Listed below are the instructions, question, and tables. The tables must be translated in your findings. Bible perspectives must be included, Marginal Productivity Theory for theoretical review,and articles that are attached as well as others must be included.
This is due: 10am on Thursday June 23, 2022 (Eastern Time Zone). NO LATE WORK!!
PLEASE READ ALL ATTACHED MATERIAL BELOW!
Criminal Justice
ATTACHED FILE(S)
Criteria Ratings Points
Understanding
of Quantitative
Research
Methods&
Data Analysis
20 to >18.0 pts
Advanced
Shows a deep
understanding of
quantitative research
methods and data
analysis in criminal
justice.
18 to >16.0 pts
Proficient
Shows a basic
understanding of the
role of quantitative
research methods and
data analysis in
criminal justice.
16 to >0.0 pts
Developing
Shows a poor understanding
in quantitative research
methods and data analysis in
criminal justice.
0 pts
Not
Present
20 pts
Research
Design,
Research
Questions, &
Hypotheses
20 to >18.0 pts
Advanced
The research design,
hypotheses, and
research questions are
appropriately named and
tested.
18 to >16.0 pts
Proficient
The research design,
hypotheses, and
research questions are
mostly named and
tested.
16 to >0.0 pts
Developing
The research design,
hypotheses, and research
questions are not named and
incorrectly tested.
0 pts
Not
Present
20 pts
Use of the
Selected
Analytical
Method
20 to >18.0 pts
Advanced
Appropriate and accurate
selection and use of
analytic methods.
18 to >16.0 pts
Proficient
Mostly appropriate and
accurate selection and
use of analytic
methods.
16 to >0.0 pts
Developing
Somewhat appropriate
and/or somewhat accurate
selection and use of analytic
methods.
0 pts
Not
Present
20 pts
Interpretation
of the Results
30 to >27.0 pts
Advanced
Appropriate and
comprehensive
explanation of the results
obtained from the
quantitative analysis in
the context of the original
problem.
27 to >25.0 pts
Proficient
Mostly appropriate
explanation of the
results obtained from
the quantitative
analysis in the context
of the original problem.
25 to >0.0 pts
Developing
Somewhat appropriate
explanation of the results
obtained from the
quantitative analysis.
Explanation of the context is
somewhat incorrect or
incomplete.
0 pts
Not
Present
30 pts
Use of IBM
SPSS®
20 to >18.0 pts
Advanced
Excellent use and
application of SPSS.
18 to >16.0 pts
Proficient
Good use and
application of SPSS.
16 to >0.0 pts
Developing
Fair to poor use and
application of SPSS.
0 pts
Not
Present
20 pts
Quantitative Analysis Report Grading Rubric | CJUS745_B01_202230
Criteria Ratings Points
Use of
Sources from
Course
15 to >13.0 pts
Advanced
Use of all relevant
sources from the Learn
material.
13 to >11.0 pts
Proficient
Use of most relevant
sources from the
Learn material.
11 to >0.0 pts
Developing
Use of some relevant
sources from the Learn
material.
0 pts
Not
Present
15 pts
Grammar,
Writing, & APA
15 to >13.0 pts
Advanced
Proper grammar, writing,
and current APA format
13 to >11.0 pts
Proficient
A few grammar,
writing, and APA
errors.
11 to >0.0 pts
Developing
Numerous grammar, writing,
and APA errors.
0 pts
Not
Present
15 pts
Page Length 15 to >13.0 pts
Advanced
4-5 double-spaced pages
of content in length (not
counting the title page or
references).
13 to >11.0 pts
Proficient
1 page more or less
than the required
length range (not
counting the title page
or references);
double-spaced.
11 to >0.0 pts
Developing
More than 1 page more or
less than the required length
range (not counting the title
page or references);
double-spaced.
0 pts
Not
Present
15 pts
Total Points: 155
Quantitative Analysis Report Grading Rubric | CJUS745_B01_202230
American Review of Public Administration
2016, Vol. 46(4) 399 –417
© The Author(s) 2014
Reprints and permissions:
sagepub.com/journalsPermissions.nav
DOI: 10.1177/0275074014555645
arp.sagepub.com
Article
Understanding Multiplexity
of Collaborative Emergency
Management Networks
Naim Kapucu1 and Qian Hu1
Abstract
This article explores the multiplex relationships among organizations within the context of
emergency management. It examines the role of friendship networks and disaster preparedness
networks in predicting sustainable collaborative disaster response networks. Furthermore, it
examines the impact of emergency management systems on network building and sustainability.
This article applies inferential network analysis methods in analyzing relationships among
emergency management networks and examines the predictive power of preestablished
network arrangements. This research suggests that friendship networks are important for
encouraging organizations to be involved in disaster preparedness networks. Yet it is the
collaboration ties during disaster preparedness that influence the formation of collaborations
during disaster response. Structural attributes of emergency management systems have impacts
on the development of multiplex relationships among organizations within various networks.
These findings not only contribute to developing sustainable emergency management networks
but also provide insights for building collaborative networks in a broader context.
Keywords
networks, multiplexity, friendship networks, emergency management networks
Introduction
Intergovernmental collaborations among government agencies and cross-sector collaborations
among public, private, and nonprofit organizations are not new. Yet, the scope and depth of cross-
sector collaborations in public policy and management during the past few decades is unprece-
dented (McGuire, 2006). Government agencies collaborate with other government organizations
at different levels as well as with nonprofit organizations and businesses to provide public ser-
vices (Milward, Provan, Fish, Isett, & Huang, 2010; O’Toole, 1997), promote economic develop-
ment (Agranoff & McGuire, 2003; Lee, Feiock, & Lee, 2011), and manage disasters and crises
(Comfort, Waugh, & Cigler, 2012; Kapucu, 2006a).
Intergovernmental and cross-sector collaboration have become common disaster response and
recovery practices due to the need for sharing resources and coordinating efforts (Kapucu &
Ozerdem, 2013; McGuire, Brudney, & Gazley, 2010). Local governments work closely with
1University of Central Florida, Orlando, USA
Corresponding Author:
Naim Kapucu, School of Public Administration, University of Central Florida, HPA II Suite 238M, Orlando, FL 32816,
USA.
Email: kapucu@ucf.edu
555645ARPXXX10.1177/0275074014555645The American Review of Public AdministrationKapucu and Hu
research-article2014
mailto:kapucu@ucf.edu
http://crossmark.crossref.org/dialog/?doi=10.1177%2F0275074014555645&domain=pdf&date_stamp=2014-10-23
400 American Review of Public Administration 46(4)
federal and state governments to coordinate efforts to meet disaster preparedness goals.
Furthermore, representatives of public, nonprofit, and private organizations form formal and
informal networks during disaster preparedness, response, and recovery. Recent research sug-
gests that building collaborative networks has been crucial for the effectiveness of emergency
management (Comfort et al., 2012; Waugh & Streib, 2006). Through building and sustaining
functional interorganizational networks, emergency management organizations can not only
share information, financial resources, and human capital but also effectively coordinate their
efforts in response to disasters and subsequent recovery (Kapucu & Garayev, 2012).
It takes time and a great amount of effort and resources to form and build emergency manage-
ment networks. Furthermore, to ensure an effective emergency management network, it is impor-
tant to foster trust, sustain relationships, and build collaborations before and after disasters
(Kapucu & Garayev, 2012). Most existing research on emergency management networks focuses
on analyzing key actors, interactions among organizations, and the network structures within a
single type of emergency management network (e.g., Choi & Brower, 2006; Choi & Kim, 2007).
Relatively fewer studies have examined the multiplex relationships between organizations within
various emergency management networks and the evolution of networks (Kapucu, 2009), let
alone the dynamic development of emergency management networks (Robinson, Eller, Gall, &
Gerber, 2013). In addition, research that examines emergency management networks at the
advanced analytical level remains limited.
This article explores the multiplex relationships among organizations from different sectors
within the context of emergency management. It also examines the role of friendship networks
and disaster preparedness networks in predicting sustainable collaborative disaster response net-
works. Furthermore, it examines the impact of emergency management systems on network
building and sustainability. As part of a federally funded project, this research focuses on the
emergency management networks within two metropolitan counties in a southeastern state that
is prone to hurricanes and other natural disasters. This article addresses the following research
questions:
Research Question 1: What is the relationship between friendship networks and collabora-
tion networks during disaster preparedness?
Research Question 2: Can disaster response networks be predicted based on preestablished
friendship networks and disaster preparedness networks?
Research Question 3: Do structural characteristics of emergency management systems affect
the relationships among friendship networks, preparedness networks, and response
networks?
After reviewing relevant literature and proposing the theoretical framework, the article first
examines the structural characteristics of three types of emergency management networks: (a)
friendship networks, (b) preparedness networks, and (c) response networks. Next, it studies the
correlations among different types of networks through inferential network analysis. Furthermore,
it examines the impact of emergency management systems on network building and
sustainability.
Collaborative Emergency Management Networks
Public organizational networks can be defined as “a group of three or more organizations con-
nected in ways that facilitate achievement of a common goal” (Provan, Fish, & Sydow, 2007, p.
482). Interorganizational networks can help organizations better address issues that one single
organization cannot resolve (Provan & Milward, 2001). Although the traditional command and
control approach remains important in emergency management, the collaborative approach is
Kapucu and Hu 401
crucial to current emergency management practices (Comfort et al., 2012; Kapucu, 2009, 2012).
Collaborative networks are fundamental to emergency management as community organizations,
nonprofit, and private organizations play significant roles in response to and recovery from disas-
ters (Kapucu, 2006b; Waugh, 2003; Waugh & Streib, 2006). Networks of emergency manage-
ment organizations have been built and sustained to better utilize resources and coordinate efforts
to prepare for and respond to disasters.
Researchers have examined the key actors and the structural characteristics of emergency
management networks (e.g., Choi & Brower, 2006; Choi & Kim, 2007; Kapucu, 2006a; Kapucu
& Demiroz, 2011; McGuire & Silvia, 2010; Robinson et al., 2013). Many of these studies focus
on analyzing the formal interorganizational networks that are defined by the emergency manage-
ment plans, or they compare the planned networks with actual networks. For instance, Choi and
Brower (2006) and Kapucu and Demiroz (2011) conducted social network analysis to examine
the structural differences between the actual response networks and the planned networks. Few
studies have examined the informal networks and the multiplexity of interorganizational interac-
tions (Isett, Mergel, LeRoux, & Mischen, 2011; Robinson, 2006), which is focus of this research.
