Case Study Analysis Paper 2: A Tale of Two Coaches

Order Description

Write a 575 word paper that analyzes the two leadership case studies found in the topic materials for this module, “Coach Knight: A Will to Win” and “Coach K: A Matter of the Heart.”
Address the following questions and concepts:
1. Based on the models of Robert Katz and Michael D. Mumford and colleagues (see Week 1 and Week 2 assigned readings and lectures), which skills do you think accounted for the success of Coach K and Coach Knight? Which skills appear to be deficient?
2. Compare and contrast Coach K’s and Coach Knight’s leadership styles using Blake and Mouton’s leadership grid. How are they similar? How are they different? Are they both effective? Why or why not?
Prepare this assignment according to the APA guidelines found in the APA Style Guide. An abstract is not required.
Objectives:
1. Evaluate the strengths and weaknesses of the three-skills approach.
2. Explain the new skills-based model of organizational leadership.
3. Evaluate the strengths and weaknesses of the style approach to leadership.
4. Explain the leadership/managerial grid and the five major leadership styles.

Case Study Analysis Paper 2: A Tale of Two Coaches (Benchmark Assessment)

Details:
Write a 575 word paper that analyzes the two leadership case studies found in the topic materials for this module, “Coach Knight: A Will to Win” and “Coach K: A Matter of the Heart.”
Address the following questions and concepts:
1.    Based on the models of Robert Katz and Michael D. Mumford and colleagues (see Week 1 and Week 2 assigned readings and lectures), which skills do you think accounted for the success of Coach K and Coach Knight? Which skills appear to be deficient?
2.    Compare and contrast Coach K’s and Coach Knight’s leadership styles using Blake and Mouton’s leadership grid. How are they similar? How are they different? Are they both effective? Why or why not?
Prepare this assignment according to the APA guidelines found in the APA Style Guide. An abstract is not required.
Objectives:
1.    Evaluate the strengths and weaknesses of the three-skills approach.
2.    Explain the new skills-based model of organizational leadership.
3.    Evaluate the strengths and weaknesses of the style approach to leadership.
4.    Explain the leadership/managerial grid and the five major leadership styles.

This assignment uses a grading rubric. Instructors will be using the rubric to grade the assignment; therefore, students should review the rubric prior to beginning the assignment to become familiar with the assignment criteria and expectations for successful completion of the assignment.

Case Study Analysis Paper 2: A Tale of Two Coaches (Benchmark Assessment)
3
Satisfactory
79.00%    4
Good
87.00%    5
Excellent
100.00%
70.0 %
Content
30.0 %
Analyzes the leadership styles from the required leadership perspective.    Analyzes the leadership styles from the required leadership perspective.    Analyzes the leadership styles from the required leadership perspective. Provides specific evidence from the case to support analysis and address the required questions and concepts.    Analyzes the leadership styles from the required leadership perspective. Provides specific evidence from the case to support analysis and address the required questions and concepts. Demonstrates a high level of critical thought to analyzing the case by identifying details evident within the case which support the analysis.
40.0 %
Evaluates the leadership styles against the required leadership perspective.    Evaluates the leadership styles against the required leadership perspective.    Evaluates the leadership styles against the required leadership perspective. Supports evaluation by citing references which describe characteristics, actions, or outcomes attributable to effective leadership and evident within the case.    Evaluates the leadership styles against the required leadership perspective. Supports evaluation by citing references which describe characteristics, actions, or outcomes attributable to effective leadership and evident within the case. Evaluation is accurate, clear and concise.
20.0 %
Organization and Effectiveness
7.0 %
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8.0 %
Argument Logic and Construction    Argument is orderly, but may have a few inconsistencies. The argument presents minimal justification of claims. Argument logically, but not thoroughly, supports the purpose. Sources used are credible. Introduction and conclusion bracket the thesis.    Argument shows logical progressions. Techniques of argumentation are evident. There is a smooth progression of claims from introduction to conclusion. Most sources are authoritative.    Clear and convincing argument that presents a persuasive claim in a distinctive and compelling manner. All sources are authoritative.
5.0 %
Mechanics of Writing (includes spelling, punctuation, grammar, language use)    Writing is unclear and not concise. Spelling, punctuation, and/or grammar errors significantly distract from the purpose and organization of the paper. Language use is inappropriate for the academic setting.    Clarity and conciseness in writing could be improved. Spelling, punctuation, and/or grammar errors distract from purpose and organization of the paper. Language use could be improved for the academic setting.    Writing is clear and concise. Spelling, punctuation, and/or grammar errors are mostly error free. Language use is appropriate for the academic setting.
