Solution :
Short run Phillips curve ( SRPC) :
Inflation(π) = Expected Inflation + 0.2-4* Unemployment rate.
π = πe + .2 - 4*u
(a) :- Expected Inflation (πe) = 0
Then SRPC : Inflation = 0.2 - 4*u
At natural rate of Unemployment
π = πe, so, 0.2 = 4u
Unemployment rate = 0.2/4 = 0.05 = 5%
so, Long run Phillips curve( LRPC) is Vertical at 5%.
(b) :- If govt needs to runs 4% inflation =
0.04
Then 0.04 = 0.2 - 4*u
4u = 0.2 - 0.04 = 0.16
U* = 0.16/4 = 0.04 = 4%
Thus Unemployment rate falls below natural rate by 1%>
(c) :- In long run, SRPC will shift upwards in a
way , that SRPC cuts LRPC at 4% inflation rate, thus in long run
economy will be at LRPC where unemployment rate is back to its
natural level of 5% with permanently higher inflation of 4%.
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