Consider the simple discrete job search model that we studied in class. Only the unemployed can receive one offer per period from F(w) that is a uniform distribution on [0,2]. There is a constant probability of being laid off at the end of each period while employed. Assume that she can get a new offer right away when laid off. We want to understand the reservation wage, WR, in this model. Assume that u(c) = c. The parameters are a discount factor ẞ and an unemployment benefit b.< (a) Define a mapping T:R->R and show that T is contraction on [0, ∞). Explicitly state any additional assumptions that you may need.(Grading guide line: 5pt for the exact form of T, 10pt for showing contraction, and 5pt for stating correct assumptions.)< (b) Discuss why (a) is useful to understand the reservation wage wд in this economy.< (c) We write WR = WR (b,ẞ,λ) to reveal its dependence on (b,ẞ,λ). Show that 0 ≤ aWR дь OWR дл ≤1 and ≥0. What about ? awR ав State any additional assumptions that you may need.< (d) Briefly explain the results obtained in (c).
Consider the simple discrete job search model that we studied in class. Only the unemployed can receive one offer per period from F(w) that is a uniform distribution on [0,2]. There is a constant probability of being laid off at the end of each period while employed. Assume that she can get a new offer right away when laid off. We want to understand the reservation wage, WR, in this model. Assume that u(c) = c. The parameters are a discount factor ẞ and an unemployment benefit b.< (a) Define a mapping T:R->R and show that T is contraction on [0, ∞). Explicitly state any additional assumptions that you may need.(Grading guide line: 5pt for the exact form of T, 10pt for showing contraction, and 5pt for stating correct assumptions.)< (b) Discuss why (a) is useful to understand the reservation wage wд in this economy.< (c) We write WR = WR (b,ẞ,λ) to reveal its dependence on (b,ẞ,λ). Show that 0 ≤ aWR дь OWR дл ≤1 and ≥0. What about ? awR ав State any additional assumptions that you may need.< (d) Briefly explain the results obtained in (c).
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter26: Factor Markets: With Emphasis On The Labor Market
Section: Chapter Questions
Problem 10QP
Related questions
Question
![Consider the simple discrete job search model that we studied in class. Only the
unemployed can receive one offer per period from F(w) that is a uniform distribution on
[0,2]. There is a constant probability of being laid off at the end of each period while
employed. Assume that she can get a new offer right away when laid off. We want to
understand the reservation wage, WR, in this model. Assume that u(c) = c. The
parameters are a discount factor ẞ and an unemployment benefit b.<
(a) Define a mapping T:R->R and show that T is contraction on [0, ∞). Explicitly state
any additional assumptions that you may need.(Grading guide line: 5pt for the
exact form of T, 10pt for showing contraction, and 5pt for stating correct
assumptions.)<
(b) Discuss why (a) is useful to understand the reservation wage wд in this
economy.<
(c) We write WR = WR (b,ẞ,λ) to reveal its dependence on (b,ẞ,λ). Show that 0 ≤
aWR
дь
OWR
дл
≤1 and ≥0. What about ?
awR
ав
State any additional assumptions that you may need.<
(d) Briefly explain the results obtained in (c).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb78c85cc-72f3-4295-a385-26416adebb8f%2F32795991-1df7-473b-be25-d730eff72a50%2Fgfe2ff8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the simple discrete job search model that we studied in class. Only the
unemployed can receive one offer per period from F(w) that is a uniform distribution on
[0,2]. There is a constant probability of being laid off at the end of each period while
employed. Assume that she can get a new offer right away when laid off. We want to
understand the reservation wage, WR, in this model. Assume that u(c) = c. The
parameters are a discount factor ẞ and an unemployment benefit b.<
(a) Define a mapping T:R->R and show that T is contraction on [0, ∞). Explicitly state
any additional assumptions that you may need.(Grading guide line: 5pt for the
exact form of T, 10pt for showing contraction, and 5pt for stating correct
assumptions.)<
(b) Discuss why (a) is useful to understand the reservation wage wд in this
economy.<
(c) We write WR = WR (b,ẞ,λ) to reveal its dependence on (b,ẞ,λ). Show that 0 ≤
aWR
дь
OWR
дл
≤1 and ≥0. What about ?
awR
ав
State any additional assumptions that you may need.<
(d) Briefly explain the results obtained in (c).
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