Dynamic Macroeconomics

15.4 The Phillips Curve and Inflationary Expectations
We have already demonstrated that the main difference between the original
Keynesian models and the corresponding classical models is the assumption
of nominal rigidity in both prices and wages, or (in the case of the AD-AS
model) only nominal wages. The assumption of complete nominal rigidity in
either prices or wages is clearly not realistic and was rightly considered as
one of the main weaknesses of Keynesian models. Economies are
characterized by the simultaneous existence of inflation and unemployment, a
phenomenon that implies the adjustment of both prices and wages even in the
short run.
15.4.1 The Phillips Curve and the Trade-off between Inflation and Unemployment
Since the late 1950s, a central point of reference for Keynesian models has
been the Phillips curve, a negative relationship between unemployment and
inflation identified and estimated econometrically by Phillips [1958]. The
Phillips curve was combined with the IS-LM model of aggregate demand to
simultaneously determine both inflation and unemployment. Thus, the Phillips
curve essentially replaced the aggregate supply curve of the AD-AS model,
which was based on fixed nominal wages, and helped determine both
unemployment and inflation.
The curve that Phillips estimated econometrically for the United Kingdom
took the form
where φ(u
0
) = 0 and φ′(u) < 0. In equation 
(15.37)
, π denotes inflation, u is
the unemployment rate, and u
0
is the zero inflation unemployment rate. The
function φ relating inflation and unemployment estimated by Phillips is
nonlinear. Its shape is depicted in 
figure 15.7
.
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Figure 15.7
The Phillips curve.
In the context of the basic Keynesian model, combining the IS-LM model
of the determination of aggregate demand with the Phillips curve, one could
deduce that an increase in aggregate demand would lead to higher real output
and employment, lower unemployment, and a rise in inflation along the
Phillips curve. Conversely, a decline in aggregate demand would lead to a
lower level of real output and employment, higher unemployment, and a
reduction of inflation along the Phillips curve.
Inspired by Phillips [1958] Samuelson and Solow [1960] estimated a
Phillips curve between price inflation and unemployment for the United
States. These authors argued that the short-term problem of macroeconomic
policy could be seen as the determination of the level of aggregate demand in
order to select the socially desirable combination of inflation and
unemployment on the Phillips curve. In times of recession, an increase in
aggregate demand will lead to a reduction in unemployment, but at the cost of
higher inflation. In times of economic boom and high inflation, inflation could
be reduced through a reduction in aggregate demand, but this would result in
higher unemployment.
The Samuelson-Solow argument can be understood with the help of 
figure
15.8
, which depicts the Phillips curve and the indifference map of

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policymakers between inflation and unemployment. Because both inflation
and unemployment are assumed to be undesirable, the indifference curves are
concave to the origin. The closer an indifference curve is to the origin, the
higher will be the implied social welfare. Samuelson and Solow argued that
because the Phillips curve implies a negative relationship between inflation
and unemployment, it acts as a constraint on the options of policymakers. The
latter will maximize social welfare at point E in the figure, where the
Phillips curve is tangent to the highest-possible indifference curve. Point E is
thus associated with the optimal feasible combination of inflation and
unemployment under a discretionary macroeconomic policy.
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