Read Chapter 2 in Pissarides (2000).

Summary of Chapter 1:

1. The model demonstrates how both unemployment and vacancies can exist concurrently in labor market equilibrium. The reason is that searching frictions.

2. The frictions are formed by matching function.

3. In steady state, job creation rate is equal to job destruction rate.

4. Out of steady state, changes in the productivity (or other parameters) have an immediate effect on the wage because wages can be renegotiated any time. Firms are able to adjust their vacancies immediately, hence v and tightness variable jump. The unemployment rate u is pre-determined as it is tied to the matching function. Hence vacancies have the tendency to overshoot.

Related papers:
New developments in models of search in the labor market.
Job reallocation, employment fluctuations and unemployment