Policymaking is much easier when the stae of the economy is easily observable than when there is uncertainty about how the economy is doing, as this...

Policymaking is much easier when the stae of the economy is easily observable than when there is uncertainty about how the economy is doing, as this problem illustrates. Suppose that the economy is either in an expansion or a recession. Suppose that in an expansion, monetary policy ideally sets the interest rate on federal funds (loans between banks) at 6%, whereas if the economy is in a recession, the federal funds rate is ideally set at 2%. 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.)