10.0 %
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5.0 %
Paper Format (Use of appropriate style for the major and assignment)    Appropriate template is used. Formatting is correct, although some minor errors may be present.    Appropriate template is fully used. There are virtually no errors in formatting style.    All format elements are correct.
5.0 %
Research Citations (In-text citations for paraphrasing and direct quotes, and reference page listing and formatting, as appropriate to assignment and style)    Reference page is included and lists sources used in the paper. Sources are appropriately documented, although some errors may be present.    Reference page is present and fully inclusive of all cited sources. Documentation is appropriate and citation style is usually correct.    In-text citations and a reference page are complete and correct. The documentation of cited sources is free of error.
100 %
Total Weightage

Sciences de Gestion, n° 65 p. 287 à 306
Leadership Styles and Organization: a Formal
Analysis
Jacques Thépot
Professor
Université Louis Pasteur, Strasbourg
Large (France)
In the management literature three types of leadership styles are
commonly considered: directive, transactional and transformational
leadership. This paper is aimed at exploring the analytical content of
this typology and then bridging the gap between management and
industrial organization on a crucial issue for the collective action.
Keywords: Leadership, organization, vertical relations.
Dans la littérature en management, trois types de styles de
leadership sont habituellement considérés : le leadership direct,
transactionnel et transformationnel. Cet article vise à explorer le
contenu analytique de cette typologie afin d’établir un lien entre le
management et l’organisation industrielle, sur un sujet important
pour l’action collective dans les organisations.
Mots-clés : Leadership, organisation, relations verticales.
En la literatura de management, habitualmente se consideran tres
tipos de estilos de liderazgo: le liderazgo directo, el transaccional y el
transformativo. Este artículo intenta explorar la organización
industrial sobre un tema importante para la acción colectiva en las
organizaciones.
Palabras claves: Liderazgo, organización, relaciones verticales.
288 Jacques THÉPOT
1. – Introduction
The leadership literature is overwhelming: the role of leaders
within the organization has been extensively analyzed by social
scientists of any field. Management scholars recognize that the
successful firms are those which can identify individuals with the
capabilities, the personal skills and the overall vision which make the
collective action effective. However, some mismatching of leaders is
often observed. There are many examples of organizations which are
provided with so called leaders who are not in tune with their rules
and objectives and are therefore a cause of mismanagement and poor
performances. There is not just one way to being the leader of an
organization. It is the leadership style which matters and can
contribute to the success of the organization in specific conditions of
environment and regulatory rules.
In the management literature three types of leadership styles are
commonly considered:
• The directive leadership
• The transactional leadership
• The transformational leadership.
This typology is commonly based on personality traits arguments.
This paper is aimed at showing that this typology can be justified even
in the pure rational decision making framework. It is postulated that
the organizational leader is a rational decision maker operating on two
different sides: on the behavioral side through actions of animation,
motivation, communication towards the members of the organization,
on the economic side through decisions on rewards, contracts and
punishments. According to the organizational context and the tradeoff
made by the leader between both types of actions, the leadership
will be of directive, transactional or transformational type.
The article is organized as follows: In section (2), the standard
leadership styles are presented. Modeling the behavioral and
economic side actions is made in section (3). In section (4), the resale
price maintenance problem is revisited: it is proved that it can be seen
as resulting either from a directive or a transactional manufacturer
leadership on the distribution channel. Avenues for further researches
are indicated in section (5).
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 289
2. – Leadership styles: from psychology to management
Leadership results evidently from personality factors, intelligence
and communications skills. Besides this trait approach, leadership
research has shifted from leadership behavior to leadership style
(Yulk, 2006). It is what the leaders do which matters and not only
their personal characteristics.
A general leadership is a behavior that gives purpose, meaning and
guidance to collectivities by articulating a collective vision that
appeals to ideological values, motives and self-perceptions of
followers” (House, 1995, p.413)
In other words a leader of group is a person
1. whose behavior can influence the behaviors of other members of
the group,
2. who is aware of it,
3. use this influence to achieve collective goals.
Let us present briefly the main features of the directive,
transactional and transformational leadership. Quotations are drawn
from Aronson (2001).
