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## An equation for the Phillips Curve

As you do more economics you will start recognising a Phillips Curve equation, it often comes up in slightly different forms, the basic features are always the same, it will be an expression which expresses the rate of inflation in year t, in terms of things like the unemployment rate in year t, the inflation rate in year t-1, the natural rate of unemployment, and a parameter in there which shows how responsive inflation is to unemployment. Often you will get a (+ supply shock) bit stuck on the end.

As usual on this blog I use Olivier Blanchard’s notation, but if you get used to this you will be able to recognise the Phillips Curve as presented in different forms.

Remember the basic idea of the Phillips Curve is a relationship between inflation and unemployment.

You can express it in an equation like this: $\pi_t = \pi^e + (\mu + z) - \alpha u_t$

$\mu$ and $z$ have come from the price-setting and wage-setting process. $\mu$ is the mark-up which firms put over and above labour costs in their price-setting, to cover non-labour costs and also, depending on the amount of market power the firm has, a profit margin. $z$ is the ‘catch-all‘ variable referring to conditions in the labour market that influence wage-bargaining power outside of the rate of unemployment (trade union power, employment legislation etc). These two variables don’t change much in the short run so they generally get treated as being static in the short run but they are in the equation because any significant changes in these factors will change the position of the Phillips Curve.

So this equation is saying:
Inflation in year t depends on expected inflation in year t, the pricing mark up, conditions in the labour market and the rate of unemployment in year t. Because the mark up and labour market conditions are treated as static it is really expected inflation and the rate of unemployment that matters here. $\alpha$ is a parameter which shows the responsiveness of inflation to unemployment.