Consider a model of unemployment where the change in the unemployment rate (u) is given by Δu = (b+s)-(b+s+f)u, where b is the rate of entry in the labor force, s is the separation rate, and f is the job findings rate.

a. Derive an expression for the steady-state unemployment rate u*.

b. The job finding rate f is a function of vacancies (v), the intensity of job search (i), and the ease of matching (m). With what sign do you expect f to depend on each of these three variables? What is the slope of the Beveridge curve in (u,v) space and why?

c. Considering the creation of jobs by firms, do you expect higher unemployment to come with higher or lower vacancies created? Describe a mechanism for this relation.

d. Plot the Job Creation curve that comes with your answer to c, and the Beveridge curve from b and define the equilibrium in the labor market.

e. Say that there is an increase in the rate of growth of the labor force. How does this affect equilibrium unemployment and vacancies?