2.1. Directive leadership
Directive leadership is a mode of influence which is based upon
coercion and commandment. The leader knows what the follower has
to do and why. He does not take care of the preferences of the
followers. In practice, the job of the leader is to impose his view
and/or to convince the subordinates to act according to his decision.
There is no great feedback between the parties. Of course directive
leadership covers a broad range of attitudes, from autocratic… :
I’ll tell you what we are going to do because I’m the boss.
…to consensus seeking:
We’ll all meet and discuss it until everyone agrees on a
decision but the result is the same.
2.2. Transactional leadership
Transactional leadership is based upon participation and bargaining.
It involves an exchange between leader and subordinate such
that each receives something from the other in return for
something else.
290 Jacques THÉPOT
This mode of leadership does not intend to control the behavior of
the subordinates but to build contracts with them so as to align their
interests with those of the collectivity. Two manifestations of
transactional leadership can be identified in the literature (Bass, 1978):
• Contingent reward: the leader is able to establish agreements
with their followers on the tasks to be done and the rewards
attributed in case of successful completion.
• Management by exception when the control of the leader is
exerted only in case of significant divergence from planned
results.
In the same vein, Waldman et al. (2001) defines the transactional
leadership as follows:
A transactional leader is one who operates within an existing
system or culture (as opposed to trying to change them) : (1)
attempting to satisfy the current needs of followers by focusing on
exchanges and contingent reward behavior and (2) paying
attention to deviations, mistakes or irregularities and taking action
to maker corrections.
2.3. Transformational leadership
Transformational leadership gives emphasis on the charismatic
behavior of the leader who acts to stimulate changes in the
subordinates attitudes and values. The leader does not try to command
followers’ actions but he seeks to influence some of their
determinants. According to Conger (1999), the transformational leader
role encompasses the following elements:
(a) influencing followers by establishing a vision for a better
future, (b) inspiring followers as opposed to controlling them (c)
leading by example (d) contributing to subordinates’ intellectual
simulation, (e) enhancing meaningfulness of goals end behaviors
(f) fulfilling followers’ self actualization needs, (g) empowering
followers through intrinsic motivation, (h) exhibiting confidence in
subordinates’ ability to attain higher levels of achievement and (i)
enhancing collective identity,
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 291
3. – Modelling leadership styles
These three leadership styles can be represented in a dyadic
structure in which a leader faces an unique follower (cf. Farmer and
Aguinis, 2005). The previous analysis of leadership styles suggests
that a leader within an organization is a person who is able to
intervene on two different and in practice rather disconnected worldsof
the collective action, as represented on figure (1):
• On the behavioral side by appropriate actions designed to
enhance the motivation of the follower (meetings, seminars,
communication, etc…). These actions are encapsulated in a
behavioral action variable ? ? A
• On the economic side, the leader takes standard decisions of
management in terms of allocation of resources, monetary
transfers, contracts. These decisions are described by an
economic decision variable x ? X.
The pair [x, ?] stands for the action set of the leader. On the other
hand the behavior of the follower is represented by a variable b ? B,
which is, among other factors, determined by the behavioral action of
the leader, i.e.
b = b(?) (1)
I
In this context, the follower is a pure economic decision maker,
with a decision variable y ? Y (quantity, effort, acceptance of
contracts, etc..) and an utility function of the form v(x, y, b). The
utility function of the leader is u(x, y, ?) = w (x, y) -c(?),where c(.)
stands for the cost incurred by the behavioral action.
This general framework includes situations of constraining
leadership where the behavior b of the follower does not influence his
utility function, i.e. v = v(x, y) but determines the set of decisions he is
able to consider, i.e. Y = Y (b).
292 Jacques THÉPOT
This particular case resorts to our general formalism by defining a
new utility function v(x, y, b) = v(x, y)?(y, b) with :
At this stage of generality, nothing is said neither about the
information structure – who knows what in the organization? How
uncertain is the environment? -nor about the timing of decisions – who
plays the first ? -. These elements have to be specified in particular
situations. Le us examine now how the leadership styles can be
reshaped within this framework.
3.1. The directive leadership
For simplicity of exposure, we assume that all the variables take value
in <+, and that all the functions satisfy all the requested properties of
regularity and concavity. In this context, the directive leadership is
characterized by 4 elements:
?
? ?
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 293
• The leader is a pure behavioral actor; his action set is reduced
to [?]. He has a costless and effective control of the
follower’s behavior b, i.e. c = 0 and ?v/?b ? 0
• The leader utility coincides with the collective utility and
depends only on the follower decision ; namely
u = w(y) (3)
• The information is perfect.
