Part 1 - Question 2.a - Labor market · Introducció a la Macroeconomia UPF 2018

a. Formulate the analytical equations for wage setting (WS) and price setting (PS), assuming labor productivity A = 1. Explain clearly how each relation formalizes the mechanism described in the excerpt.

Solución: WS relation: $W = P^e F(u, z)$, or in real terms when $P = P^e$: $\frac{W}{P} = F(u, z)$, with $\frac{\partial F}{\partial u} < 0$. PS relation: $P = (1 + \mu)W$, or in real terms: $\frac{W}{P} = \frac{1}{1 + \mu}$.

b. Interpret the equilibrium point determined by their intersection.

Solución: The equilibrium yields the natural rate of unemployment ($u_n$), where the real wage implied by price setting equals the real wage demanded in wage setting: $F(u_n, z) = \frac{1}{1 + \mu}$.

b. Illustrate both relations in a diagram with real wage on the vertical axis and unemployment rate on the horizontal axis.

Solución: A diagram with $W/P$ on the vertical axis and $u$ on the horizontal axis. The PS relation is a horizontal line at $\frac{W}{P} = \frac{1}{1+\mu}$. The WS relation is downward-sloping. Their intersection at point $A$ determines the natural rate of unemployment $u_n$ on the horizontal axis.