Transcript Document

Samuel Bowles
Santa Fe Institute
University of Siena
Diego Rivera, The Ford Plant River Rouge
Labor, Employment
And Wages
Employment: what is the principal agent problem?
• e 0 [0,1] = effort per hour of work (e.g. % of time “on”)
• Per period output is:
y = y(he) + µ , with y'>0 and y" <0;
where h is the number of worker "hours" hired
µ is a mean zero disturbance term.
• the employer selects
i) termination probability t(e,m)0[0,1] (te<0 and tm>0
ii) a wage rate, w, and
iii) monitoring expenditure per hour of labor hired, m
• the worker selects e to max his present value of utility
• the worker is paid, and is renewed or terminated, the
latter occurring with probability t(e,m).
The Worker’s Best Response
• Per period utility (experienced at the end of the period)
u = u(w,e)
• Fallback asset Z: what is it?
• Present value of the job (game is stationary):
V = {u(w,e)+(1-t(e,m))V+t(e,m)Z}'(1+i)
V = {u(w,e)-iZ}'(i+t(e,m) + Z
• The worker selects e so as to set Ve = 0
• which requires: ue = te(V-Z)
• Interpretation of the foc?
• Given that P knows A’s brf, he also knows the resulting
e. Why then is there a P-A problem?
The Worker’s Fallback Position
• At the end of each period there is a probability λ that the
unemployed worker will find work, exiting the
unemployment pool, so the expected duration of
unemployment is 1/λ.
• Thus
Z = {u(b,0)+λV+(1-λ)Z}'(1+i) = {u(b,0)+λV'(i +λ)
Employee’s best response function: ue = te(V-Z)
• slope of iso-v?
• {e , w}?
v=z
Effort
e(w,m; z)
v = v*
e
w
Wage
Profit Maximizing
• π = y(he(w,m;Z)) - (w+m)h
• πh = y'e - (w+m) = 0
• πw = y'hew - h = 0
• πm = y'hem - h = 0
• which requires that
w*+m*
ew = e/(w+m) = em
y'= (w+m)/e
• Meaning of the second foc?
y'e*
h*
Employment hours, h
The Solow condition: ew = e/(w+m) = em
• What does it mean?
• Show that a
Effort
Walrasian
equilibrium is a
special case of this
e*
model.
• What does it require
of the nature of work
e
and the scarcity of
-m*
goods?
e(w,m; z)
a
v = v*
w
w*
Wage
Comparative Statics
• Let (w+m)/e / μ
the cost of a unit
effort
• dμ/dZ > 0; and
dπ/dZ < 0
• What is the
economic meaning
of these results?
Effort
e(w,m; z)
e*
a
e
-m*
w
w*
Wage
General Equilibrium
• The zero profit condition π - δ = 0
• λ varies with the level of aggregate
employment (nh=H), so
• λ = λ(H, ...) with λ’> 0
• Z = Z(H, ..) with Z’ > 0
• Recall that (w+m)/e / μ the cost of a unit
effort and dμ/dZ > 0 and dπ/dZ < 0
• Because these relationships are all
monotonic, there is a unique μ0 and hence a
unique Z0 and H0 that satisfies the zpc.
• Thus the level of unemployment,
employment, number of firms are
determined. Why is H<1?
• No reference to aggregate demand?
H*


Total hours, nh = H
e*, w*is Pareto-inefficient. Why? How to show this?
Effort
b
e(w,m; z)
e*
a
•
Ve = 0 but πe > 0 and
e
Vw > 0 but πw = 0;
-m*
• thus there exists some (arbitrarily
small) values (Δe,Δw) such that
V(e*+Δe,w*+Δw)>V(e*,w*) and
π(e*+Δe,w*+Δw,...)>π(e*,w*) 
• Where is the efficient contract
locus in the figure?
v = v*
w
w*
Wage
Why is w*, m* technically inefficient?
w
w*+w
w*
e = e*
isocost
m*-m m*
In what sense is m unproductive labor?
m
Pareto sub-optimal workplace amenities
• Suppose the employee's utility function is expanded to
include a measure of work amenities provided (per hour of
work), τ
u=(w,τ,e)
with uτ > 0 over the relevant range, and that amenities cost
pτ for the employer to provide.
