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The Tradeoff Between Inflation And Unemployment Notes

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Chen Li

Macroeconomics, Paper 2, Part IIA 1st Dec 2009 Supervision 04 Discuss the notion of a trade­off between inflation and unemployment from a theoretical and empirical
perspective. The notion o a trade­off between inflation and unemployment is derived from the Phillips curve. It is
named after William Phillips, who discovered a negative relationship between changes in nominal
wages and unemployment. Since changes in wages are strongly correlated with changes in the price
level, the Phillips curve was used later on to describe the empirical negative relationship between
inflation and unemployment. The theoretical construct of the Phillips curve is developed as follows: Wage determination depends
positively on the expected price level, negatively on the unemployment rate and another catchall
variable:

W = P e F (u , z )

(1)

Wages depend on the expected price level, as workers and firms care about real, not nominal wages
and as the actual price level in the future is not yet known when the wages are set. Wages also
depend on the unemployment rate as higher unemployment weakens the worker's bargaining power,
forcing them to accept lower wages. In not perfectly competitive markets, firms can charge a price for their goods higher than marginal
cost, by setting a markup:

P = (1 + µ )W

( 2)

where μ is the markup.
Putting these two equations together gives us

P = (1 + µ) P e F (u , z )

(3)

Assuming that F has a specific form

F (u , z ) = 1 − αu + z

(4)

where α captures the strength of the effect of unemployment on the wage gives us

Pt = Pt e (1 + µ )(1 − αu t + z )

(5)

Now, we divide both sides by the past period's price level

Pt Pt e
=
(1 + µ )(1 − αu t + z ) Pt −1 Pt −1

1 + π t = (1 + π te )(1 + µ )(1 − αu t + z )

Rearranging and assuming that inflation, expected inflation and the markup are not too large gives us:

π t = π te + ( µ + z ) − αu t

( 6)

1

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