• The leader is the first-mover decision-maker.
Let y? = arg maxyw(y), the socially optimal value of the follower
decision. and y(?) = arg maxyv(y, b(?)), the best decision of the
follower according to the behavioral action ?. For the leader, the
optimal behavioral action is ?? = arg max? w(y(?)), solution of
w?(y(?))y? (?) = 0. (4)
When y?(?) ? 0,i.e. ?u2/?b ? 0,relation (4) yields : (5)
y(??) = y?.
In words, thanks to a perfect and costless control on the behavior
of the follower, the leader pushes the follower to choose the right
decision. The decision of the follower is independent on his utility
function v.
3.1.1. Costly control
When the cost c(?) is taken into consideration since, equation (4)
becomes :
w?(y(?))y?(?) + c?(?) = 0, (6)
and the decision of the follower depends on his own utility function.
3.1.2 Uncertainty on behaviour
Let us assume that there is a noise affecting the relation between
the behavioral action i.e.
b = b(?, ?), (7)
294 Jacques THÉPOT
where ? is a random variable. The leader has an imperfect
knowledge on the impact of the behavioral action on the follower’s
behavior. Two cases may be distinguished
1. The follower does not observe the noise on his behavior
The sequence of decisions is ? ? y ? ?. The uncertainty is
revealed a posteriori. The risk-neutral follower best response is
namely ?(?) = argmaxy E [v(y, b(?, ?))] and the optimal ? is
solution of
w?(? (?)) ??(?) = 0. (8)
equivalent to relation (4). Hence ?(?) = y* and the follower’s
decision is still independent on his utility.
2. The follower observes the noise
The sequence of decisions is ? ? ? ? y. In this context, the best
response of the follower is the random variable y(?, ?) = argmaxy
v(y, b(?, ?)). Then the optimal behavioral action ? of the (risk
neutral) leader is solution of the equation:
In this case, the
follower’s strategy is the random variable y(?, ?) ? y?, which
generally depends on utility v.
3.1.3. Constraining leadership
Let us consider the particular situation where the functions v =
v(y), u = w(y) – c(?) are concave functions of their arguments. In
addition we assume that c? > 0. The behavior of the follower is
measured by the range of values in which he takes a decision, i.e. Y
(b) = [0, b] . For the sake of simplicity we assume that b = ?, so that
the leader has a direct control on the upper bound of the follower’
decision.
?
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 295
Proof. see Appendix 1. ?
y? represents the first-best solution, since the leader seeks here to
maximize the collective utility less the cost of control. y0 is the best
solution for the follower. Then the proposition states that the leader’s
power of restricting the feasible set of the follower can be used to
achieve the best choice for the leader; but this is not always the case.
It may occurs that the leader can only sustain the follower’s best
decision1.
3.2. The transactional leadership
The transactional leadership role is based on the following points
• The leader is a pure economic actor; his action set is reduced
to [x] .
• The leader’s utility may partly incorporate the collective
utility. There are mutual interdependencies between the
follower and the leader, so that both utility functions depend
on x and y :
v = v(y, x) (10)
u = w(x, y). (11)
• The information is imperfect or incomplete.
• The leader has a first mover advantage
Formally, a transactional leader is involved in a standard
Stackelberg leadership or in a principal-agent relationship when his
action takes the particular form of a contract. His action deals with
designing contracts in order to align the follower’s action to his own
objectives. In this category, all the literature on incentive and
contracting in Industrial Organization can be put. Let examine two
specific contributions coping explicitly with the leadership problem.
???????????????????????????????????????? ????????????????????????????????
1. This contrats with the directive case as the modified utility ˜v which endogenizes the
constraint has no derivative ?v/?b defined everywhere.
296 Jacques THÉPOT
3.2.1 The model of Rotemberg & Saloner
Rotemberg & Saloner (1993) consider a relationship between a
manager who proposes projects and a CEO in charge of implementing
them. The profit of an implemented project is a random variable G.
Let us reformulate the model by exhibiting the underlying extensive
form game, as represented on figure (2):
• At stage 1, the CEO chooses a remuneration level k on the
basis of effort or profit
• At stage 2, the manager exerts a non observable effort e ? {0,
1}
• • At stage 3 :
– if e = 0, no project is proposed by the manager and both the
manager and the CEO get 0,
– if e = 1,the value of G is realized.