Multiplexity of Networks
Various components of organizations, such as people, knowledge, resources, and tasks, along
with organizations, interact with one another and form different types of networks, such as social
networks, knowledge networks, resource networks, and interorganizational networks (Carley,
2012). Organizations may build multiple types of connections with other organizations. Thus,
interorganizational networks can be further categorized into different types. Multiplex ties refer
to the multiple types of interactions among organizations (Borgatti, Everett, & Johnson, 2013).
Multiplexity indicates a higher level of tie strength between organizations, and multiplex ties
show organizations’ commitments to multiple collaborative activities (Provan & Milward, 2001).
Furthermore, broader levels of involvement with diverse activities allow organizations to
exchange information and coordinate efforts relatively easily, which may contribute to long-term
network development and evolution.
There are four phases of emergency management: mitigation, preparedness, response, and
recovery. Various emergency management networks are formed to share information, plan for
emergency scenarios, and coordinate response and recovery efforts during and after an emer-
gency (Kapucu & Ozerdem, 2013). The number of organizations involved in each phase can
change, and the type of interorganizational interactions can vary in different phases of emergency
management. Therefore, it is necessary to further analyze various types of interactions among
organizations. This research examines three types of emergency management networks: friend-
ship networks, disaster preparedness networks, and disaster response networks.
Within friendship networks, organizational representatives know other public, nonprofit, and
private organizations working in the field of emergency management. Friendship networks do
not involve formal collaboration actions: They are informal networks. Krackhardt and Hanson
(1993) noted that informal networks may differ significantly from the formal organizational
chart. Managers need to understand the patterns of informal networks to leverage untapped
resources and expertise, and to make sure the informal networks are aligned with organizational
goals (Krackhardt & Hanson, 1993). Similarly, Cross and Parker (2004) suggested that managers
need to understand informal structures and take advantage of the “hidden power of networks” (p.
3). Informal networks, including friendship networks, although not defined by any formal con-
tracts or agreements, may serve as important venues for organizations to share information, solve
problems, and build capacity. Informal networks can play crucial roles in fostering the develop-
ment of long-term formal networks. Moreover, informal networks tend to formalize in the long
run, which may encourage the organizations within the informal networks to secure and share
resources (Isett et al., 2011).
402 American Review of Public Administration 46(4)
Social capital plays an important role in building and sustaining collaborative networks.
Social capital was introduced to study interorganizational relationships and its impact on organi-
zational structure, coordination, and network performance (Burt, 1997; Furst, Schuber, Rudoph,
& Spieckermann, 2001; Lin, 1999; Provan & Lemaire, 2012). The effectiveness of interorgani-
zational networks is contingent upon the levels of trust, commitment, and social capital that exist
among interacting organizations (Agranoff, 2007; Ansell & Gash, 2008; Bryson, Crosby, &
Stone, 2006; Thomson & Perry, 2006). Scholars suggest that the existence of social capital can
help reduce transaction costs, enhance trust and commitment, and encourage cooperative behav-
ior in collective actions (Agranoff, 2007; Provan & Lemaire, 2012). Many studies have high-
lighted the importance of social capital and preestablished relationships in emergency management
networks (Jaeger et al., 2007; Kapucu, 2006a; Kapucu, Hawkins, & Rivera, 2013; Kendra &
Wachtendorf, 2003). Kapucu (2006b), in his study on public–nonprofit partnerships in emer-
gency planning and response, noted that social capital is “a resource that is inherent in the rela-
tions among actors in a variety of locations and sectors” (p. 209). He further noted that regular
working relationships would enable communities to function well when faced with disaster sce-
narios, as trust can be built between public and nonprofit organizations prior to disasters. Kapucu
and Garayev (2012) proposed that network relationships are important for the sustainability of
functionally collaborative emergency management networks. They argued that organizations are
more likely to sustain their collaborative relationships with other organizations when these orga-
nizations are interdependent and rely on each other for sharing information or resources.
This article identifies friendship ties and collaboration ties in disaster preparedness efforts as
indicators of social capital. Representatives of emergency management organizations were asked
to identify others as a friend in emergency management networks. The concept of social capital
can manifest in emergency management networks in two ways: First, it is assumed that a certain
level of social capital exists if the organizational representatives have friendship ties with others
in emergency management networks. Second, collaborative ties in disaster preparedness net-
works, which play out in the emergency response stage, can indicate the existence of social capi-
tal. Thus, we propose the first set of hypotheses as follows:
Hypothesis 1: Friendship ties among emergency management organizations positively cor-
relate with formal collaboration ties during disaster preparedness.
Hypothesis 2: Friendship ties among emergency management organizations positively cor-
relate with formal collaboration ties in disaster response.
Different from friendship networks, disaster preparedness networks and emergency response
networks often involve more formal collaborations among organizations during disaster pre-
paredness and response. Multiple ties may make it more likely to build common goals through
multiple levels of participation within the organizational network (Provan & Lemaire, 2012).
These multiplex relationships are usually developed at the preparedness stage, where different
agencies are involved in common emergency drills, exercises, and trainings. Relationships are
also strengthened and developed during actual disasters where agencies can discover new part-
ners when working toward common goals (Kapucu & Garayev, 2012; Robinson et al., 2013).
Collaborative ties that are developed formally through mandates, Memoranda of Understandings
(MoUs), or common preparedness drills and exercises may indicate a higher level of social capi-
tal. Friendship ties do not necessarily transform into work relations, while previous work rela-
tions are more likely to breed new and multiple ties (Isett & Provan, 2005; Larson, 1992) during
the disaster response stage. Thus, friendship networks may not necessarily be developed accord-
ing to the needs or resource dependencies identified during the disaster response stage. The
resource needs of organizations at the response stage are better met through preparedness net-
works. Hence, the second set of hypotheses proposed is as follows:
Kapucu and Hu 403
Hypothesis 3: Formal collaboration ties in disaster preparedness are positively related with
the formation of collaboration ties in disaster response.
Hypothesis 4: The correlation between disaster preparedness networks and disaster response net-
works is higher than the correlation between friendship networks and disaster response networks.
Structural Characteristics and Network Formation and Development
There are multiple types of collaborative emergency management systems. We can categorize
them into three types: vertical or hierarchical, horizontal or decentralized, and a combination of
the two (Kapucu & Garayev, 2014). In the United States, three different systems are practiced:
the Emergency Support Function (ESF)1-based system (horizontal), the Incident Command
System (ICS; vertical), and the hybrid combination of the two systems. The ESF-based system
was introduced in the Federal Response Plan (FRP) in the early 1990s to improve the coordinat-
ing mechanism of emergency management operations at the national level. After the terrorist
attacks of September 11, 2001, and Hurricane Katrina, in 2005, the National Response Framework
(NRF) was established in 2008 based on lessons learned to enhance coordination across govern-
ment agencies as well as among the public, nonprofit, and private sectors. Emergency manage-
ment agencies operate based on 15 ESFs, which demand a collaborative approach to emergency
management (Kapucu & Garayev, 2012).
The ICS-based approach, the foundation of the National Incident Management System
(NIMS),2 emphasizes a hierarchy of authority as well as standard operational structures for man-
aging disasters (Lester & Krejci, 2007). This is because a unified command is needed when
response to incidents requires efforts from multiple organizations across a particular jurisdiction
(Moynihan, 2009). ICS is organized around five functional areas, including command, opera-
tions, planning, logistics, and finance/administration (Department of Homeland Security [DHS],
2008). When an incident occurs, a single incident commander is responsible for the overall inci-
dent management and decision-making processes. The commander is supported by command
staff, consisting of a public information officer, a safety officer, and a liaison officer. When inter-
organizational collaboration is required, representatives of agencies involved make joint deci-
sions to create a unified command (DHS, 2008).
Overall, the ICS-based approach demonstrates a relatively hierarchical command-and-control sys-
tem, whereas the ESF-based system exhibits a horizontal collaborative structure (Kapucu, Arslan, &
Demiroz, 2010). Compared with the vertical structure of the ICS-based approach, the horizontal struc-
ture of the ESF-based system allows for more flexibility, enabling emergency management organiza-
tions to reach out to other partner organizations in the network to share resources and coordinate
efforts. Therefore, existing friendship ties are more likely to correlate with the formation of formal
collaborative ties in the ESF-based horizontal system than in the ICS-based vertical system. Given the
high level of reliance on hierarchy and command and control within the ICS-based emergency man-
agement system, formal connections during disaster preparedness are more likely to lead to more
formal collaborations during emergency response. The third set of hypotheses is as follows:
Hypothesis 5: Friendship ties within horizontal emergency management networks have stron-
ger predictive power in the formation of formal collaboration ties in disaster preparedness
than do the counterparts within hierarchical emergency networks.
Hypothesis 6: Friendship ties within horizontal emergency management networks have
higher predictive power in the formation of formal collaboration ties in disaster response than
do the counterparts within hierarchical emergency management networks.
Hypothesis 7: Collaboration ties during disaster preparedness within horizontal emergency
management networks have lower predictive power in the formation of collaboration ties in
disaster response than do the counterparts within hierarchical emergency management
networks.
404 American Review of Public Administration 46(4)
Networks and Homophily
According to social network research, individuals and organizations are more likely to establish
interactions with other individuals and organizations that share some attributes (McPherson,
Smith-Lovin, & Cook, 2001). For instance, organizations that are similar in staff size, budget
size, and sector affiliation are more likely to interact with each other for information and resource
sharing. In this study, sector affiliation (public, private, or nonprofit) and differences in organiza-
tional staff size and budget were used to measure the extent to which emergency management
organizations are similar to each other. Matrices reflecting the differences in staff size and bud-
gets were created as control variables.
As shown in Figure 1, this research mainly focuses on the relationships among the three types
of networks: friendship networks, disaster preparedness networks, and disaster response net-
works. This research also takes into consideration the structure of the networks (hierarchical
versus horizontal) along with three control variables: (a) sector affiliation, (b) budget difference,
and (c) staff size difference. The conceptual map suggests that friendship ties influence the for-
mal collaboration ties during disaster preparedness and response. Moreover, the figure also
shows that formal collaboration ties in disaster preparedness networks influence the formation of
collaborative ties in the disaster response phase. We hypothesize that the correlation between
disaster preparedness networks and response networks is higher than the correlation between the
friendship and disaster response networks. This is because formal collaboration at the prepared-
ness stage identifies potential partners categorically through common exercises, drills, and train-
ings, and also leads to formalizing partnerships and relationships through emergency management
plans, policies, mandates, and MoUs.
