2. Suppose we have an economy with Phillips curve π^² = π + (m + z) - au. Recall the price setting equation P = (1+m)W= (1+m)P^eF(u,z) = (1+m)P^e(1-au+z)

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Chapter10: Consumer Choice Theory
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2. Suppose we have an economy with
Phillips curve T^e = t + (m + z) – au. Recall
the price setting equation
P = (1+m)W = (1+m)P^eF(u,z) =
(1+m)P^e(1-au+z)
Suppose a = 1/5 , m = z = 1/20 .
a) Calculate the natural rate of
unemployment.
b) Now suppose that half of the working
population has its wages indexed - that is,
they have a constant real wage w. Derive
the new Phillips curve in this economy.
(Hint: first work out what the function F
looks like for workers with indexed wages,
then average this with the original F. You
should end up with a function that looks
like F *(u,z) = 1-a^*u+z^* - then plug the
values of a, z, m into the equation for the
Phillips curve.)
c) What's the new natural rate of
unemployment? Is it higher or lower than
before?
Transcribed Image Text:2. Suppose we have an economy with Phillips curve T^e = t + (m + z) – au. Recall the price setting equation P = (1+m)W = (1+m)P^eF(u,z) = (1+m)P^e(1-au+z) Suppose a = 1/5 , m = z = 1/20 . a) Calculate the natural rate of unemployment. b) Now suppose that half of the working population has its wages indexed - that is, they have a constant real wage w. Derive the new Phillips curve in this economy. (Hint: first work out what the function F looks like for workers with indexed wages, then average this with the original F. You should end up with a function that looks like F *(u,z) = 1-a^*u+z^* - then plug the values of a, z, m into the equation for the Phillips curve.) c) What's the new natural rate of unemployment? Is it higher or lower than before?
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