ECON 522 - Macroeconomics of the Labor Market
Stan Rabinovich
UNC Chapel Hill
Problem set 10
1. Effects of unemployment insurance in the equilibrium search model
Consider the equilibrium search model from class. The matching function is
m = µu1−γ v γ ,
where m is the number of matches, u is unemployment, v is vacancies, and µ is matching efficiency. Firms have
a vacancy posting cost of k. Workers, when employed, produce y. An unemployed worker receives b. Worker
bargaining power is φ, a number between 0 and 1. The job separation rate is δ.
Graphically illustrate the effect of an increase in unemployment benefits, b, on equilibrium unemployment
and vacancies. Clearly illustrate which curve(s) shift(s), and in which direction. Briefly explain.
2. Effects of the minimum wage in the equilibrium search model
Consider again the equilibrium search model from class. The matching function is
m = µu1−γ v γ ,
where m is the number of matches, u is unemployment, v is vacancies, and µ is matching efficiency. Firms have
a vacancy posting cost of k. Workers, when employed, produce y. An unemployed worker receives b. Worker
bargaining power is φ, a number between 0 and 1. The job separation rate is δ.
Suppose that the government imposes a minimum wage of wmin .
(a) Under what conditions will the minimum wage bind? (Your answer should be an inequality relating to
the parameters of the model.)
(b) Assuming that the conditions are such that the minimum wage binds, graphically illustrate the effect of
the minimum wage on equilibrium unemployment and vacancies. Clearly illustrate which curve(s) shift(s),
and in which direction. Briefly explain.
3. Effects of layoff costs in the equilibrium search model
European economies have more strict employment protection laws than the United States, such as restrictions
on firing or mandated severance payments that an employer must pay its workers in case of layoff. Theoretically,
these restrictions would be expected to discourage firms from firing, and thus reduce the job separation rate.
However, many economists claim that this strict employment protection is in fact responsible for the high
unemployment rates we observe in European countries.
We will analyze the effects of such layoff taxes in the equilibrium search model. Consider again the equilibrium
search model from class. Suppose that a firm’s profits from hiring a worker are J = y − w − Z rather than
J = y − w. Here, Z is the expected cost associated with the possibility of layoff, which could be one of
two things: (1) there is some probability that the firm may need to lay off its worker, in which case it will
suffer a cost (e.g. severance payments); (2) alternatively, anticipating this cost, the firm might need to expend
additional effort on retaining a worker, or retain a worker even if that worker is unproductive, which is also a
cost to the firm.
Suppose that a layoff tax results in a decrease in the job separation rate δ, in conjunction with an increase
in Z.
(a) Graphically illustrate the effects on equilibrium unemployment and vacancies. Clearly illustrate which
curve(s) shift(s), and in which direction. Is the effect on unemployment ambiguous?
(b) Explain why the effect on unemployment is ambiguous by using the equation
u=
1
δ
δ+f