in an expansion (and thus a 10% chance that it is now in a recession.) And suppose that if the economy was in a recession three months ago, there is a 75% chance that it is still in recession (and a 25% that it is now in an expansion.) Given these probabilities, what would you guess is the right setting for the federal funds rate if the economy was in a recession three months ago? What is the right setting for the federal rate if the economy was in an expansion three months ago? (Note: To answer these questions, you must make an assumption about the ideal federal funds rate when you do not know what the state of the economy is you may make any reasonable assumption you want, but you must justify it.)

Consider three alternatives policies, each with a different set of outcomes in terms of output and inflation,as shown in the following tables:

Output---------Output-------Output----------------Inflation------------Inflation-------Inflation
Policy A------Policy B-------Policy C-------------Policy A------------Policy B------Policy C
500.0--------500.0-----------500.0------------------3.0------------------3.0-------------3.0
515.0--------500.0-----------520.0-----------------3.0-------------------2.8-------------3.2
530.5-------520.0-----------535.0------------------3.0-------------------2.0-------------4.0
546.4-------540.0-----------550.0------------------3.0-------------------1.5-------------4.5
562.8-------562.8-----------562.8------------------3.0-------------------1.5-------------4.5

Potential output is 500 in period 1 and rises 3% per year. The Fed's objective function is E{-2+(w x -2)} yt nt where w=1, and the inflation target is 2.0%.

A. Calculate the value of the objective function over the 5-year period for each of the 3 policies.

B. Which policy is best? Why?

C. Would the answer to part B change if w =5? If so explain.