Moreover, the influence of friendship ties on developing formal collaborative ties is also
dependent on the overall structure of the networks. In the case of a traditional command-and-
control-based hierarchical structure, the predictive power and influence of a friendship network
on the formation of formal collaboration in response networks is relatively weak. However, if the
H1+
H3+
H4 +
H2 +
H5+
H7-
H6+
Preparedness
Networks
Response
Networks
Control
Variables:
Budget difference
Staff size
difference
Sector
Affiliation
Difference
Network
Structures:
Horizontal vs.
Hierarchical
Friendship
Networks
Figure 1. Conceptual framework: Multiplexity of networks.
Note. Solid lines are used to indicate Hypotheses 1 to 3. Dotted lines are used to visualize Hypotheses 4 to 7.
Kapucu and Hu 405
friendship ties are arranged in a horizontal configuration, they have a stronger predictive power
in the formation of formal collaboration ties in disaster preparedness networks. On the other
hand, we hypothesize that if collaboration ties are arranged in a hierarchical network, they exert
a higher level of predictive power on the formation of collaborative ties in the disaster response
phase. Thus, the conceptual framework emphasizes the role that network structure plays in pre-
dicting the formation of collaborative ties in preparedness and response networks. The frame-
work also shows that factors such as the financial standing of agencies (depicted through budget
differences) and the size of the organizations (staff size) influence the development of collabora-
tive ties in all three networks studied.
Context of the Study
In most states, disaster preparation, mitigation, response, and recovery fall on the local govern-
ments. County governments play a vital role in local emergency management (Waugh, 1994).
County governments may establish emergency management agencies, such as the Office of
Emergency Management, and coordinate with other local public agencies, nonprofits, and for-
profit organizations to prepare for and to respond to disasters. This study examines the emer-
gency management networks within two counties of the state of Florida, which is one of the most
at-risk states for disasters in the United States. The emergency management system in this state
has been recognized as a model for the entire country (Kapucu & Garayev, 2014). The emergency
management system in Orange County demonstrates a more horizontal network structure,
whereas Duval County has a hierarchical network structure for emergency management.
Horizontal Networks in Orange County
Orange County is one of seven counties comprising Central Florida and serves a population of
about 1 million. It is a charter government with an elected mayor and six commissioners repre-
senting six county districts. Per Section 252.38 of the Florida State Statutes, the county mayor
directs county governments to establish an emergency management agency and delegates the
authority to manage emergencies and disasters to the Director of Emergency Management.3 The
director administers the County Office of Emergency Management (OEM) and operates the
Emergency Operation Center (EOC) in times of disasters (Kapucu & Garayev, 2012). When a
local disaster occurs, the director of the EOC will follow the guidelines specified in the county’s
Comprehensive Emergency Management Plan (CEMP) and activate the EOC, depending on the
level of threat or risk.
Despite the compliance of OEM with the NIMS-based ICS structure, the main system of
referral in Orange County is based on horizontally arranged ESFs. It is primarily the ESFs that
provide coordination structures and guidelines to organizations when dealing with emergency-
related operations. The relationships and ties among agencies represented at the EOC in times of
emergencies are structured around 20 ESFs and their respective primary and support agencies.
The NIMS-based ICS structure, however, remains the main scheme for classification of the
ESFs, as well as other parts of the Emergency Response Team (ERT), for guidance and efficiency
purposes (Kapucu & Garayev, 2014).
Hierarchical Networks in Duval County
Duval County is located at the eastern side of the state of Florida and serves a population of about
850,000. Like Orange County, Duval County is a charter government with an elected mayor and
a council of 19 members. The Emergency Preparedness Division (EPD) Chief of the Fire and
Rescue Department of the (organization name removed for the blind review) is in charge of
406 American Review of Public Administration 46(4)
emergency and disaster management in Duval County. When a local emergency occurs, the EPD
activates the EOC to respond to the threat. EOC operations activate the Emergency Preparedness
Organization (EPO), which is structured in line with NIMS (Kapucu et al., 2010). As a widely
practiced standard, the head of the EPO is the city mayor, who is assisted by the County Security
Coordinator, an Executive Group, an Operations Group, and 22 other members known as the
EOC Management Team. The Executive Group comprises the EPD Chief and department or
agency directors for advisory purposes, while the EOC Management Team consists of sections,
branches, groups, and units structured in line with ICS principles and standards. Compared with
Orange County, the emergency management system in Duval County has a more hierarchical
structure (Kapucu & Garayev, 2014).
Data and Method
Following the “nominalist approach” in setting network boundaries (Carpenter, Li, & Jiang,
2012; Laumann, Marsden, & Prensky, 1989), we analyzed CEMPs of two metropolitan counties
in a southeastern state to generate the list of organizations and their representatives responsible
for responding to disasters and crises. The CEMPs, adopted in 2010, clearly identified organiza-
tions responsible for each ESF. This list includes primary and support agencies from public, for-
profit, and nonprofit sectors in two counties. Each organization also identifies and provides
names of the representatives and contact information to the county emergency management
office. This article utilizes the whole network design perspective to compare three types of net-
works (Scott, 2013). Before distributing the survey, we asked a few emergency management
officers (EOC directors and communication specialists) to pretest the survey to ensure that the
survey questionnaire was easy to understand. The survey addresses the emergency managers or
executive directors of the organizations that are part of an ESF/ICS as specified in the two coun-
ties’ CEMPs, with the purpose to prepare for and/or respond to disasters in metropolitan regions
in this southern state. A roster of all involved organizations listed in the CEMP was provided to
the respondents. We asked one respondent from each organization to identify among the list of
organizations whom they know, with whom they collaborate during disaster preparedness, and
with whom they collaborate during disasters response.4 These questions identified the existence
of friendship ties and collaboration ties in emergency preparedness as well as in emergency
response.
We conducted multiple regression with quadratic assignment procedure (MRQAP) to analyze
the relationships among the friendship ties, collaboration ties in disaster preparedness networks,
and collaboration ties in disaster response networks. Quadratic assignment procedure (QAP) is
an inferential statistical procedure that randomly permutes identical matrices of the same set of
network actors and calculates their standard error to analyze the level of association between
them (Hanneman & Riddle, 2005; Krackhardt, 1988). Each matrix represents a different type of
network tie (e.g., formal versus informal) or the same network tie at different points in time (i.e.,
longitudinal analysis of a network). Unlike conventional statistical procedures, such as the ordi-
nary least square (OLS) regression, QAP does not assume independence of observations; that
makes this method appropriate for analyzing relational data. Statistical procedures such as mul-
tiple regression and correlation become available for network data by using QAP.
In addition to QAP, we used degree centrality and density measures to provide descriptive
statistics for network relationships. There are two types of degree centrality: in-degree and out-
degree. In-degree centrality shows the number of incoming ties to an actor, whereas out-degree
centrality shows the number of outgoing ties from an actor. The summation of both scores gives
the total number of ties that an actor has. If a type of relationship is reciprocal, meaning that two
actors send out and receive ties from each other, it counts for both in-degree and out-degree mea-
sures. Overall, degree centrality depicts the level of social capital that may be directed to nodes/
Kapucu and Hu 407
agencies (ego networks; Borgatti, Carley, & Krackhardt, 2006). For instance, an organization
with a high degree centrality is considered more embedded, central, and powerful in the network
(Borgatti & Foster, 2003; Prell, 2012). Density measures are used to gauge the level of connectiv-
ity and linkage among agencies operating within a network (Scott, 2013); the higher the density
of a network, the higher the connectivity in terms of communication flow and information
exchange. A low density depicts a sparse network that contains isolates and restricts communica-
tion, information, and resource flow (whole network; Scott, 2013). Before reviewing the details
about the results of the study, the following section introduces the two collaborative emergency
management systems, within which emergency management networks are examined in this
study.
Results and Discussion
In this section, we first report the descriptive statistics and structural characteristics of the emer-
gency management networks. Then, we present the relationships among friendship networks,
disaster preparedness networks, and disaster response networks. We discuss the results and
hypothesis testing and the implications of the findings.
In the ESF-based system in Orange County, 40 emergency management organizations
responded to the survey questionnaire, out of which 32 are public organizations, 6 are nonprofit
organizations, and 2 are private organizations.5 In the ICS-based system in Duval County, 20
organizations come from the public sector, 1 organization comes from the nonprofit sector, and 1
organization comes from the private sector. As Table 1 shows, the majority of the organizations
have more than 50 staff members and a budget over US$5 million.
The friendship ties in the ESF-based system are denser than the counterparts in the ICS-based
system (shown in Figure 2). As shown in Table 2, within the ESF-based system, more organiza-
tions reach out to other organizations during daily operations. In both the ESF-based system and
the ICS-based system, friendship networks have higher density than disaster preparedness net-
works and response networks. In the ICS-based system, the in-degree centralization scores are
Table 1. Descriptive Statistics of Emergency Management Organizations.
Attributes
ESF-based system in
Orange County (n = 40)
ICS-based system in
Duval County B (n = 22)
Organization type
Public 32 20
Nonprofit 6 1
Private 2 1
Staff size
Over 50 27 14
26-50 2 2
16-25 0 4
6-15 4 1
1-5 7 1
Budget
$5,000,001 and more 26 17
$1,000,001-$5,000,000 2 4
$500,001-$1,000,000 4 1
$100,001-$500,000 3 0
0-$100,000 5 0
Note. ESF = emergency support function; ICS = incident command system.
408 American Review of Public Administration 46(4)
Table 2. Network Descriptive Statistics.
Networks Density Centralization (out-degree) Centralization (in-degree)
Orange County: ESF-based emergency management system
Friendship networks .571 .541 .209
Preparedness networks .288 .641 .371
Response networks .326 .602 .386
Duval County: ICS-based emergency management system
Friendship networks .526 .521 .155
Preparedness networks .323 .588 .536
Response networks .310 .622 .550
Note. ESF = emergency support function; ICS = incident command system.
higher in both preparedness networks and response networks than the counterparts in the ESF-
based system. This indicates that the formal connections in disaster preparedness and response
networks may be centered on a few key actors in the ICS-based system (Borgatti et al., 2013;
Prell, 2012).
To examine the multiplex relationships among organizations, we present QAP correlations in
Table 3. As the network data are binary, Jaccard Coefficients instead of Pearson Correlations are
reported (Hanneman & Riddle, 2005). Jaccard Coefficients measure the ratio of the number of
common dyads to the total number of dissimilar dyads within the two networks (Hanneman &
Riddle, 2005). Friendship ties are positively associated with collaboration ties during disaster
preparedness and response in both the ESF-based emergency management system and the ICS-
based system. Within the ESF-based system in Orange County, the Jaccard Coefficients between
friendship and preparedness networks and between friendship and response networks are 0.422
and 0.389, respectively; the coefficients are statistically significant. The Jaccard Coefficient
between disaster preparedness and response networks is 0.576, and it is statistically significant.
