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## What determines the natural rate of unemployment

The ‘natural’ rate of unemployment is one of those controversial concepts that will immediately provoke angry rants from the anti-capitalists in any economics class when it gets brought up. The answer from the hard core free-marketeers would be that unemployment is a signal of market failure, and that if you had perfectly working labour markets (no minimum wage, no benefits, no trade unions etc) then wages would fall to a low enough level to eliminate unemployment. I will leave this moral debate alone here and just focus on how this labour market model explains the natural rate of unemployment…

We had a wage-setting relation $W=P^e F(u,z)$ and a price-setting relation $P=(1+\mu )W$. We can think of these in terms of real wages $\frac{W}{P}$.

For the wage-setting relation, we will have to assume $P^e =P$ for this. This is often seen as a medium-run assumption. When you have something in economics being ‘expected’, like expected prices, expected inflation, the idea is usually that the expected and the actual values can differ in the short-run, but peoples’ expectations won’t be wrong indefinitely, eventually expectations will adjust to the point where expectations catch up with reality, this is the ‘medium run’.

So in the medium-run the wage-setting relation is $W=P F(u,z)$, so $\frac{W}{P}=F(u,z)$.

And the price-setting relation is $\frac{W}{P}=\frac{1}{(1+\mu )}$

The natural rate of unemployment is defined as the unemployment rate such that the real wage determined in wage-setting and price-setting relations is the same – this is equilibrium in the labour market. You can represent this with a diagram with (W/P) on the vertical axis and u, unemployment, on the horizontal axis.

The rate at which the two come into equilibrium gives the natural rate of unemployment.

The wage-setting curve is downward sloping, capturing the fact that higher unemployment leads to lower wages. So what about the other variables in this model, the ‘catch-all’ variable and the ‘mark-up’?

If things in the ‘catch all’ variable change, this will shift the wage-setting curve up or down. For instance if there is an increase in trade union power, or increase in benefits, this will increase workers’ bargaining power, so it will shift the WS curve up. This will lead it to intersect the price-setting curve at a higher ‘natural’ rate of unemployment. This is the issue of ‘insiders v outsiders’ that sometimes comes up in relation to debates about trade unions, often when unions get more power, they increase the wages of those already working, at the expense of making it more difficult for outsiders to find work in the industry.

If things in the ‘mark-up’ change (such as an increase in non-labour costs for firms, or an increase in market power allowing them to charge prices further above costs) then this will shift the price-setting relation, but remember that because in terms of real wages, $\frac{W}{P}=\frac{1}{(1+\mu )}$, the mark-up is on the denominator here, so those cases mentioned above which would increase the mark-up, increase the denominator of this equation so they shift the PS curve downwards. This will also increase the natural rate of unemployment.