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.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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.
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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