Within the ICS-based system, the Jaccard Coefficients are also statistically significant between
friendship networks and disaster networks, friendship networks and response networks, and pre-
paredness networks and response networks. However, when compared with the ICS, within the
ESF-based system, the correlations between friendship, preparedness, and response networks are
Figure 2. Structural attributes of the three types of networks across the two systems.
Kapucu and Hu 409
relatively stronger. By contrast, the correlation between preparedness and response networks is
stronger in the ICS-based system than in the ESF-based system.
To test the seven hypotheses, we conducted MRQAP to take into account the influence of
control variables and to separate the influence of the correlations between disaster preparedness
networks and response networks. To avoid autocorrelation and collinearity problems, we used
the Double Dekker Semi-Partialling method (Dekker, Krackhardt, & Snijders, 2007).
Hypothesis 1 examines the relationship between friendship ties and collaboration ties during
disaster preparedness. As shown in Table 4, the regression coefficients for friendship ties within
the ESF-based system and ICS-based systems are 0.358 and 0.272, and the coefficients are sta-
tistically significant. Hence, Hypothesis 1 is supported. The existence of friendship ties can con-
tribute to the formation of collaboration ties during disaster preparedness. Hypothesis 2 assumes
a positive relationship between friendship ties and collaboration ties during disaster response.
The regression coefficient of the friendship networks for predicting the collaboration networks
during disaster response is not statistically significant when the matrix of collaboration networks
during disaster preparedness is added to the model (shown in Table 5). Hypothesis 3 tests the
positive relationship between collaboration ties during disaster preparedness and collaboration
ties during disaster response. As Table 5 shows, the regression coefficients for the preparedness
networks for predicting response networks in both the ESF-based system and ICS are strong
Table 3. QAP Correlations Between Three Networks With the Same Actors.
Three networks in two counties Preparedness networks Response networks
Orange County: ESF-based system
Friendship networks .422*** .389***
Preparedness networks .576***
Duval County: ICS-based system
Friendship networks .395*** .336***
Preparedness networks .738***
Note. As the data are binary data, Jaccard Coefficients are reported here. QAP = quadratic assignment procedure; ESF =
emergency support function; ICS = incident command system.
*p ≤ .05. **p ≤ .01. ***p ≤ .001.
Table 4. QAP Multiple Regression Results for the Disaster Preparedness Networks.
Model I for the ESF-based
system in Orange County
Model I for the ICS-based
system in Duval County
Friendship ties 0.358*** 0.272***
Sector affiliation 0.122* 0.217**
Staff size dissimilarity −0.122 −0.008
Budget dissimilarity 0.029 0.020
Intercept 0.000 0.000
R2 .187 .135
Adjusted R2 .185 .128
Number of observations 1,560 462
Number of permutations 2,000 2,000
Note. The dependent variable in this analysis is the collaboration ties within disaster preparedness networks. Numbers
in each variable represent standardized coefficients. QAP = quadratic assignment procedure; ESF = emergency sup-
port function; ICS = incident command system.
*p ≤ .05. **p ≤ .01. ***p ≤ .001.
410 American Review of Public Administration 46(4)
(0.591 and 0.774, respectively) and statistically significant at the .001 level. Therefore, Hypothesis
3 is also supported. Hypothesis 4, which argues that collaboration ties during disaster prepared-
ness have higher predictive power in the formation of collaboration ties during disaster response
than friendship ties, is also supported.
These findings speak to previous research, which suggests that analyzing the relationships
between the perceived emergency management networks and the actual emergency management
networks can assist policy makers to better utilize and allocate resources (Choi & Brower, 2006;
Choi & Kim, 2007). According to Kapucu and Garayev’s (2012) research, prior interorganiza-
tional relationships are crucial to build sustainable emergency management networks. Hence, it
is worthwhile to understand the relationships among different types of emergency management
networks and to further explore the possibility of building collaboration in emergency manage-
ment at a deeper level as well as on a broader scale. All four hypotheses speak to the role of social
capital in building and sustaining emergency management networks, as suggested in previous
research (Kapucu, 2006b). Social capital, manifested in existing friendship ties or collaboration
ties, can increase the likelihood of building further collaborations in emergency management.
Higher levels of social capital, measured by collaboration ties during disaster preparedness, are
more likely to encourage the formation of collaboration ties during emergency response rather
than friendship ties. A statistically significant relationship was not found between friendship ties
and collaboration ties during disaster response. This may indicate that the friendship ties are not
a strong predictor of response networks. This may be because a large proportion of the positive
correlation between friendship networks and disaster response networks can actually be accounted
for by the positive relationship between preparedness and response networks, as friendship net-
works correlate with disaster preparedness networks.
Hypothesis 5 tests whether friendship ties within horizontal emergency management networks
can better predict the formation of collaboration ties in disaster preparedness than can their coun-
terparts within hierarchical emergency networks. As shown in Table 4, the coefficient of friend-
ship ties is 0.358 within the horizontal emergency management networks, which is higher than
the coefficient of friendship ties (0.272) within the hierarchical emergency management net-
works. Hence, Hypothesis 5 is supported. Hypothesis 6 is not supported, given that neither
regression coefficient is statistically significant, as shown in Table 5. The MRQAP results indi-
cate that the correlation between friendship networks and response networks is not statistically
Table 5. QAP Multiple Regression Results for the Emergency Response Networks.
Model I for the ESF-based
system in Orange County
Model I for the ICS-based
system in Duval County
Friendship ties 0.036 −0.036
Collaboration ties during EM preparedness 0.591*** 0.774***
Sector affiliation 0.008 0.074*
Staff size dissimilarity −0.071 0.050
Budget dissimilarity 0.031 −0.031
Intercept 0.000 0.000
R2 .381 .618
Adjusted R2 .379 .613
Number of observations 1,560 462
Number of permutations 2,000 2,000
Note. The dependent variable in this analysis is the collaboration ties within disaster response networks. Numbers in
each variable represent standardized coefficients. QAP = quadratic assignment procedure; ESF = emergency support
function; ICS = incident command system; EM = emergency management.
*p ≤ .05. **p ≤ .01. ***p ≤ .001.
Kapucu and Hu 411
significant in either the ESF-based system or the ICS-based system. In the full models, it is sur-
prising that friendship ties do not seem to be a good predictor of response networks, although
friendship ties correlate with collaboration ties within preparedness networks in the previous
model. This may be explained by the characteristics of disaster response. Disaster response dif-
fers from disaster preparedness in that the former requires more formal and timely actions. More
friendship ties may lead to a broad involvement of organizations during disaster preparedness but
not necessarily the actual actions during emergency response. In other words, friendship ties can
help produce better collaborations in actual response networks only when friendship ties actually
lead to the engagement of organizations in formal preparedness or planning processes.
Hypothesis 7 is supported; this hypothesis suggested that, when compared with the ESF-based
system, collaboration ties during disaster preparedness have higher predictive power in the for-
mation of collaboration ties during disaster response in the ICS-based hierarchical structure of
emergency management system. Collaboration ties during disaster preparedness correlate highly
with formal collaboration ties during emergency response in both the ESF-based system and the
ICS-based system, with the regression coefficients at 0.591 and 0.774, respectively. This can be
explained by the characteristics of the ICS-based approach in emergency management. The ICS-
based approach emphasizes hierarchy and formality, although this approach still carries the attri-
butes of network governance (Moynihan, 2009). Given the high level of command and unity,
collaboration ties during disaster preparedness tend to be more formal in the ICS-based approach,
which later will more likely lead to the formation of formal collaborations during disaster
response.
In sum, Hypotheses 1, 3, 4, 5, and 7 are supported based on the MRQAP analysis. Friendship
networks correlate with preparedness networks, and preparedness networks correlate with
response networks. The correlation between collaboration networks during disaster preparedness
and disaster response is strong in both the ESF-based system and the ICS-based system. The cor-
relation between the preparedness network and the response network is stronger in the ICS-based
system. Hypotheses 2 and 6 are not supported in the MRQAP analysis. The correlation between
friendship ties and collaboration ties during emergency response is not statistically significant
when we consider the impact of collaboration ties during disaster preparedness on the formation
of collaboration ties during disaster response.
This research reiterates the importance of developing strong relationships prior to a disaster.
Friendship networks correlate with both disaster preparedness networks and response networks.
Friendship ties are important for encouraging organizations to be involved in disaster prepared-
ness networks. There are more friendship ties than formal collaboration ties during disaster pre-
paredness and response in the two counties we examined. During daily operations, many
organizations reach out to build friendships with other emergency management organizations
and partner agencies.
It is crucial for organizations to build formal collaborations during the disaster preparedness
stage. Although organizations may establish multiple types of connections, formal connections
during disaster preparedness matter more in fostering formal, sustainable collaborations during
actual disaster response. When the impact of preparedness networks on response networks is held
constant, the correlation between friendship networks and response networks is not statistically
significant. That is to say, although friendship ties correlate with collaboration ties during disas-
ter preparedness and response, it is formal collaboration ties during disaster preparedness that
influence the formation of collaborations during disaster response. This lends support to research
that highlights the importance of involving emergency management organizations, including
nonprofits and local communities, in early emergency planning (Brudney & Gazley, 2009). The
activities and planning activities and exercises during the preparedness phase can help strengthen
existing friendship ties and develop new formal ties that will play out in the response stage of
managing disasters.
412 American Review of Public Administration 46(4)
This research finds evidence that structural attributes of emergency management systems
need to be considered when researchers explore the multiplex relations among organizations
within various networks. Within the ESF-based system, friendship ties have higher predictive
power in the formation of collaboration ties in disaster preparedness than do their counterparts
within hierarchical emergency networks. Within the ICS-based system, formal collaboration ties
during disaster preparedness have higher predictive power in the formation of collaboration ties
during disaster response. This may be explained by the hierarchical characteristics of the ICS-
based (vertical) approach to emergency management, since the relationships tend to be more
formal and stabilized in the ICS-based approach.
There has been an ongoing debate among practitioners and in academic communities about
whether a hierarchical network model or a centralized coordination system is more suited to
managing disasters or if a more flexible and horizontal coordination model is better suited
(Groenendaal, Helsloot, & Scholtens, 2013). This study shows that the correlation between disas-
ter preparedness and disaster response networks is strong in both the ESF-based system and the
ICS-based system, although the correlation between the preparedness network and the response
network is stronger in the ICS-based system. Thus, both ICS- and ESF-based systems are feasible
approaches and warrant a deeper analysis of factors that may influence the precedence of one
approach over the other.
