Where the natural rate comes from: wage-setting and price-setting

Price-setting. Firms with some market power charge a mark-up m over what a unit of output costs them in wages. With output per worker A, a unit costs W/A in wages, so P = (1 + m)W/A, and dividing by P gives the real wage the firms can afford to pay: W/P = A/(1 + m). It does not depend on unemployment, so on a diagram of the real wage against the unemployment rate it is a flat line. More monopoly power, a bigger m, lowers it.

Wage-setting. Workers and firms bargain over the wage. The more unemployed there are, the less bargaining power workers have, because losing the job is more costly and replacing them is easy. So the real wage workers can claim falls as unemployment rises: a downward-sloping curve. Unemployment benefits, union strength and the like shift it up.

A number to fix the idea. A 25% mark-up and a wage-setting relation W/P = 1 − u (with A = 1) give 1 − u = 1/1.25 = 0.8, so u_n = 20%. With a mark-up of 20% it is 0.2/1.2, about 17%. In general, for W/P = 1 − u, uₙ = m/(1 + m).

• A higher mark-up lowers the real wage price-setting allows, so the flat line moves down and meets the wage-setting curve at higher unemployment. A law that makes entry harder raises the monopoly power of firms and so raises m. This is the opening question.
• Stronger bargaining power or more generous benefits shift the wage-setting curve up. Workers claim more at every unemployment rate, so the curves meet where unemployment is higher.
• Better information about jobs. The natural rate contains frictional unemployment, and a way of increasing information on job availability would reduce it (Hyderabad 2013).
• Aggregate demand does not. In the monetarist view the natural rate of unemployment, like the natural level of output, is determined by real things such as the capital stock, the size of the labour force and technology, and not by aggregate demand (CUET 2025).

Now the opening question. In the medium run output is at the level the natural rate implies, Yₙ = L(1 − uₙ). The law raises m, so uₙ rises and medium-run output falls (A). With the money supply fixed, lower output goes with a higher price level on the aggregate demand curve, so the medium-run price level is higher (C). In the short run the expected price level is stuck at its old value, but firms raise prices at each level of wages, so the short-run supply curve shifts up and, with demand unchanged, output is lower and prices higher (B and D). All four are true.

Four wage-setting rules appear in past papers. The Workbench has all four. Start with the first, raise the mark-up and watch the red line fall and the gold line move right. Then switch rule and raise productivity A. The table under the plots recomputes the natural rate for each change, and the last box checks two identities for you: at uₙ actual inflation equals expected inflation, and uₙ does not depend on expected inflation.

What does a rise in productivity do to the natural rate? Past papers have set this question with three different answers: it raises the natural rate, it has no effect, it lowers it. All three are right, because each paper puts productivity into the wage claim differently. The deciding question is how the wage claim moves with productivity, compared with how the real wage that firms can afford moves.

• The claim rises one for one with productivity (W/P = A(1 + z − u)). Both curves scale with A, so the crossing point does not move: no effect.
• The claim rises with productivity but the firms’ offer does not (W = Pᵉ F(u, A) with F increasing in A, and price-setting P = (1 + m)W). Workers capture the gain and firms do not offer more, so unemployment must be higher to hold the claim down: the natural rate rises.
• The claim rises less than one for one (W/P = Aᵅ(1 − u)¹⁻ᵅ with α below 1, against W/P = A/(1 + m) from price-setting). Firms can afford more than workers claim, so the crossing moves to lower unemployment: the natural rate falls.

One explanation for involuntary unemployment, people who would work at the going wage and cannot find a job, is that the wage does not adjust immediately to changes in labour demand (Hyderabad 2016). Three theories say more about why a wage above the market-clearing level can last.

• Efficiency wages. If a firm cannot watch how hard its workers work, it may pay more than it needs to, so that losing the job is costly. The wage is then higher than the one that would clear the market, and unemployment is the price. The theory is associated with Yellen and Stiglitz (UGC NET 2024). It also explains why the wage firms need to pay falls as unemployment rises: losing the job costs more, so a smaller premium keeps workers working hard.
• Insiders and outsiders. Workers who hold jobs (insiders) set wages in bargaining, and the unemployed (outsiders) have little say. Insiders have no reason to cut the wage to employ the unemployed.
• Hysteresis. If actual unemployment feeds back into the natural rate, a recession leaves the natural rate higher than it was. Long spells of unemployment can cost workers skills and attachment to work, and if wages are set by the insiders who still hold jobs, a shock that cuts employment leaves the outsiders without a voice and the wage claim is not cut to bring them back. A rise in the natural rate that outlasts the shock that caused it is called hysteresis.

So far prices were correctly expected. Now let workers bargain for a wage in terms of the price level they expect: W = Pᵉ × (their real claim at unemployment u). Firms then set the price from the wage they actually pay: P = (1 + m)W/A. Dividing,

At u = uₙ the ratio ws/ps is exactly 1, so π = πᵉ: the natural rate is the unemployment rate at which actual and expected inflation agree, which is why it is also the rate at which inflation does not accelerate (the NAIRU, when expectations follow last year’s inflation). Below uₙ the workers’ claim exceeds what the firms allow, the ratio is above 1 and inflation is above expected inflation; above uₙ it is the reverse. For small gaps the relation is approximately a straight line, the curve of Lesson 7:

The Delhi School of Economics’ entrance questions on wage-setting and price-setting are collected in Lesson 12, by technique.