Labor Economics

Winter 2014/2015

Problem set 6

November 3, 2014

Inflation-unemployment trade-off

Consider and economy which is characterized by the following equations (lower-case letters

denote logarithms):

pt = wt + at, (1)

yt = at + lt, (2)

yt = mt − pt, (3)

lt = l + η(wt − pet ), (4)

where pt is the aggregate price level, wt is the nominal wage, at is aggregate TFP, yt is output, lt

is total labor input, mt is money supply, l and η are constants and pet is the expected aggregate

price level. Assume that at = 0 and ∆mt = ∆m ∀t.

Question 1

Using (2) and (3) derive the price-schedule, i.e. an expression of inflation as a function of un-

employment and money supply growth. Using the lag of (1) in (4) derive the wage-schedule,

i.e. and expression of unemployment as a function of the NAIRU and inflation.

Question 2

Consider the case of adaptive expectations. In particular, assume that workers form the fol-

lowing inflation expectations: ∆pet = 1/2(∆pt−1 + ∆pt−2). Furthermore, assume ∆m = 2, the

NAIRU u = 6 and η = 1.

1

a) How does the above economy react to a money supply growth shock compared to the

case when workers form inflation expectations according to ∆pet = ∆pt−1?

b) What is the long-run equilibrium of the above economy?

c) Assume that in period t = 0, the economy is in the long-run equilibrium. In period t = 1

the central bank unexpectedly increases money supply growth to ∆m = 4 forever. Derive the

path of inflation and unemployment for the first 3 periods following the money supply increase.

d) Compare the results in c) to those derived in class (for the case when ∆pet = ∆pt−1). Do

they confirm your intuition from question a)?

2