Conclusion
This research contributes to existing literature in multiple respects. First, this research focuses on
an understudied issue in pubic management network literature—the multiplexity of collaborative
networks. Scholars called for more research attention to studying the diversity of networks, the
evolution of networks, and multiplex relationships among organizations within networks (Isett et
al., 2011; Robinson, 2006; Robinson et al., 2013). Previous emergency management network
research has compared the planned networks with the actual response networks (e.g., Choi &
Brower, 2006; Choi & Kim, 2007; Kapucu & Demiroz, 2011). This research examines three
emergency management networks and explores the multiplex relationships among organizations
within these networks. Examining the multiplex interorganizational relationships can help us
better understand the nature of interorganizational interactions. This research is among one of
few attempts to examine the role of informal networks in the context of public management. The
focus on friendship ties and collaboration ties during disaster preparedness and response can
enrich our conversation about interorganizational relationships in the context of emergency
management.
Second, this research goes beyond descriptive network analysis and applies inferential net-
work analysis methods to examine the relationships among various emergency management net-
works and the predictive power of preestablished networks on disaster response networks. This
research differs from earlier network research, which mainly describes the structural characteris-
tics of emergency management networks. The use of MRQAP allows us to test the relationships
among friendship networks, preparedness networks, and response networks. Furthermore, net-
work research has been critiqued for paying little attention to the context within which networks
emerge and grow (Borgatti, Brass, & Halgin, 2014). This research considers the influence of the
broad contextual factors—the horizontal and vertical emergency management systems—on
interorganizational collaborations. This research provides preliminary support that collaboration
ties during disaster preparedness within a hierarchical emergency management system are more
likely to evolve into collaboration ties during disaster response than the counterparts within a
horizontal emergency management system. Future research may delve into other contextual fac-
tors such as political culture to further understand the formation and development of interorgani-
zational collaborations.
Kapucu and Hu 413
Finally, not only may findings from this research contribute new knowledge about developing
sustainable emergency management networks, but they may also have implications for building
collaborative networks in a broader context. The importance of building preestablished networks
for developing formal collaborations can apply to other management domains. Future research-
ers may further test the relationships among various types of networks in other management
areas. Public managers, including but not limited to emergency managers, need to gain better
knowledge about the informal networks within their organizations and beyond organizational
boundaries. It is important to realize the advantage of developing multiplex interorganizational
interactions before a formal collaboration becomes a necessity. Managers may help create a sup-
portive culture that encourages developing multiplex relationships with other potential partners.
Public managers can also take a lead role in tapping the resources embedded within informal
networks and ensuring the consistency between informal networks and organizational goals.
This research is not without limitations. This study examined three types of emergency man-
agement networks in two counties in one southern state. Future research should extend to mul-
tiple metropolitan areas to increase the generalizability. Furthermore, future research designs
should consider the time dimension and explore innovative approaches to collect longitudinal
network data. In addition, qualitative narratives can be included to enrich the data and enable
researchers to address more complex network development questions. This research may have
raised more questions than it answered and calls for more systematic research on building, devel-
oping, and sustaining emergency management networks.
Acknowledgment
Dr. Vener Garayev assisted in data collection while he was a doctoral student.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or
publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publi-
cation of this article: This research is partially funded by National Science Foundation (Award 0943208;
Title: “VOSS: Creating Functionally Collaborative Infrastructure in Virtual Organizations”; PI Dr. Naim
Kapucu).
Notes
1. The Emergency Support Functions (ESFs) align needed resources into operational areas. Emergency
managers activate ESFs depending on the type of incident. Each ESF is assigned a coordinator, a
primary agency, and at least one support agency or organization to manage and coordinate resource
requests during an incident (Federal Emergency Management Agency [FEMA], 2008). For additional
information, see FEMA (2008).
2. National Incident Management System (NIMS), established according to the National Response Plan
in 2004, is a centralized, unified, and standardized coordination system (Kapucu, 2009). Under this
system, the federal government can exert more control over local emergency management practices
(Birkland, 2009).
3. In Orange County, when an emergency is manageable at the local level, the Board of County
Commissioners has the main responsibility of managing the countywide incidents. The Board, per
County Ordinance #94-11, has delegated this authority to the mayor.
4. These questions asked the respondents to reflect on their existing friendship ties and collaboration ties.
We did not collect longitudinal network data, as it is very challenging to retain the same emergency
organizations in the study for multiple years, not to mention collect network data from the same orga-
nizational representatives.
414 American Review of Public Administration 46(4)
5. Even though the overall response rate seems low, the representation of key informants and organizations
with key emergency management functions is higher. For instance, according to the Comprehensive
Emergency Management Plan (CEMP) of Orange County, there are 20 ESFs. Under each ESF, organi-
zations are designated as primary organizations or support organizations. There are 22 primary emer-
gency management organizations listed in the CEMP of Orange County, among which 14 (64 %)
responded to our survey. The participation from nonprofit organizations (especially small nonprofit
organizations) and private organizations was relatively low. In this research, we were able to receive
completed surveys from organizations with critical roles in emergency management. Furthermore,
certain network centrality measures, such as in-degree centrality, are quite robust under the conditions
of missing data (Borgatti, Carley, & Krackhardt, 2006; Costenbader & Valente, 2003). When we use
network analysis methods, especially the visual networks, the survey with a relatively low response
rate may still allow the researcher to describe the major characteristics of a network, given that the
majority of organizations that are playing critical roles responded to the survey.
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Author Biographies
Naim Kapucu, PhD, is professor of public policy and administration and director of the Master of Public
Administration program at the School of Public Administration at the University of Central Florida. He
chairs the Section on Public Administration Research of American Society for Public Administration. His
main research interests are emergency and crisis management, decision making in complex environments,
collaborative governance, and social inquiry and public policy. His work has been published in Public
Administration Review, Administration & Society, Journal of Public Administration Research and Theory,
the American Review of Public Administration, and Disasters, among many others. His book Network
Governance in Response to Acts of Terrorism: Comparative Analyses was published in 2012 by Routledge.
Kapucu and Hu 417
He teaches network governance, public and nonprofit management, emergency and crisis management,
research methods, and analytic techniques for public administration courses.
Qian Hu, PhD, is an assistant professor in the School of Public Administration at the University of Central
Florida. Her research interests include collaborative governance, network studies, policy informatics, and
strategic and performance management. Her work has been published or is forthcoming in academic jour-
nals such as Public Administration Review, American Review of Public Administration, Public Managemet
Review, American Behavioral Scientist, Journal of Community Informatics, Research Policy, and Journal
of Public Affairs Education. She teaches public organization management, research methods, and strategic
planning and management courses.
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How Do Public Organizations Learn? Bridging Cultural and Structural Perspectives
Moynihan, Donald P;Landuyt, Noel
Public Administration Review; Nov/Dec 2009; 69, 6; ProQuest
pg. 1097
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PRODUCTIVITY
The Quantitative Analysis Report: Multiple Regression Analysis Assignment uses the Productivity. sav dataset. Address the following research question using a multiple regression (MR) model. Provide all assumptions for the MR test:
RQ 8: Is there a significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk)?
· H08: There is no statistically significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk).
· Ha8: There is a statistically significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk).
There are several assumptions for a multiple regression that must be met:
1. First, the dependent variable must be normally distributed.If not, it must be converted to z scores (see page 32-33 in Cronk).
2. To test for normal distribution, run the Shapiro-Wilk test (See Testing Normality of Dataset.pdf).
3. When you run the Multiple Regression, ensure you select options for multicollinearity and residual plots (see Cronk).
Table 1. Knowledge to perform job Responsibilities
Table 2. Extent to which Workers are treated fairly
Table 3. Use and effectiveness of teams
Table 4. Extent to employee has authority to make decisions while performing job
Table 5. Extent to which recognition and awards are fair
Table 6. Number of workdays missed during las 12 months due to illness
Table 7. Length of time as public employee
Table 8. Employee’s unit
Table 9. Employee evaluation of unit productivity
Table 10. Unit Productivity
Table 11. Department employee’s unit is located within
Table 13. Department productivity
Table 14. Dept1
Table 15. dept2
Table 16. dept3
Table 17. dept4
Table 18. Zscore: Employee evaluation of unit productivity
Table 19. Standardized Residual
Table 20. Studentized Residual
Table 21. Mahalanobis Distance
Table 22. Cook’s Distance
Table 23. Centered Leverage Value
Multiple Regression Tables
Table 1a.
Table 1b.
Table 2a.
Table 2b.
Table 3a.
Table 3b.
Table 4a.
Table 4b.
Charts for Regression
Sharpiro-Wilk test
CJUS 745
Quantitative Analysis Report: Multiple Regression Analysis Assignment Instructions
Assignment #5: Productivity
DUE DATE: by 10am on Thursday June 23, 2022. NO LATE WORK!!!!
BIBLE PERSPECTIVES MUST BE INCLUDED!!
Overview
You will take part in several data analysis assignments in which you will develop a report using tables and figures from the IBM SPSS® output file of your results. Using the resources and readings provided, you will interpret these results and test the hypotheses and writeup these interpretations.
Instructions
· Copy and paste all tables and figures into a Word document and format the results in APA current edition.
· Interpret your results.
· Final report should be formatted using APA current edition, and in a Word document.
· 4-5 double-spaced pages of content in length (not counting the title page or references).
The Quantitative Analysis Report: Multiple Regression Analysis Assignment uses the Productivity. sav dataset. Address the following research question using a multiple regression (MR) model. Provide all assumptions for the MR test:
RQ 8: Is there a significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk)?
· H08: There is no statistically significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk).
· Ha8: There is a statistically significant predictive relationship of employee productivity (productivity) from levels of Teamwork (teamwork), Technical Knowledge (jobknowl), Adequate Authority to do job well (jobauthr), Fair Treatment (wkrtrtmt), and Sick Days (wrkdyssk).
There are several assumptions for a multiple regression that must be met:
1. First, the dependent variable must be normally distributed.If not, it must be converted to z scores (see page 32-33 in Cronk).
2. To test for normal distribution, run the Shapiro-Wilk test (See Testing Normality of Dataset.pdf).
3. When you run the Multiple Regression, ensure you select options for multicollinearity and residual plots (see Cronk).
General Instructions
As doctoral students, your assignments are expected to follow the principles of high-quality scientific standards and promote knowledge and understanding in the field of public administration. You should apply a rigorous and critical assessment of a body of theory and empirical research, articulating what is known about the phenomenon and ways to advance research about the topic under review. Research syntheses should identify significant variables, a systematic and reproducible search strategy, and a clear framework for studies included in the larger analysis.
Manuscripts should not be written in first person (“I”). All material should be 12-point, Times New Roman type, double-spaced with margins of one inch.