• At stage 4, the CEO decides to implement the project (I = 1)
or not (I = 0).
?
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 297
The utility of the manager is E(k) – de, where d stands for the
disutility and E(k) for the expected remuneration. The payoff of the
CEO is differently evaluated at stage 1 and 3; Hence for the sake of
exposure, it is convenient to split up the CEO into two different
players of the game, CEOa and CEOb:
• At stage 1, the CEOa utility coincides with the shareholder
expected profit E(G) – k.
• At stage 3, the CEOb utility is a weighted sum of the profit
and the utilities of the managers I [(1 – t) (G – k) + tk], with
a parameter2 t ? [0, 1] measuring the degree of empathy of the
CEOb with the manager.
The manager is effectively paid only when the project is
implemented. These authors show that, in highly stochastic
environments, the firm is better off when the CEO adopts an empathic
style, as it is a proper way to reduce the moral hazard effects which
makes the manager less reluctant to exert effort as he knows that an
unprofitable project would be rejected. In this context who is the
leader?
1. The distinction between CEOa and CEOb is implicit in the
model. The argument given to justify that the CEO maximizes the
profit at stage1 and something else at stage 3 (except when t = 0) is
not quite convincing3 .
2. The interpretation of parameter t is somewhat misleading. It
measures a behavioral characteristic rather than a leadership style
in the sense used in the literature as presented above.
3. The actual leader of the organization is not CEOb but CEOa
who proposes a remuneration contract and has a first-mover
advantage; he is a typical transactional leader who maximizes the
profit of the whole organization. Formally CEOb is the follower of
(i) the manager and, (ii) indirectly of CEOa, although he is a key
actor within the organization.
???????????????????????????????????????? ????????????????????????????????
2. Parameter t is denoted ? in Rotemberg and Saloner’s paper. This change is made to
avoid confusion with the notations used in Hermalin’s paper considered below
3. ”The shareholders would choose a compensation level for the manager that is just
sufficient to elicit effort. Thus they would insist that the CEO set k = d, even though the
CEO would like to pay the manager more”, p. 1308. Why the manager will not continue
to maximize the profit in the same way at stage 3 ?
298 Jacques THÉPOT
3.2.2. The model of Hermalin
Version 1 (mechanism-design solution)
• At stage 1, the regulator proposes a contract {wn(., .)} ,where
wn(V, ?) is the wage paid to worker n when total value is V
and the announced value of ? is ˆ?,
• At stage 2, the leader announces the value ?,
• At stage 3, the workers exert efforts,
• At stage 4, the random variable ? is realized.
Hermalin proves that a linear optimal contract with equal share of
V can be found that induces truth-telling: the leader is better off when
revealing the true value of ?, at stage 2. The optimal contract includes
a sort of side-payment from the leader to the other workers that can
interpreted as the sacrifice paid by the leader to make his
announcement of ? credible.
Version 2 (leading by example)
• At stage 1, the regulator proposes a contract {wn(.)} ,where
wn(V ) is the wage paid to worker n when total value is V.
• At stage 2, the leader exerts effort, taking into account his
private information on ?.
• At stage 3, the other workers exert efforts.
• At stage 4, the random variable ? is realized.
Here, the leader does not announce ?; he expands effort before the
other workers who can observe this.
Hermalin exhibits a contract and a separating perfect Bayesian
equilibrium in which the workers mimic the leader’s effort, yielding a
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 299
better aggregate welfare than in the mechanism-design game. For d(e)
= e2/2, the equilibrium strategy of the leader ?(?) providing the
optimal contract is found.
Clearly, the regulator who is able to write a second-best efficient
contract (in version 1) or more (in version 2) is the transactional leader
of the organization. Un leader peut en cacher un autre…
3.3. The transformational leadership
The transformational leader acts upon the behaviors of other agents in
the organization. This is the more general framework which can be
considered. As we have seen, the directive leadership is a polar case of
transformational leadership based on coercion and allegiance. Besides
this, is not easy to elaborate an economic content to the notion of
behavior. Formalizing how the behaviors are affected by stimuli
triggered by others is a tricky task. However, the two above presented
models provide some fruitful examples of transformational leaders in
Organizations
1. The transformational leader acts upon behavior through
appropriate hiring decisions. Rotemberg and Saloner consider (p.
