[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

unemployment rate is 5 percent (i.e., U 1 = U * = 5 percent).
Now suppose in year 2 the unemployment rate falls to 4
percent and remains there. Complete the next four rows
of the table. What is the inflation rate in year 7?
Expected
Year Unemployment Inflation Inflation
1 5 percent 4 percent 4 percent
2 4 percent 4 percent 4.5 percent
3 4 percent 4.5 percent 5 percent
4
5
6
7
5. Return to the situation of year 1 in the previous problem.
By how much would unemployment need to rise to lower
inflation in year 2 to 3 percent? Suppose unemployment
is kept at this higher level. What happens to inflation in
year 3? In year 4? How many years does it take to get
inflation down to zero? Make a table like the one in the
previous problem to show your results.
6. Suppose the Phillips curve in Problem 5 is replaced by
π t =π t-1 − (U t − U * ).
Redo Problem 5 with this new Phillips curve. What can
you conclude about the role that the slope of the Phillips
curve plays in determining the effects of a decline in
unemployment?
7. The relationship between the output gap and
unemployment summarized in Okun’s law takes
the form
U t − U * = –.5 × (Y t − Y f )/Y f ,
where (Y t − Y f )/Y f is the percentage gap between
output at time t and full-employment output. Use this
expression for Okun’s law and the Phillips curve from
Problem 6 to derive the inflation adjustment curve
linking inflation and the output gap.
8. The United States at the end of the 1990s witnessed
rapid growth in real income and historically low rates of
unemployment. Suppose two hypotheses for this decline
are offered. The first is that productivity has increased
owing to new technologies and that the natural rate of
unemployment has fallen. The second is that the economy
has been in a cyclical boom and unemployment has
fallen well below the natural rate. How might you distinguish
between these two hypotheses? Do they have
different implications for inflation?
9. Suppose people expect higher inflation in the future.
What are the short-run effects of this change in expectations
on unemployment and actual inflation? How
can monetary policy maintain the economy at full
employment? If policy succeeds in maintaining full
employment, what happens to inflation?
10. Using the ADI-SRIA framework, show how the economy
adjusts to a negative aggregate demand shock in the
short run and in the long run.
11. If individuals based their expectations of inflation on
inflation in the recent past, we can write the SRIA
schedule as
π t =π t−1 + a × (Y t − Y f ),
where a is a constant, π t is inflation at time t, Y t is output
at time t, and Y f is potential output. Suppose the ADI
curve is given by
Y t = A − b ×π t .
Assume that initially output is equal to potential and
inflation is 8 percent. If A = 116, Y f = 100, a = .25, and
b = 2, fill in the rest of the following table to show how
the economy would respond if A falls by 5.
Period Inflation Expected Inflation Output
0 8 percent 8 percent 100
1 7.17 percent 8 percent 96.67
2
3
4
5
Use an ADI-SRIA graph to explain why output and
inflation behave in the way you calculated.
12. Using a spreadsheet program, repeat Problem 11 but
calculate inflation, expected inflation, and output for
twenty periods. Does output return to Y f ? What is the
new long-run equilibrium rate of inflation? Plot output
and inflation on the vertical axis, with the time period on
the horizontal axis, to show how they move over time.
REVIEW AND PRACTICE ∂ 835