All manuscripts should be clearly and concisely written, with technical material set off. Please do not use jargon, slang, idioms, colloquialisms, or bureaucratese. Use acronyms sparingly and spell them out the first time you use them. Please do not construct acronyms from phrases you repeat frequently in the text.
Structure of Assignment Paper
1. Use the following structure for your research article: Abstract, Introduction, Literature Review/Theory, Methods, Results, Discussion, and Conclusion. Include a robust discussion section distinct from your conclusion.
2. Give your article a Title that is both descriptive and inviting to prospective readers. Your article title should appeal to both scholars and practitioners. Use a shortened version of the main idea of your article in the title.
3. Your Abstract should inform readers what your article is about and its most important findings. Readers, including scholars and practitioners, should be able to understand your topic, argument, and conclusions. Make your abstract straightforward and do not use technical language or jargon.
4. In the Lit Review/Theory, cite only literature and theory pertinent to the specific issue and not those that are of only tangential or general significance. When summarizing earlier works, avoid nonessential details; instead, emphasize pertinent findings, relevant methodological issues, and major conclusions. Citation of relevant earlier literature is asign of scholarly responsibility and it is critical for the growth of a doctoral student in public administration.
5. Methods: The Methods section “describes in detail how the study was conducted, including conceptual and operational definitions of the variables used in the study. Different types of studies will rely on different methodologies; however, a complete description of the methods used enables the reader to evaluate the appropriateness of your methods and the reliability and the validity of your results” (APA current edition).Include a description of your sample size and procedure, participants, how data collected, and research design.
6. Results include data analysis used, results of the analysis including tables and figures.
7. Discussion section includes interpretations from the analysis. How do your analyses relate to the results found by scholars in your lit review/theory section. In this section, evaluate and interpret their implications, especially with respect to your original hypotheses.
8. Provide a distinct Conclusion that tells readers what you found, why it is important, and what difference it will make for research and practice. Ensure you separate your discussion section from the conclusion of the article. Synthesize your article; do not summarize it. Show readers how the pieces of your article fit together. Answer the question “So what?” Why is your article significant, and how is it relevant?
Page 2 of 2
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Electronic copy available at: https://ssrn.com/abstract=3235427
1
The Mistakes of the Marginal Productivity Theory of Income Distribution
by Dimitrios Nomidis*
Abstract
The debate that took place at the end of 19th and the beginning of 20th century on the
neoclassical income distribution theory based on the marginal productivity ofthe production
factors is well known. The debate evolved especially around the question whether the product
is exactly exhausted through its distribution to the factors of production according to the value
of their marginal products. This question is now considered resolved and closed by the proofs
presentedbyWicksell,Walrasandlateronbyotherdistinguishedeconomists(Chapman,
Hicks etc).
The purpose of this paper is to demonstrate that the proofs which were presented to
support the product exhaustion theorem are mistaken and consequently the theory of income
distributiononthebasisofthemarginalproductivityoftheproductionfactorsiswrong.
Furthermore, this paper attempts to detect and explain the profounder reasons that presumably
led to these mistakes, as well as to identify and propound the new relations that replace the
wrong ones ofthe product exhaustion theorem. Last, it attempts to formulate the equilibrium
ofthewholeeconomicsystem(demand,supply,production,factorsof productionetc)
through a holistic-way equation system.
* Dimitrios Nomidis, Athens University of Economics and Business
National Technical University of Athens
E-mail: d.nomidis@yahoo.com
Author’s ID: https://ssrn.com/author=2246677
mailto:d.nomidis@yahoo.com
https://ssrn.com/author=2246677
Electronic copy available at: https://ssrn.com/abstract=3235427
2
1. Introduction
Asisknown,theneoclassicalmarginalproductivitytheoryofincomedistribution
states that under perfect competition the factors of production are rewarded with the value of
their marginal product. Also well known is the debate that took place at the end of 19 th and the
beginning of 20th century on this issue and especially on the question whether the product is
exactly exhausted by its distribution to the factorsof production according to the value of
their marginal products. More specifically, on the question whether the following equation is
valid:
q ( L , K ,….)=
∂ q
∂ L
L+
∂ q
∂ K
K +…. =MPL·L+MPK·K+…. where:
q (L , K,….) the quantity of production, a function of the production factors L (labor), K
(capital) and possibly other production factors (land etc).
L the quantity of labor employed in the production.
K the quantity of capital used in the production.
MPL=∂q/∂L the marginal product of labor of quantity L.
MPK=∂q/∂Κ the marginal product of capital of quantity Κ.
We shall remind this debate here very briefly1. Clark is considered the Father of this
idea (1889, 1891, 1899) (although germs of the theory were already contained in the Walras’s
book“ElementsofPureEconomics”,chapter36,1874,reissue1896).ButClarkdidnot
provideanymathematicalproofoftheproductexhaustionproblem.Thefirstattemptof
mathematical proof was done by Wicksteed (1894), but it was quite inadequate since it was
based on specific production functions, namely onhomogeneous of first degree production
functions,forwhichtheproofofthe productexhaustionproblemisbasedonasimple
application of the Euler’s theorem for mathematical functionshomogeneous of first degree.
Next, Wicksell (1900, 1901, 1902) gave a proof of theproduct exhaustion theorem for
the point where the production function presents the minimum average cost of production and
which constitutes the equilibrium point of the market under pefect competition in the long
run. At this point the production function -whichever the form of the production function is-
presents constant returns to scale and thus the properties of a homogeneous function of first
degree (i.e. if the factors of production increase proportionally, then production increases at
1Accounts of the debates surrounding marginal productivity abound. Those of Joan Robinson (1934), George Stigler (1941:
Ch. 12) and John Hicks (1932a,b) are probably the best. Also worthwhile are the accounts by Henry Schulz (1929), Dennis
H. Robertson (1931) and Paul Douglas (1934).
Electronic copy available at: https://ssrn.com/abstract=3235427
3
the same proportion), and consequently the Euler’s theorem can apply there. Walras (1874,
reissue1896)hadexpressedarationalesimilartothatofWicksell,butinamannerabit
confusing and not so explicit.
The resolution of Wicksell closed, in essence, the question of the product exhaustion
through its distribution to the factors of production on the basis of their marginal products and
constituted the mathematical (and at the same time ethical) foundation of the economic theory
of income distribution based on the marginal productivity of the production factors, which has
been scientifically accepted and established till today.
2. The Confutation of the Classic Theory of Competition and Distribution
Thepurposeofthispaperistodemonstratethattheabovetheoryofincome
distribution iswrong. Before we adduce the proof that follows in the next section, we must
mention that the mistake lies firstly in the fact that the equilibrium point of the market under
perfectcompetitiondoesnotlieattheminimumpointoftheaveragecostcurve(asthe
neoclassicaleconomictheory argues), where the Eulertheorem for theproductexhaustion
could be applied. As it is indisputably proved and extensively analyzed in the works of the
writer (Nomidis 2015a, 2015b, 2016a, 2016b, 2018a, 2018b), the market equilibrium point
under perfect competition is not determined by the intersection of the total supply and the
total demand (see Figure 1, point A), as the conventional theory argues (which intersection, in
fact, occurs at the minimum average cost), simply because that point does not maximize the
profits of the firms, whereas it should maximize them according to the conventional theory
itself (even if the economic profits -i.e. the profits beyond normal- become zero under perfect
competition).
Conversely, in order for this basic condition of free market, i.e. profits’ maximization,
to be accomplished, the market equilibrium point under perfect competition is determined by
the intersectionM of the total supply(marginal cost)and the marginal revenue that comes
from the total demand (and not the total demand itself), which gives the equilibrium point E.
Butthentheequilibriumdoesnottakeplaceattheminimumpointa oftheaveragecost
curve, as the conventional theory argues, but at a higher cost and smaller production (point e,
corresponding to the intersection of marginal cost LMC=SMC and marginal revenue mr, for
profitmaximization);whiletheindividualdemandcurveforthefirmdd (whichisnot
horizontal,astheneoclassicaltheorysays)becomes(withtheentryofnewfirmsdueto
Electronic copy available at: https://ssrn.com/abstract=3235427
4
perfect competition and the elimination of economic profit) tangent to the average cost curve
atthisequilibriumpoint.Thesethingsunavoidablyentailamonopolisticcharacterofthe
marketevenunderperfectcompetitionandzeroeconomicprofit,whichresultsinthe
equilibriumpointnotbeingattheminimumoftheaveragecostcurve,wheretheEuler’s
theorem for the product exhaustion could be applied.
3. The Mistake of the Conventional Distribution Theory
But even if we ignore all of the above that confute the conventional economic theory
for the equilibrium of the firm and the market and examine the issue of income distribution in
the framework of this conventional economic theory, even then the neoclassical distribution
theory based on the marginal productivity of the production factors is wrong. Because in order
to prove the product exhaustion theorem it applies a proportional variation of the production
factors, while it is known that the variations in the quantities of the production factors should
always follow the rule that equalizes the marginal ratio of technical substitution (MRTS) of
those inputs with the ratio of their prices (MRTS=MPL/MPK=w/r, where w the price-reward of
labor (wage) and r the price-reward of capital (rate of return)), which is not consistent with a
proportional variation of the inputs. More spesifically:
Let’s suppose that the production function contains as inputs the two basic factors of
production, labor and capital:
q=q ( L , K ) where:
q (L , K)the quantity of production as a function of the production factors L (labor) and
K (capital).
L the quantity of labor employed in the production.
K the quantity of capital used in the production.
As the conventional microeconomic theory itself teaches, when the entrepreneur varies
his production (e.g. he increases it), then he varies the quantities of the employed production
factors in a way that the ratio of their marginal products be always equal to the ratio of their
prices(i.e.theirrewards,whichareexogenouslydeterminedatthemarketsoflaborand
capital)inorderthat theminimumcostbealwaysobtained(andthereforeprofit
maximization) for the new production level. Specifically:
MPL/MPK = w/r where:
Electronic copy available at: https://ssrn.com/abstract=3235427
5
MPL=∂q/∂L the marginal product of labor of quantity L.
MPK=∂q/∂Κ the marginal product of capital of quantity K.
w the reward of labor.
r the reward of capital.