1310) that the shareholders can previously hire the right CEO : at
stage 0, they choose the best value of parameter t which
maximizes the profit of the firm, taking into account a hiring and
training cost C(t). In this context, the shareholders act as a
transformational leader.
2. The transformational leader benefit from private information.
The leader considered in Hermalin’s model can influence the
behaviors of the organization members through signaling. He is in
a transformational leader position with respect to the other workers
since he benefits from an informational advantage. He has a
”better vision of the future” (cf. above the quotation of Conger).
Regardless these specific situations, to what extent behavioral
actions differ from economic decisions (cf. figure 1) ? Let us elaborate
on this issue using the popularized concept of marketing mix. Clearly,
in the relationship between the marketer and the customer, the
marketer plays the role of the leader and the customer the role of
follower.
300 Jacques THÉPOT
The marketing mix is made of 4 elements (the four Ps !) : product,
price, place and promotion. As it is well known in the marketing
literature:
• Product stands for all decisions on product quality, design,
packaging, branding.
• Price stands for all decisions on discounts, allowances, credit
terms.
• Place stands for the various activities concerning channel
distribution, assortments, location, etc.
• Promotion stands for the various activities undertaken to
communicate and promote the product; this concerns
advertising, public relations, direct marketing.
Clearly, product, price and place activities resort to economic
decisions while promotion activities that aim at persuading the
customer to buy the product are behavioral actions. Hence, the
marketer is by essence a transformational leader on his targeted
market. He has no authority on the consumer since buying is a
voluntary activity. Advertising is a signaling activity where the
marketer wants to provide information on the product and to build
brand preferences. But the marketing mix strategy is the art of
combining and funding all theses 4 components in order to gain a
competitive advantage.
More generally, the marketing mix example suggests that the
behavioural actions, more than economic decisions:
• are long run actions whose effects are displayed over time. A
brand image cannot be created ex nihilo,
• are strongly affected by uncertainties ; the effectiveness of an
advertising program is not a deterministic function of the
advertising expenditures.
These elements are probably the key characteristics of the
behavioral actions in any transformational leadership organization.
This is an open issue for further investigations.
4. – Directive vs transactional leadership: an illustrative
example
Resale price maintenance (RPM) is a type of vertical restraints
involved in relationships between manufacturers and retailers.
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 301
It typically resorts to the directive leadership of the manufacturer,
in which the leader imposes some constraint on the decision of the
follower (cf. subsection 3.1.3); In the RPM case, the manufacturer
prevents the retailer to charge a price lower than some value.
A great deal of literature has been devoted to discussing the
implications in terms of efficiency of various vertical restraints (e.g.
Mathewson and Winter, 1983, Rey and Tirole, 1986). One of the
arguments in favor of RPM is that it avoids the double marginalization
externality which makes vertical integration socially more desirable
(Spengler, 1950). This result is somewhat puzzling as it tends to
justify a directive leadership that evidently hurts the free economy
principles !
We are going to prove that we could get the same Pareto
improving property in a transactional leadership framework: it turns
out that in a vertical relationship, maximum RPM can rationally be
accepted by the retailer and the manufacturer, if both parties are able
to design the ”good” contracts. Analytically, this amounts to say that
maximum RPM can be defined as the Nash condition of a contracting
game. In this case the leadership of the manufacturer becomes an
transactional leadership.
Let us consider a monopolistic manufacturer selling a product
through an unique retailer. The information is assumed to be perfect
so that no moral hazard problems are involved. The unit costs are
assumed to be constant (c for the manufacturer, ?, for the retailer). The
manufacturer sells at wholesale price s and the retailer resells at price
p to the consumers. The global demand function is given by q =
D(p),with D? < 0 and D” ? 0. The manufacturer and retailer profits are
respectively P (s, p) = (s-c)D(p), R(s, p) = (p-s-?)D(p).
4.1. Doublemarginalization andmaximumresale-pricemaintenance
The double marginalization price-fixing arises from the Nash
conditions of the two-stage game where the manufacturer and the
retailer successively decide prices s and p. It then results in prices p*,
s* solutions of the following program:
?
?
?
302 Jacques THÉPOT
Let P? and R? be the profits of the manufacturer and the retailer
.The joint profit maximization (vertical integration) situation does not
depend on wholesale price s ; it deals with a retail price p? = argmax
(p – c – ?)D(p) and a quantity sold, qm = D(pm). Under the standard
assumptions made on the demand function, price pm is determined by
(pm – c – ?)D?(pm) + D(pm) = 0. (13)
As it is well known, pm ? p?, (pm – c – ?)qm ? P? + R? and S(pm) ?
