2. Consider a version of the labor market model of Pissarides (1985) in which the matching function M(u, v) is M(u, v) and the discount factor ẞ is one. (a) Derive an expression for the worker's job-finding probability p(e) and for the firm's worker-finding (or job-filling) probability, q(6). (b) Express the equilibrium market tightness 9 in terms of the parameters of the model, k, 5, 7, b, and y- (c) Express the equilibrium unemployment u in terms of the parameters of the model. (d) Compute the effect of a small increase in the productivity of labor y on the equilibrium market tightness 0. Explain your findings. (e) Compute the effect of a small increase in the productivity of labor y on the equilibrium unem- ployment. Explain your findings.
2. Consider a version of the labor market model of Pissarides (1985) in which the matching function M(u, v) is M(u, v) and the discount factor ẞ is one. (a) Derive an expression for the worker's job-finding probability p(e) and for the firm's worker-finding (or job-filling) probability, q(6). (b) Express the equilibrium market tightness 9 in terms of the parameters of the model, k, 5, 7, b, and y- (c) Express the equilibrium unemployment u in terms of the parameters of the model. (d) Compute the effect of a small increase in the productivity of labor y on the equilibrium market tightness 0. Explain your findings. (e) Compute the effect of a small increase in the productivity of labor y on the equilibrium unem- ployment. Explain your findings.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.11P
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![2. Consider a version of the labor market model of Pissarides (1985) in which the matching function
M(u, v) is
M(u, v) =
u+ v
and the discount factor 3 is one.
(a) Derive an expression for the worker's job-finding probability p(8) and for the firm's worker-finding
(or job-filling) probability, q(8).
(b) Express the equilibrium market tightness 0 in terms of the parameters of the model, k, 5, 7, b, and
(c) Express the equilibrium unemployment u* in terms of the parameters of the model.
(d) Compute the effect of a small increase in the productivity of labor y on the equilibrium market
tightness 0. Explain your findings.
(e) Compute the effect of a small increase in the productivity of labor y on the equilibrium unem-
ployment. Explain your findings.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a9f6bb4-0fd0-4dac-869c-76ce68e54dff%2Ffeb21882-a6f5-4dbf-aa52-5caf87f1d454%2Flqvwmq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider a version of the labor market model of Pissarides (1985) in which the matching function
M(u, v) is
M(u, v) =
u+ v
and the discount factor 3 is one.
(a) Derive an expression for the worker's job-finding probability p(8) and for the firm's worker-finding
(or job-filling) probability, q(8).
(b) Express the equilibrium market tightness 0 in terms of the parameters of the model, k, 5, 7, b, and
(c) Express the equilibrium unemployment u* in terms of the parameters of the model.
(d) Compute the effect of a small increase in the productivity of labor y on the equilibrium market
tightness 0. Explain your findings.
(e) Compute the effect of a small increase in the productivity of labor y on the equilibrium unem-
ployment. Explain your findings.
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