Assume that the Phillips curve is given as: _t = _t^e + 0.1 - 2_t a) What is the natural unemployment rate? Now the expectations for inflation are: _t^e = (1 - ) + _t-1 can be any constant value, either 0 or another number above zero. First assume that = 0 and that _t = _n (ie the unemployment rate is equal to the natural unemployment rate). In year the government authorities decide to reduce unemployment to 3% and keep it there forever. b) Determine inflation for the years + 1, + 2, + 3, + 4, + 5. c) Do you think the answer you gave to b) makes sense? d) Now suppose that the year + 6 increases from = 0 to = 1 and that the authorities are still determined to keep at 3% forever. e) Why does it make sense for to increase in this way? f) Determine inflation for the years + 6, + 7 and + 8. Also show your answer diagrammatically