lecture ii: constructing a theory of equilibrium unemployment microeconomic foundations of the wage...
TRANSCRIPT
![Page 1: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/1.jpg)
Lecture II: Constructing a theory of equilibrium unemployment
Microeconomic foundations of the wage curve
![Page 2: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/2.jpg)
How are wages set?
• Wages can be thought of as the sum of three terms:– A compensation for the disutility of labor– An outside option which determines what the
worker would get outsidr the employment relationship (alternative wage = OC of labor)
– A rent which tells us how much he can grab beyond that
![Page 3: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/3.jpg)
When is unemployment involuntary?
• If the employed are better-off than the unemployed, the latter would prefer to be employed
• Therefore, involuntary unemployment rent = 0
• Does that mean we are at the Walrasian equilibrium?
![Page 4: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/4.jpg)
What is a Walrasian equilibrium?
• WE holds if outside option = flow of utility corresponding to a zero wage
• But Unemployment Benefits and Welfare Minima can raise OO above that level
• Unemployment is then voluntary but above the walrasian level
![Page 5: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/5.jpg)
Do we need rents in the model?
• Assume no rent
• For h(u) to be downward sloping, unemployment must negatively affect the outside option
• This cannot be true if the employed are no better-off than the unemployed
• We thus have a flat h(u) curve and are back to the wage floor model
![Page 6: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/6.jpg)
Three classes of models:
• Collective bargaining models rents come from the union’s monopoly on jobs
• Individual barganing models rents come from turnover costs
• Efficiency wage models rents come from informational issues + incomplete contracting
![Page 7: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/7.jpg)
Collective bargaining models
• There are three of them:– Monopoly Union– Efficient Bargaining– Right-to-Manage
![Page 8: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/8.jpg)
Monopoly Union
)1(
1
)1()1(
1)1( s.t.
)(max
uwb
u
ubwubwuw
ww
wL
KAw
LNwwL
![Page 9: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/9.jpg)
What is going on?
• The union maximizes the total expected income of members
• It takes the LD curve as given• Wages = markup on OC of labor• Markup inversely related to elasticity• OC of labor reflects job finding prospects
goes down with u• If UB indexed on wages, natural rate only
depends on replacement ratio and elasticity
![Page 10: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/10.jpg)
Membership effects
• Note that union membership N has no impact on the outcome
• We can get membershif effects by introducing nonlinearities
• Example: unions maximize the median members’ expected income
• His employment probability is nonlinear in L/N
![Page 11: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/11.jpg)
Getting membership effects:
)1)(/()1(
')/(
)/(
)/()1( s.t.
))/(1()/(max
NLuwuwuw
NLNL
NL
NL
wNL
NLw
L
KAw
NLwNLw
![Page 12: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/12.jpg)
Comments:
• If elasticity of φ falls, then lower membership => higher wages and more unemployment
• If membership depends on past employment => persistence mechanism
• Membership rules matter (encompassing unions vs. Guilds)
![Page 13: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/13.jpg)
Efficient Bargaining
wMPL
LV
LU
wMPLV
wwU
wLLAKV
LwwNwLNwwLU
VUwL
)1(
0)()1()( :FOCs
)()(
max
1
1
,
![Page 14: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/14.jpg)
Comments:
• Employment is determined at the privately efficient level from the match’s point of view
• Absent institutional rigidities, employment would be at its walrasian level
• Wage bargaining only affects the way the surplus is split wages are a pure transfer, the true allocative price is the OCL
![Page 15: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/15.jpg)
Right-to-manage:
wwU
ww
VU
ww
L
KAw
wLLAKV
LwwU
VUw
001
1
)1(1
)1(
)(
max
1
1
![Page 16: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/16.jpg)
Comments
• Generalization of monopoly union model
• Generates suboptimal employment
• The rent now depends on the workers’ bargaining power in addition to the elasticity of labor demand
![Page 17: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/17.jpg)
Individual bargaining
• In collective models, the firms cannot hire workers competitively at the margin
• Nor can other firms in the same sector do so
• Under individual bargaining, the firm could drive the surplus of the match to zero by simply hiring more people
• Turnover costs are needed to create a positive surplus
![Page 18: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/18.jpg)
The dynamic insider/outsider model
• A representative firm can hire as much as it wants from the pool of unemployed
• Once hired, people negotiate their wage
• The firms incurs a cost F upon separation due to disagreement
![Page 19: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/19.jpg)
The plumbing:
))(1()(
))(1()()()(
)()()()()(
))(/()1()(
)())()()(()(
)())()(()()(
tuNtL
tustuthtu
tJtsJtwtmtrJ
tLKAtm
tVtVtVthwtrV
tVtVtVstwtrV
uueu
eeue
![Page 20: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/20.jpg)
Wage formation
FVVJ
FJVV
FJVV
FtJtVtV
ue
ue
ue
uetw
10
)(1
1 FOC
))()(ln()1())()(ln(max)(
![Page 21: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/21.jpg)
The hold-up problem:
• The intertemporal rent is fixed
• It goes up with the turnover cost
• It goes up with the worker’s bargaining power
• The turnover cost is a specific investment which can be appropriated by the incumbent worker
• F could equivalently be a hiring cost
![Page 22: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/22.jpg)
Deriving the steady state wage schedule
Fu
srbw
sh
su
bwFhsrVVhsr ue
1)(
1)())((
![Page 23: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/23.jpg)
Wage pressure goes up with
• Turnover costs
• Insider bargaining power
• Unemployment benefits
• Turnover
• Real interest rates
![Page 24: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/24.jpg)
The shirking model
• Employee effort e imperfectly observable (flow probability q)
• Penalty upon shirking limited to dismissal• In equilibrium, employees must be paid
rents• Otherwise, no penalty from dismissal: a
job is found instantaneously• Thus, unemployment duration acts as a
discipline device
![Page 25: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/25.jpg)
Same plumbing as the insider model
))(1()(
))(1()()()(
)()()()()(
))(/()1()(
)())()()(()(
)())()(()()(
tuNtL
tustuthtu
tJtsJtwtmtrJ
tLKAtm
tVtVtVthbtrV
tVtVtVsetwtrV
uueu
eeue
![Page 26: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/26.jpg)
Deterring shirking:
q
e
u
srbew
q
eVV
tVtV
tVtVtVqstwtrV
tVtVtVsetwtrV
ue
Se
SueS
eeue
)(
binding )()(
)())()()(()()(
)())()(()()(
![Page 27: Lecture II: Constructing a theory of equilibrium unemployment Microeconomic foundations of the wage curve](https://reader036.vdocuments.mx/reader036/viewer/2022070307/551a78495503463e778b6294/html5/thumbnails/27.jpg)
Comments:
• The model is equivalent to I-O model
• Just replace rent by e/q
• Rent now depends on effort levels and on the monitoring probability
• Effects of s and r are the same