This rule establishes an interrelation between L and K, which in the cartesian level of L
and K generates the so called “expansion path”, which gives the combinations of L and K that
obtain the least average cost for each production level. It is this expansion path from where
the curve of the long run average cost (LAC) comes (see Figure 1), which gives the average
cost of production for each point of the expansion path, that is the least average cost for each
productionlevel(theterm“longrun”isintroducedtoshowthatfor eachvariationof the
production, some time is necessary for the production factors -and especially capital- to be
adjusted to the new production level). This curve of the long run average cost (LAC), which
givestheleastaveragecostforeachproductionlevel,hasaminimumpoint,wherethe
average cost of production becomes the minimum possible (minimum of minimum) among all
the combinationsL, K of the production factorsand the respective production levels. This
minimumpointofLACis,accordingtotheclassic(conventional)theory,theequilibrium
point of the firm and the market and at that point the production function indeed presents
constant returns to scale, that is it presents the properties of a homogeneous function of first
degree and consequently the Euler’s theorem for the product exhaustion could be applied.
ButthepreviouslymentionedcostminimizationconditionMPL/MPK=w/r doesnot
allowfortheEuler’stheoremfortheproductexhaustiontobeapplied,becausethelatter
requires a proportional change of the production factorswhile according to the former the
change of the production factors generally is not proportional. More analytically:
The product exhaustion theorem states that:
q=MPL·L+MPK·Kor
(1) 1=MP L
L
q
+MPK
K
q
Proof according to the neoclassical distribution theory
Supposethattheproductionfunctioncontainsasvariableinputsthetwobasic
production factors, labor (L) and capital (K):
Electronic copy available at: https://ssrn.com/abstract=3235427
6
q=q ( L , K )
dq=
∂ q
∂ L
dL+
∂ q
∂ K
dK or dq=MP L dL+MP K dK or
dq
q
=MP L
L
q
dL
L
+MP K
K
q
dK
K
or
(2) 1=MP L
L
q
dL / L
dq / q
+MP K
K
q
dK / K
dq / q
Fortheproofoftheproductexhaustiontheorem,then,initspreviousform(1),it
should hold:
dL/ L
dq / q
=1=
dK / K
dq / q
If we symbolize byC=C(q)the total cost of labor and capital, then at the minimum
point of the long run average cost curve (LAC=C/q) we have:
d (C / q)
dq
=0 or
C ΄ q−Cq ΄
q
2
=0or C ΄ q−Cq ΄ =0 and since q ΄ =
dq
dq
=1 :
C ΄ q−C=0or C ΄ =
C
q
that is:
dC
dq
=
C
q
or
dC
C
=
dq
q
Consequently, at the minimum point of LAC the previous relation (2) becomes:
(3) 1=MP L
L
q
dL / L
dC / C
+MP K
K
q
dK / K
dC /C
At this point the classic theory, in order to prove the product exhaustion theorem, says
thatifthevariationsoflaborandcapitalwereproportionaltotheirinitialquantities(i.e.
dL/L=dK/K), then:
dL
L
=
dK
K
=
wdL
wL
=
rdK
rK
=
wdL+rdK
wL+rK
=
dC
C
and therefore:
dL/ L
dC / C
=1=
dK / K
dC /C
Hence 1=MP L
L
q
dL / L
dC / C
+MP K
K
q
dK / K
dC /C
= MPL
L
q
+MP K
K
q
Electronic copy available at: https://ssrn.com/abstract=3235427
7
Ergoq=MP L L+MP K K
and in this way the classic theory prooves the product exhaustion theorem at the minimum
point of LAC.
Buthereaverysignificantmistake hasbeeninserted.Thevariationsoflaborand
capital cannot be proportional to their initial quantities (as they were considered), since they
mustmeettheruleofleastcostthroughoutthesubstitutionprocessbetweeninputs
(MPL/MPK=w/r),sothatthenewpointofproductionlieontheexpansionpath2.Inother
words, by simply applying the Euler’s theorem to prove the product exhaustion theorem at the
minimum point of the average cost curve LAC (as Wicksell and Walras did), we have not
takenintoconsiderationtheconditionofcostminimization,whileweshould(function
extremum under condition).
Therefore, the theorem of product exhaustion through its distribution to the production
factors on the basis of their marginal products does not hold even at the minimum point of the
average cost curve LAC of the long run equilibrium under perfect competition as the classic
(conventional) economic theory argues.
4. The Mistake of the Chapman’s Proof
Chapman (1906) attempted to present a diagrammatic proof of the product exhaustion
theorem (see Figure 2).
Heconsideredanindustryconsistingofn homogeneousagriculturalunits,eachof
which is cultivated by the same number of laborers L that are remunerated with their marginal
physical productaspresented inFigure2. The total labor remunerationisOAEL for each
agricultural unit. The total physical product of each unit is OMEL and consequently the land
revenue in each agricultural unit is AME. Chapman attempted to prove that this revenue, that
simply istheremainder of the totalproductOMEL after the subtraction of thetotal labor
remuneration OAEL (remunerated with its marginal product), constitutesalso the marginal
product of the land. To calculate, though, the marginal product of land, he did not increase
marginally the area of the agricultural unit keeping the number of its laborers constant, but he
consideredthatanewagriculturalunitisaddedintheindustryandkeptthenumberof
2 Marshall, already long before Hicks, had conceived of this concept by what he called “net marginal product”, which he
defined as the increase in output that arises from the employment of an extra unit of the varying factor after all the other
factors have been adjusted to their new optimal (i.e. profit maximizing ) levels (cf. Marshall, 1890: p.426-30).
Electronic copy available at: https://ssrn.com/abstract=3235427
8
laborers of the whole industry constant (L·n). This total number of laborers is now equally
distributed to n+1 firms of the industry, which thus decreases the previous number of laborers
and the product (AMCL΄) per agricultural unit. Chapman calculated the marginal product of
land as the difference between the total productions of the industry in the previous two states
with n+1 and n firms. The calculation in this way results in fact in:
marginal product of land = BMC+n·CDE
whichtendstoAMEwhennincreasesinfinitely,whichprovestheproductexhaustion
theorem.
But by considering the problem in this way, that is by considering the production to
consist of the production of n business units, Chapman has fallen in the error to have taken as
production function a function in which the total production, total labor and total land area are
allproportionaltothetotalnumberoffirmsn(agriculturalunits),thatisafunctionthat
clearly presents the distinctive feature (definition) of a homogeneous function of first degree
wheretheproportionateincreaseof theproductionfactorsincreasestheproductionby the
same proportion (with step of one business unit). Consequently, since the production function
is homogeneous of first degree, it is naturally expected the product exhaustion theorem to be
valid,duetotheEuler’stheoremwhichisvalidforeveryhomogeneousfunctionoffirst
degree.
5. The Mistake of the Hicks’s Proof
Hicks (1932, 1963) provesthe product exhaustion theorem at the point of minimum
cost oflong run equilibrium in his famous book “The Theory of Wages” (in the mathematical
appendix) without recourse to a constant returns to scale assumption (that is without recourse
to theEuler’s theorem), but with a direct differentiation of a production function of general
formandmakinguseoftheequalitybetweenpriceandaveragecostduetoperfect
competition. But he also falls in the same error, that is he does not take into consideration the
condition of cost minimization throughout the inputs’ substitution (MPL/MPK = w/r), while he
should (function extremum under condition).
The amazing thing in the case of Hicks is that thiscondition of cost minimization by
means of the substitutability between the production factors is one of the major contributions
of Hicks himself to the neoclassical Distribution Theory and is considered his hallmark in that
theory.Thus,itseemsaverystrangething forHicksnottotakeintoconsiderationthis
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9
condition, which is considered his discovery, in his proof of the product exhaustion theorem
in the mathematical appendix of his book “The Theory of Wages”. To the contrary, he actually
talks there (p.238) about proportionate variations of the production factors as output varies:
“If, as before, we assume that the prices of the factors are constant, and if we assume
further that the proportions in which the factors are employed remain unchanged as output
varies, we can construct a (very specialised) cost curve for the firm, giving the cost per unit of
producing various outputs.”
6. The complete Confutation of the Neoclassical Distribution Theory
In the case of a market of monopolistic character, as the perfect competition under the
new consideration is (Nomidis 2015a, 2015b, 2016a, 2016b, 2018a, 2018b), the conventional
(neoclassical) distribution theory argues that the factors of production are rewarded not with
the value of their marginal product(p·MP) but with the marginal revenue of theirmarginal
product(mr·MP)(where mr themarginalrevenueatthefirmlevel,seeFigure1),thus
undergoing a monopolistic exploitation by the entrepreneurs. It would be interesting here to
examine whether the product exhaustion theorem holds by applying this form of the marginal
productivity law in the new theory of equilibrium under perfect competition (which does not
take place at the minimum pointa of the average cost curve LAC but at the pointe, having
therefore a monopolistic character, see Figure 1).
It must, then, be proved that:
p·q=mr·MPL·L+mr·MPK·K
Due to the profit maximization by the entrepreneurs we havemr=MC (=SMC=LMC,
see Figure 1) and due to theperfect competition and zero profit we havep=c, wherec=C/q
the average cost of production (LAC). Consequently the above relation can be written:
(1) 1=MP L
L
q
MC
c
+MP K
K
q
MC
c
Proof according to the neoclassical distribution theory
Let the production function be: q=q ( L , K )
dq=
∂ q
∂ L
dL+
∂ q
∂ K
dK or dq=MP L dL+MP K dK or
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10
dq
q
=MP L
L
q
dL
L
+MP K
K
q
dK
K
or
(2) 1=MP L
L
q
dL / L
dq / q
+MP K
K
q
dK / K
dq / q
For (2) to be equivalent to (1), it should be proved that:
dL/ L
dq / q
=
MC
c
=
dK / K
dq/ q
or
dL
L
c=
dq
q
MCor
dL
L
C
q
=
dq
q
dC
dq
or
dL
L
=
dC
C
and likewise
dK
K
=
dC
C
If the variations of labor and capital were proportionate (i.e. dL/L=dK/K), then indeed:
dL
L
=
dK
K
=
wdL
wL
=
rdK
rK
=
wdL+rdK
wL+rK
=
dC
C
and consequently the initial relation (1) would be fulfilled and hence the product exhaustion
theorem would hold (with the form of the marginal revenue product now).
But the variations of labor and capital cannot be proportionate,since they must meet
the rule of least cost throughout the substitution process between inputs (MPL/MPK = w/r), so
that the new point of production lie on the expansion path (unless on the expansion path holds
dL/L=dK/K, butthen theproductionfunctionislinearly homogeneous)or, in otherwords,
duringthevariationsofinputs wemusttakeintoconsiderationtheconditionofcost
minimization.
Therefore,thetheoremofproductexhaustionbyitsdistributiontothefactorsof
production on the basis of their marginal revenue product (mr·MP) does not hold in this case
of monopolistic-character perfect competition either, unlike what the classic (conventional)
economic theory says.