S(p?). Consequently the double marginalization is associated with a
loss of efficiency for the firms and the consumer; it can be
implemented through a vertical restraint imposing to the retailer a
maximum retail price equal to pm and a wholesale price sm taking any
value of interval [c, pm – ?] , so that the sum of the profits of the firms
is (pm – c – ?) qm. The question is to know how this resale-price
maintenance constraint can be written in a contract.
4.2. A contract to sustain maximum resale-price maintenance
We will prove that the maximum resale-price maintenance can be
derived as a Nash equilibrium condition of two types of games
between the manufacturer and the retailer where both parties are
?
LEADERSHIP STYLES AND ORGANIZATION: A FORMAL ANALYSIS 303
ensured to get higher profits than those given in the double
marginalization. Let us define the two following multi stage game as
follows (cf. 3):
• Stage 1: The manufacturer proposes a contract (s, p) .
• Stage 2: The retailer accepts or refuses.
• Stage 3: (i) In case of acceptance, contract (s, p) is enforced.
(ii) in case of refusal, the firms are involved in the double
marginalization two-stage game, resulting in prices (s*, p*)
and profits P* and R*, as computed above.
The (subgame perfect) Nash contract (sM, pM ) is solution of
program PM
where (p – s – ?)D(p)
? R? stands for the participation constraint.
Proposition 2 The solutions of program PM is given by the following
conditions
:
1. pP = pm,
2. (pm – sP – ?)D(pm) = R? with (sP – c)D(pm) ? P?,
Proof. The Lagrangian of problem PM is
L = (s – c)D(p)+ ? [(p – s – ?)D(p) – R?] . First order conditions
(which are also sufficient because of the concavity of the profit
functions) are :
(s – c)D?(p) + ? [(p – s – ?)D?(p) + D(p)] = 0 (14)
D(p) (1 – ?) = 0
? [(p – s – ?)D(p) – R?] = 0.
It follows ? = 1, (p – c – ?)D?(p)+D(p) = 0, (p – s – ?)D(p) = R?.
Hence the result; note that (s?, p?) belongs to the feasible sets of PM. ? .
?
304 Jacques THÉPOT
Then condition 1 of proposition (4.2) means that the RPM
constraint can be written in a contract acceptable by both parties as it
expresses a Nash equilibrium condition. It yields the second-best
solution of the distribution channel, i.e. the solution given by the
vertical integration of the manufacturer and the retailer. To
summarize, better contracting than constraining. The manufacturer
may act as a contractual leader for the sake of the distribution channel
welfare.
5. – Concluding remarks
This paper was aimed at discussing the analytical content of the
leadership notion and its relation to the organization type. Of course
this formal approach does not exhaust the subject and two general
questions would deserve attention (i) What is the right leader of the
right organization ? i.e. is there a one-to-one relationship between the
leadership style and the network of contracts defining the
organization? (ii) Why various leadeship syles may coincide in the
same organization, perhaps at different levels and how do they
articulate together? these questions are crucial for driving the
organizations and a formal approach may explain some stylized facts
on leadership leading to more accurate recommendations in human
resource management.
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Appendix 1: The constraining leadership: proof of proposition (1)
Then the optimization program of the follower is
First-order conditions are:
v?(y) = ?, ? ? 0, (b – y) ? 0, ? (b – y)) = 0 (16)
Relations (16) can be considered as the constraints of the program of
the leader4 , which can be written as:
The
Lagrangia
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4. This technique is used in Thépot (1995).
? ?
?
?
306 Jacques THÉPOT
n of program (17) is L = w – c+?(v? – ?)+??+??(b – y)+ ?(b – y).
Thefirst order conditions are:
Two cases have to be considered (i) ? > 0, then b = y and ? = 0.
Hence ? = 0, and (18i) yields w?(y) – c?(y) = 0, namely, y = y*. This is
the optimum if ? = u?(y*) > 0. Because of the concavity of u, this is
true if y* < y?.(ii).? = 0,then v?(y) = 0 and y = y0. It results from (18iii)
that ? = c? > 0, then b = y0, ? = ? ? 0. This is the optimum when
w?(y0)-c?(y0) = -?v”(y0) ? 0,i.e. when y* ? y0. This completes the
proof.
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