Question

Problem 3.(36 points) Suppose the natural rate of unemployment equals 5%, and the Phillips curve is given by πt = πte − 0.25(ut − u∗t ). Suppose originally the economy is in the long run equilibrium, in which πte = 4%. 1. Determine unemployment and inflation rates corresponding to the original equilibrium. 2. Draw the Philips curve diagram with SRPC and LRPC. Mark the original long run equilibrium. 3. Suppose now the central bank performs a monetary expansion and raises inflation to 5%. Suppose the expansion was not foreseen by economic agents. Determine the new unemployment rate that will realize in the short run. 4. Depict the new unemployment rate and new inflation rate on the Phillips curve diagram. 5. In the long run, expectations will adjust to the new inflation rate. How would this affect the position of the SRPC? 6. Depict the new long run equilibrium on the Phillips curve diagram.

Answer 1

1) original eqm is long run eqm

πt = .04 - .25(ut - .05)

Now at eqm, πt = 4%

& Ut = natural UNEMPLOYMENT rate = 5%

Graphs

SRPC slopes downwards

& LRPC is vertical at natural unemployment rate

.

2)

Graph

-0:06 (0.05, 0.04) -0:04- -0:02 SRPC LRPC O.2 0.1 UNEMPLOYMENT rate U 0 inflation raten

.

3) πt = 5%

So from SRPC:

.05 = 04 - .25(ut - .05)

.01 = .0125 - .25Ut

.25Ut = .0025

ut* = .01 = 1%

.

4) new eqm

(0.01, 0.05) -0 04- -0 02 0.15 0.2 0 0.05 0.1

.

5) now in long run, new eqm inflation rate = 5%

So SRPC will shift to right

New SRPC :

πt = .05-.25(Ut- .05)

.

6) new long run eqm

Ut= 5%

πt = 5%

0i0- |(0.05, 0.05) new SRPC O.D5 0.1 0 0.15 0.2

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