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Department of Economics
Econ 202 Macroeconomic Theory
Spring 2010
Problem Set 8 with answers Q.1 Suppose the Phillips curve is given by (all units are in percentage points): Assume that in period t1, the unemployment rate is equal to the natural rate and the inflation rate is zero.
a) What is the natural rate of unemployment in the economy?
In the medium run, . The natural level of unemployment is equal to 5%. b) Suppose that beginning in period t, the authorities bring the unemployment rate down to 3% and
keep it there indefinitely. Determine the rate of inflation in period t+1, t+2, t+3 when
do the same for
When
3%. When . , inflation must be equal to 4% for ever if they want to reduce unemployment rate to
, following inflation path will occur: c) For which of the two values of θ does
When . Then . imply an acceleration of the price level? , keeping unemployment below the its natural level necessitates an acceleration of inflation. When expectations are not adjusts, , increasing inflation once and for all is enough to reduce unemployment.
d) Suppose the authorities do not know what the natural rate of unemployment is. Can they find out
what it is, how?
When (i.e. expectations are adaptive), the naturel rate of unemployment corresponds to a constant rate of inflation: this is the NAIRU. When unemployment drops below the NAIRU;
inflation accelerates and vice versa.
e) Assume that 1/3 of the workers sign indexed labor contracts. Redo part (b) under this assumption.
When half of the workers sign indexed wage contracts, the dynamics of inflation are given by:
(
When ) ( ) , inflation must be 6% for ever if they want to reduce unemployment to 3%. When , following inflation path will occur: . f) What if half of the workers sign indexed labor contracts? Compare your answers?
( ) 1/ 2 When , inflation must be 8% for ever if they want to reduce unemployment to 3%. When , following inflation path will occur: . As share of workers whose wages are indexed increases, the pressure of decreasing unemployment
on inflation increases as well; cost of decreasing unemployment increases in terms of inflation.
Q.2 Our favorite country, Macroland’s economy is based on coconut production (it is also the only
consumption good of macrolanders). Firms charge a price per coconut which is equal to one plus a
markup times the cost of paying a Macrolander to climb up a tree and collect a coconut. Let the
( markup be 1. The wage is set following: ). Macrolanders believe the government will stop inflation every year, and expect an inflation rate of zero percent.
a) Derive the original Phillips curve for Macroland.
By approximation in Appendix of Chapter 8, we can derive Phillips curve by following formula:
(
( In our case; ) ( ) ) b) What is the NAIRU rate for Macroland? Why is it called NAIRU?
The natural rate of unemployment is the rate of unemployment required to keep the inflation rate
constant. This is why the natural rate is called the NAIRU. Inflation rate is constant if
so, . If .
c) Assume that . Write down the other form of Phillips curve that represents the relation between change in inflation and unemployment rates.
( If we write ) expression, where ,
( . d) Suppose that
( . From this ) ( ) ? Is the result surprising?
) . The result is not surprising because unemployment rate in this period is above the natural rate.
e) Suppose that the government wants to reduce the inflation to 2% in three years by following the
targeted levels as 15%; 9% and 2%. What is the cost or benefit of this policy on unemployment?
The path of inflation;
( )
( (
At the end of the )
) year, the inflation rate declined by 12 percentage points while unemployment rate increased by 1.75 percentage points.
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 Phillips Curve, Unemployment

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