Chapter 23

# Unemployment II: Market Frictions

## Quantitative Problems

1. Suppose it is discovered that 80% of unemployed workers experience an unemployment spell that lasts no longer than 3 weeks, but that the average duration of unemployment is 4 months. How is this possible? |

2. L = E + U, and δ, μ, and a have the meanings given in the text.(a) Determine the change in the level of unemployment, Δ U, between any two periods.(b) What is meant by steady-state unemployment? (c) Use your answer in part (a) to derive the steady-state unemployment rate . Depict the relationship between and μ. Explain what happens if the job-destruction rate, δ, increases.(d) Evaluate the validity of the claim that a high rate of job destruction, δ, necessarily implies a high rate of unemployment. Let |

3. δ = 2%), and that 50% of unemployed workers receive job offers each month (μ = 50%). What is the probability, a, that the average worker accepts a given job offer? Suppose that the observed steady-state level of unemployment is = 5%; 2% of jobs are destroyed every month ( |

4. b new workers join the labor force (entering the unemployment pool) and that a fraction 0 ≤ ρ ≤ 1 of workers exit it. Determine the steady-state size of the labor force and the steady-state unemployment rate. In practice, new workers constantly enter the labor market and current workers exit from it. Suppose that each period a constant |

5. μ denote the probability an unemployed worker finds a job, β denote the probability an open vacancy finds a worker, and assume a = 1 (i.e., workers accept any job offer). Suppose that the matching technology takes the form .(a) Show that the matching technology exhibits constant returns to scale (which, to recap, means that scaling U and V by the factor k > 0 results in scaling .(b) Derive and illustrate the SS locus. What happens if m_{0} increases from m_{0} = 2 to m_{0} = 3? Let |

6. μ according to w = w(μ). Is this formulation plausible? What happens to the EE locus in this case? Use your answer to explore the effects of a sudden improvement in the matching technology on the equilibrium wage and the unemployment rate. In the text, it was assumed that wages are exogenously given, and the net value of opening a new vacancy is . Suppose, instead, that the wage depends positively on |

7. Despite the fact that recessions are almost always associated with an increase in the employment rate, do they potentially confer any economic benefits? |

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