§6 The Labor Market

Wage Determination

• Workers’ wages typically exceed their reservation wage - the wage that would make them indifferent between working or being unemployed.
• Wages typically depend on labor market conditions. In particular, the lower $u$, the higher the wages.
• Workers’ bargaining power depends on:
  • How costly is for the firm to find workers.
  • How hard is for workers to find another job if they were to leave the firms.
• At the aggregate level, we can write the wage setting equation as:

$$W = P^eF(u, z); \quad F_u < 0, F_z > 0$$

Price Determination

• The prices set by firms depend on their costs, which in turn depends on the production function:

$$Y = AN$$

• Where:
  • $Y$ is output;
  • $N$ is employment;
  • $A$ is labor productivity (output per worker).
• Let’s simplify things and assume $A = 1$, so that the production function is simply

$$Y = N$$

• That is, producing one more unit of output requires one more worker.

• This production function implies that the marginal cost of production is equal to $W$.

• Assume that firms set their prices according to a markup $m$ over their marginal cost:

  $$P=(1 + m)W$$

• We can rewrite this price setting equation in terms of the real wage:

  $$\frac{W}{P}=\frac{1}{1 + m}$$

• The higher the markup $m$, the lower the real wage firms are willing to pay.

The Natural Rate of Unemployment

• Warning: there is nothing natural about the natural rate of unemployment!

• It simply means the equilibrium level of unemployment when $P^e = P$.

• For this reason, one can think of it as the average unemployment rate in the medium (and long) run.

• With the assumption $P^e = P$, we can write the wage setting equation as:

  $$\frac{W}{P}=F(u^n,z)$$

• The higher $u^n$ (called the natural rate or structural rate of unemployment), the lower the real wage consistent with the wage setting equation.

• In terms of equations, we have from the price setting equation:

  $$\frac{W}{P}=\frac{1}{1 + m}$$

• And from the wage setting equation:

  $$\frac{W}{P}=F(u^{n},z)$$

• Thus, in equilibrium:

  $$F(u^{n},z)=\frac{1}{1 + m}$$

— Apr 14, 2025

§6 The Labor Market by Lu Meng is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at About.