7. The Profounder Mistake of the Distribution Theory
Nevertheless, normally and logically theproduct exhaustion theorem should hold at
the point of long run equilibrium of a competitive economy, where the profit is zero and the
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11
value of product is distributed to the factors of production by means of their rewards. Also, for
the maximization of profit, the reward of a production factor does indeed meet the rule of its
marginalproductivityandequalstheproductMP·mr ofitsmarginalproducttimesthe
marginal revenue (which equals the price of product in perfect competition due to horizontal
individual demand curve for the firm, according to the erroneous neoclassical view, but we
don’tdiscussthisproblemnow).Wheredidgowrong,then,theneoclassicaltheoryof
Distribution when it says for the equilibrium point in perfect competition:
p·q=w·L+r·K = mr·MPL·L+mr·MPK·K (general expression)or
p·q=w·L+r·K = p·MPL·L + p·MPK·K (for horizontal demand curve of the firm),
since this relation should bevalid,almostby definition,attheequilibriumpointofperfect
competition with zero profit?
Theprofounder mistakeoftheneoclassicaltheoryofDistributiononthebasisof
marginalproductivityoftheproductionfactorsisthattheprincipleoftherewardofa
production factor based on its marginal productivity is valid only when this production factor
is the sole variable input in the production process, while all the other factors that participate
in the production remain fixed and with fixed cost, which could probably occur mainly in the
shortrun.Howevereveninthatcase,only thevariableinputwouldberewardedwithits
marginalproduct,whilethefixedcostsfortherewardsoftheotherfactorsofproduction
would not meet, in general, the rule of their marginal productivities. That is, the fixed cost of
each fixed factor of production would not equal, in general, the product of the fixed quantity
ofthefactortimesitsmarginalproduct,which,besides,varieswiththefinalequilibrium
quantity of the variable factor.
Namely, the profounder mistake of the neoclassical theory of Distribution on the basis
of marginal productivity of the production factors lies in the fact that it erroneously extented
the law for the reward of a production factor based on its marginal productivity, which is valid
only when this production factor is the sole variable input in the production while all the other
factors remain fixed and with fixed cost, to the case where all the factors of production vary at
the same time, which certainly occurs at least in the long run. More exhaustively, in the above
expressionsthe marginal productsof the production factors(MPL, MPK etc) are the partial
derivatives of the production function with regard to each production factor when all the other
production factors remain constant, which though could perhaps occur in the short run but
certainlydoesnotoccurinthelongrun. For,thepartialderivativeimpliesthemarginal
Electronic copy available at: https://ssrn.com/abstract=3235427
12
variation of a factor of production, which in the production process automatically entails the
variation of all the other factors of production at least in the long run. For this reason and
since the factors of production vary at the same time (especially in the long run), the previous
expressions of the product exhaustion theorem are not valid. They could be valid if only one
factorofproductionexisted(e.g.labor,whereuponitwouldindeedholdthat
p·q=w·L=mr·MPL·L)oriftheotherfactorsofproductionremainedconstantandwithout
reward. The above expressions could also be valid if MPL, MPKetc expressed the marginal
products under the concurrent variation of all the production factors (and exactly under the
variation conditionMPL/w=MPK/r=….for the minimization of the production cost), which
though is not mathematically feasible3.
8. Rebuilding the Distribution Theory
All the above confute thoroughly the neoclassical Distribution theory and certainly the
famous theorem of product exhaustion by its distribution to the factors of production on the
basis of their marginal productivity. It arises then the question:
Which are the new relations that replace the invalid ones and express the equilibrium
of the whole economic system?
Firstly, with regard to the product exhaustion theorem, which constitutes the core of the
Income Distribution theory, this takes now the form (in perfect competition without profit):
p·q = w·L+r·K +…..
accompanied by the condition of inputs’ substitution for the minimization of the production
cost:
MPL/w = MPK/r = …..
which leads to a relationship between the factors of production (e.g. L=f(K) or L=f(K,q)).
In the above relations the rewards of the production factors (w, r etc) are determined of
course (as in the conventional theory) exogenously in the markets of the production factors
(basedontheirsupplyanddemand),buttheproductexhaustiontheorembasedonthe
marginal productivity of the production factors is not valid in the case of multiple production
3Marshall had recognized that the marginal product concept can be a bit misleading and for this reason to solve the problem
(cf. Hicks 1932: p12-15, Machlup 1937) he proposed the concept of “net marginal product”, which he defined as the increase
in output that arises from the employment of an extra unit of the varying factor after all the other factors have been adjusted
to their new optimal (i.e. profit maximizing ) levels (see also footnote 2).
Electronic copy available at: https://ssrn.com/abstract=3235427
13
factors (which almost always occurs in praxis).
Withregardtotheequilibriumofthewholeeconomicsystem(demand,supply,
production,factorsofproductionetc)underperfectcompetitioninthelongrun,thisis
expressed in the new theory by the following equations’ system (for simplification we only
consider the basic two production factors, labor and capital) (see also Figure 1):
(1) Demand Function: p=p(Q)=p(nq)
where Q the demand(=production) for the whole market,q thedemand(=production) for
each firm and n the number of firms in perfect competition with zero profit.
Let for simplicity be: p=a-bQ=a-bnq
(2) Production Function: q=q ( L , K )
(3) Condition of Inputs’ Substitution for the minimization of cost:
MPL/w= MPK/r or
∂ q /∂ L
w
=
∂ q /∂ K
r
(4) Zero Profit:p·q = w·L+r·K or (a-bnq)·q = w·L+r·K
(5) Profit Maximization: mr=LMC or a−2bnq=
d ( wL+rK )
dq
The above five relations constitute a system of five equations that determine the point
of long run equilibrium (L, K, p, q, n).
9. Conclusions
This paper demonstrates that the proofs which were presented to support the product
exhaustion theorem are mistaken and consequently the theory of income distribution on the
basis of the marginal productivity of the production factors is wrong.
Regardlessofthishowever,firstof all theproductexhaustiontheoremisnotvalid
becausetheequilibriumpointofthemarketunderperfectcompetitiondoesnotlieatthe
minimumpointoftheaveragecostcurve(astheconventionaleconomictheoryargues),
where the Euler’s theorem for the product exhaustion could be applied. As it is extensively
analyzed in the works of the writer (Nomidis 2015a, 2015b, 2016a, 2016b, 2018a, 2018b), the
market equilibrium point under perfect competition is not determined by the intersection of
the total supply and the total demand, as the conventional theory argues (which intersection,
Electronic copy available at: https://ssrn.com/abstract=3235427
14
in fact, occurs at the minimum average cost), simply because that point does not maximize the
profits of the firms.
But even if we ignore the above consideration that confutes the conventional economic
theory and examine the issue of income distribution in the framework of this conventional
theory,eventhentheneoclassicaltheoryofdistribution onthebasisofthemarginal
productivityoftheproductionfactorsiswrong.Becauseinordertoprovetheproduct
exhaustion theorem it applies a proportional variation of the production factors, while it is
known that the variations in the quantities of the production factors should always follow the
rule that equalizes the marginal ratio of technical substitution (MRTS) of those inputs with the
ratio of their prices (MRTS=MPL/MPK=w/r, wherew the price-reward of labor (wage) andr
theprice-rewardofcapital(rateofreturn)),whichisnotconsistentwithaproportional
variation of the inputs.
Theprofounder mistake,however,oftheneoclassicaltheory ofDistributiononthe
basis of the marginal productivity of the production factors lies in the fact that it erroneously
extentedthelawforthereward ofaproductionfactorbasedon itsmarginalproductivity,
which is valid only when this production factor is the sole variable input in the production
while all the other factors remain fixed and with fixed cost, to the case where all the factors of
production vary at the same time, which certainly occurs at least in the long run.
After all of the above, theproduct exhaustion theorem, which constitutes the core of
the Income Distribution theory, takes now the form (in perfect competition without profit):
p·q = w·L+r·K+…..
accompanied by the condition of inputs’ substitution for the minimization of the production
cost: MPL/w = MPK/r = …..
which leads to a relationship between the factors of production (e.g. L=f(K) or L=f(K,q)).
Electronic copy available at: https://ssrn.com/abstract=3235427
15
10. Figures
Figure 1
Long run Equilibrium under Perfect Competition
The long run equilibrium under perfect competition does not take place at the point A (intersection of
total supply and total demand), as the neoclassical theory argues, but at the point E, which maximizes
the profits of firms (as it corresponds to the intersection M of the total supply (marginal cost) and the
marginal revenue MR that comes from the total demand).
Correspondingly at firm level (left graph), the equilibrium does not take place at the minimum point a
of the average cost curve LAC, as the neoclassical theory argues, but at the point e, which maximizes
the profit of firm (as it corresponds to the intersection m of the marginal cost (in the short run SMC
and in the long run LMC) and the marginal revenue mr that comes from the individual demand dd of
the firm). While the individual demand dd of the firm (which is not horizontal, as the neoclassical
theory argues) becomes (by the entry of new firms due to perfect competition and the zeroing of the
economic profit) tangent to the average cost curve LAC at this equilibrium point.
All of them imply unavoidably a monopolistic character of the market even under perfect competition
and zero economic profit, with the consequence for the equilibrium point not to lie at the minimum
point of the average cost curve LAC where the Euler theorem for the product exhaustion could be
applied.
LAC
d
S
M
C
e
d
q
p
q
LMC
SAC
m
r
SAC
S
M
C
D
D
Q Q
M
R
p
E
S
S
M
A
pp
m
a
Electronic copy available at: https://ssrn.com/abstract=3235427
16
Figure 2
The diagrammatic proof of Chapman for the product exhaustion theorem
Chapman proves by means of a diagram that the marginal product of land in an agricultural
unit which employs L laborers that are remunerated with their marginal product MPL is the remainder
of the total product OMEL after the subtraction of the total labor remuneration OAEL, that is the area
AME, and in this way he provesthe product exhaustion theorem. To calculate, though, the marginal
product of land, he did not increase marginally the area of the agricultural unit keeping the number of
its laborers constant, but he considered that a new agricultural unit is added in the industry (consisting
of n agricultural units) and kept the number of laborers of the whole industry constant (L·n).
But by considering the problem in this way, that is by considering the production to consist of
theproductionofnbusinessunits,Chapmanhasfallenintheerrortohavetakenasproduction
function a function in which the total production, total labor and total land area are all proportional to
the total number of firms n, that is a function that clearly presents the distinctive feature (definition) of
ahomogeneousfunction of firstdegreewhere theproportionate increaseoftheproductionfactors
increases the production by the same proportion.
O
DC
E
LL΄
A
B
M
P
MP
L
MPL
L
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17
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