• a new present value V(e,w,τ)
• a new best response function e(w,m,τ;z)
• an additional first order condition for the employer
πτ = y'eτ - pτ = 0
• Q: Why will τ* be P-suboptimal?
• A: for the same reason that the wage suboptimal: more
amenities and more effort are a pareto improvement
Can trade union bargaining implement a P-improvement over w*,e*?
(e,w)
Effort
Efficient contract locus
• (e+,w*), u(e+,w*)
b
• (e+,w+), u(e+,w+)
e(w,m; z)
e*
a
(e*,w*)
•
b
a
v = v*
•(e(w+), u(e*,w+)
e
-m*
w
w*
Wage
u(e*,w*)
u(e,w)
The Employer’s and Union’s Bargaining Problem: Per Period Payoffs (right figure)
Note the bargaining set is the area bounded by the payoffs in the non cooperative interaction and
the efficient contract locus. If the strategies available were unconditional w+ and w* for the
employer and e+ and e* for the employee, the game is a prisoners dilemma. Point a is the
equilibrium of the uncooperative game (indicated by point a in the left figure) while point b is a
point on the efficient contract locus (indicated by point b in figure 1).
Given that job rents are huge, firms could sell jobs. What
problem would the firm solve to calculate the optimal fee?
• Let B = a one time job fee.
• The employer varies h, w, and B to maximize
π = y(he(w)) -hw + iBh
subject to V(e(w), w-iB) $ Z
where i is the rate of return and V(.) is the ex ante
present value of the job with fee B.
• w-iB is the net wage taking account of the opportunity
cost to the employee of foregoing returns iB on the
employee’s wealth.
V(e,w)=Z
Effort
e*
a
e(w,m;z)
• Results:
e
• P-efficient?
-m
w*
w w*-iB*
Wage
• Labor market
Optimal job fees. The employer
clearing?
identifies point a as the solution of
• P has power over A?
max e/(m+w-iB), the effort elicited
from the employee per unit cost.
The employer then offers w* (the
employee responds with e*) with a
fee of B*.
Why do firms not sell jobs (charge an optimal fee)?
Some possible answers
• Firm’s search costs are reduced by job rationing
• Morale, reciprocity reasons
• Perhaps they do (by very low initial wages, etc)
Macroeconomic applications
• w*(h): the labor
market equilibrium
(workers and firms
foc with respect to
labor discipline); h is
total employment
• h*(w): the locus of
{w,h} s.t. excess
demand for goods =
i+b–s =0
• Upward shift in
w*(h) increases h*;
saving depends
Bowles, Samuel and Robert Boyer. 1988. "Labor Discipline
strongly on profit
and Aggregate Demand: A Macroeconomic Model." American
Economic Review, 78:2, pp. 395-400.
share
Two ways of closing the model: zpc or aggregate demand
• h* (w) could be the h for a given w that satisfies zpc
(necessarily downwards sloping) or
• …the level of employment that clears the product market.


H*
Total hours, nh = H
Evidence
• Labor effort appears to be quite variable and is rarely
subject to contract (Laffont, Lazear, Rosenzweig et al)
• Employers devote substantial personnel (Gordon) and other
resources (Baker) to monitoring their employees’ effort.
• Substantial employment rents in most jobs ( primary
/secondary labor market distinction) (Weisskopf and Green)
• Real wages tend to vary with the level of employment
(Blanchflower and Oswald, Bowles, BER)
• Econometric evidence on effort (Schor), labor productivity
(BGW), and profits (BGW) (high employment profit
squeeze)
• Experimental evidence (Fehr et al)
• Footnote: how BGW came to do this work.
Presentations of discussion questions (with .ppt or
handouts)
• Apartheid as labor discipline (22.3)
• The distribution of gains from freer North South trade
(22.2)
• An employment subsidy with endogenous effort (23)
• An incentive compatible BIG (unconditional basic income
grant) (24)
• Husbands and wives/Principals and agents (29)
A more extensive review of the evidence, if you’d like
Next : credit and wealth, read chapter 9.
Additional readings
• Bowles, Samuel, Herbert Gintis, and Melissa Osborne.
2001. "Incentive-Enhancing Preferences." American
Economic Review, 91:2, pp. 155-58
• Heckman, James and Yona Rubinstein. 2001. "The
importance of non-cognitive skills: lessons from the GED
testing progam." American Economic Review, 91:2, pp.
145-49
• Bowles, Samuel, Herbert Gintis, and Melissa Osborne.
2001. "The Determinants of Earnings: A Behavioral
Approach." Journal of Economic Literature,
XXXIX(December), pp. 1137-76.
• After NAFTA. A country (South) with a large traditional grain
growing sector protected by tariffs and subsidies shares a border with
a country (North) with ideal grain growing conditions and a highly
productive agricultural sector. The reservation position for wage
workers in the South is to return to working on their family's farm in
the traditional agricultural sector. An international trade economist
proposes a free trade area for the two countries, removing tariffs and
subsidies, showing that substantial gains from trade will result for
both countries, and claiming that employees in the South will enjoy
higher (real) wages as a result. A worker asks you if the claim is
correct. The trade economist is certainly right about the gains from
trade; but what about the wage increases? Show that i) using the no
shirking condition as the model of wage determination, the trade
economist is wrong and ii) assuming that wages and effort are
determined by a Nash bargain between employees and employers he
could be right, but need not be.
• The apartheid system in South Africa gave non-white
workers restricted access to the labor market of the modern
sector of the economy. According to the infamous pass laws,
those working in the urban areas required a pass, which was
revoked if their job was terminated, and they were required
to return to close to subsistence living in one of the socalled bantustans. South African scholars have debated
whether this system lowered profits (by restricting the
supply of labor) or raised profits (by providing businesses
with a favorable labor discipline environment). Use the
labor discipline model (the no shirking condition, or the
more general model in the text) to develop the latter
argument. What additional information would you need to
determine which position is more nearly correct?
• A wage subsidy. Employment subsidies are a widely discussed
means of increasing employment in labor surplus economies, or
among less skilled workers in the advanced countries. Suppose that n
identical firms each hire h hours of identical labor, varying both h
and w, the hourly wage, to maximize profits, which depend on total
labor effor which is the product of hours hired and effort per hour, e.
Consider two types of subsidy paid to owners of each firm: i) an
employment subsidy: the subsidy s is a fixed amount, paid per hour
of labor hired, or ii) a wage subsidy, F, the subsidy is a fixed
fraction of the wages paid. You may assume that the taxes supporting
this subsidy have no effects on this problem. Using the zero subsidy
case as a benchmark, indicate the effects of the two types of subsidy
on the equilibrium wage, effort, and employment levels, assuming a)
that z, the fallback position of each worker, is exogenous, and b) that
z varies with the level of total employment, nh
• The BIG idea. (§8) Assume all employed work for an hour. A linear tax (meaning
with a flat rate, J) is levied on every employed worker, the proceeds being
distributed unconditionally to all members of the population (for simplicity, assume
that half of those in the population are employed, a quarter are unemployed and a
quarter are not in the labor force). Because profits are not taxed and because all
workers (including those not working) are identical, we assume this proposal has no
effect on the demand for labor so the expected duration of a spell of unemployment
is unaffected. You may also abstract from any changes in labor supply. Assume that
the implementation of the BIG is accompanied by the elimination of unemployment
insurance (define this as b), the replacement income a worker receives if
unemployed) and that the net effect of the tax, the BIG, and the elimination of
unemployment insurance on the government budget is zero. If the employment
relationship is governed by the contingent renewal model in the text, with w=w*,
e=e* with b = w*/2 what is the maximum tax that can be levied without reducing the
equilibrium level of effort and what is the resulting per person grant? Check to see
that a family composed of two employed workers, one unemployed person and one
out of the labor force, experiences no change in income or total effort provided,
while those with relatively more non-employed members gain.
• Domestic labor. (§10) Consider the determination of
domestic work and the sharing of income by a husband and
wife (the amount of domestic work done is not costlessly
observable by the other adult, as much of it is bestowed on
the children, and the results of this are only evident in the
very long run). Consider only the two adults, one of whom
works for pay and other works in their home. Extend the
model in chapter 8 to determine the share of the paid
worker's income received by the home worker (w) and the
amount of domestic work done (e). Contrast this “domestic
labor discipline” model with a transactions cost approach to
this problem. What are the relevant transaction specific
investments? What are the similarities and key differences?