lted1hq4oalpwsji 4 y 5. integration of economic systems and ecosystems a dynamic

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INTEGRATION OF ECONOMIC SYSTEMS AND ECOSYSTEMS: A DYNAMIC MODEL APPLIED TO YELLOWSTONE LAKE

byChad E. Settle

A dissertation submitted to the Department o f Economics and Finance and The Graduate School o f The University of Wyoming in partial fulfillment of the requirements for the

degree o f

DOCTOR OF PHILOSOPHY in

ECONOMICS

Laramie, Wyoming December, 2000


UMI Number. 9993742

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To The Graduate School:

The members of the Committee approve the thesis of Chad E. Settle presented on September 11. 2000.

Jason F. Shogren, Chairman

Thomas D. Crocker

Robert Godby

John T. Tschirhart

ayward

APPROVED:

Phillips, Chair, DepartmentOwen Phillips, Chair, Department o f Economics and Finance

Stephen E. Williams, Dean, The Graduate School


Settle, Chad E., Integration of Economic Systems and Ecosystems: A Dynamic Model Applied to Yellowstone Lake. Ph.D., Department o f Economics and Finance, December, 2000.

This paper builds a general modeling framework to address problems o f

interacting organisms, uses that framework to model a specific problem within the

Yellowstone Lake ecosystem in Yellowstone National Park, and simulates the theoretical

model using Stella II software to explore alternative management schemes.

A general modeling framework is developed which is flexible enough to model

several different ecosystem problems using the same technique. The requirement for

using this technique is a relationship between organisms, either animal or plant, such that

one influences the abundance of the other.

The specific problem analyzed in this paper is the impact from a fish species in

Yellowstone Lake, lake trout. Lake trout are an exotic species that prey upon the native

and popular species in Yellowstone Lake, cutthroat trout. The expected impact o f lake

trout is great, potentially affecting multiple species in and around the lake. The focus of

this research is twofold: first, determine the importance o f integrating economic systems

and ecosystems; and second, explore the optimal allocation of funds toward the control of

lake trout.

Optimal control theory determines efficient harvesting o f lake trout. Stella II

software uses the resulting optimal paths determined in the general case to build the

simulation model. The model is also run both with and without interactions between the

economic system and the ecosystem to determine the importance o f explicitly modeling

those interactions. Both the steady state solutions and the optimal time path o f extraction

are analyzed for the control of lake trout.

1


Acknowledgements

To my wonderful wife, Noelle, for her continued support. She is the wonder o f my life and makes everything I do better and more fulfilling.

And,

to my committee chair, Jason Shogren, for allowing me to take on such an enormous project and giving me the guidance to finish it.

And,

to my mother, Sigrid Settle, my sister, T. Amber Settle, and my grandmother, Blanche Barnett. They deserve credit for giving me the strength and wisdom to succeed in life, for showing me how a person can overcome any obstacle with determination and hard work, and for allowing me to see how long the learning process can be if you are not afraid to keep working at it.

And,

to Tom Crocker, Rob Godby, Greg Hayward, and John Tschirhart, the members of my committee for helping me along the way and making sure my work had the broad perspective to go along with the narrow problem I was tackling.

And,

to Greg Hayward, Paul Stapp and Chris Nations for showing how economists and ecologists can work together successfully and for helping me build the ecological model for my simulations.

And,

to Wayne Hubert for helping me with specific fish biology questions that arose duringthis project.

ii


Table of Contents

Chapter I: Introduction..................................................................................................... 1

Chapter II: Major Questions That Need Answers and the State o f the Current

Literature............................................................................................................................. 6

Chapter HI: Explanation o f General Modeling Technique..........................................32

Chapter IV: Complete Yellowstone Lake M odel.........................................................41

Chapter V: Internet Experiment.................................................................................... 75

Chapter VI: Simulation M odel..................................................................................... 105

Chapter VTI: Conclusion...............................................................................................173

Appendix I: Internet Experiment Screen Captures.................................................... 177

Appendix II: Stella Model C o d e ................................................................................. 214


List of Tables

Table 1: Familiarity o f Participants to the Lake Trout Introduction..............................90

Table 2 : Participants Perceptions o f the Seriousness o f the Lake Trout

Introduction.......................................................................................................................... 91

Table 3 : Participants Preference for F ish ........................................................................93

Table 4: Percentage o f Particpants who would be affected by seeing attractions of

the park ..................................................................................................................................95

Table 5: Regression output to determine values for seeing species in Yellowstone

National P a rk ..................................................................................................................... 101

Table 6: Data Collected with Sources for Species-Species Interaction..................... 126

Table 7: Values o f being able to see the species and attractions in the p a rk 128

Table 8: Data Collected With Sources for Species-Human Interaction......................130

Table 9: Cost o f Road Work in Yellowstone National P a rk .........................................137

Table 10. Resulting cutthroat trout populations with and without feedbacks............140

Table 11: Amount o f wedge created by relaxing assumptions................................... 166

Table 12 : Fixed budgets, total value o f the park, length o f survival and level of steady

state cutthroat trout population....................................................................................... 169

iv

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List of Figures

Figure 1: Preference Reversals over T im e.................................................................... 100

Figure 2: Value o f Wildlife Lotteries over T im e.......................................................... 104

Figure 3: System Without Lake Trout (No Human Response)............................... 143

Figure 4: System Without Lake Trout (Human R esponse)....................................... 145

Figure 5: System Without National Park Service Effort

(No Human Response)................................................................................................... 148

Figure 6: System Without National Park Service Effort (Human Response) 151

Figure 7: System With Constant National Park Service Effort

(No Human Response).................................................................................................... 154

Figure 8: System With Constant National Park Service Effort (Human Response).. 156

Figure 9. System With Optimal National Park Service Effort

(No Human Response)....................................................................................................... 159

Figure 10: System With Optimal National Park Service (Human Response) 161

v


List of Diagrams

Diagram 1: Lake Trout Flow Diagram...........................................................................107

Diagram 2: Cutthroat Trout Flow Diagram...................................................................110

Diagram 3: Birds o f Prey Flow Diagram...................................................................... 113

Diagram 4: Grizzly Bear Flow Diagram.........................................................................115

Diagram 5: Human Activity Diagram.............................................................................117

Diagram 6: Human Utility Diagram ............................................................................... 119

Diagram 7: Complete Ecosystem Diagram.................................................................... 122

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Chapter I: Introduction

A small island off the coast o f Madagascar, Mauritius, is well known for a man-

made tragedy. Mauritius was the site o f the earliest known and most well publicized man-

made extinction, the Dodo (Raphus cucullatus). The slow-footed Dodo was easy prey to

both man and many types o f exotic beasts brought to the island by man: dogs, cats,

monkeys, rats, and pigs. Humans hunted the Dodo for pleasure; dogs killed the large

flightless bird; and the other animals made meals o f the bird eggs. As a result o f both this

and the island becoming a Dutch colony in 1644, the Dodo was extinct by 1680 (Day,

1981). Mans desire to kill the bird and his introduction o f exotic species (dogs, cats,

monkeys, rats and pigs) to the island led to the demise o f the Dodo.

The Dodo is by no means the only species that has been affected by exotic

invaders. The damage to species has extended to aquatic life forms as well. Many fish are

now extinct due to mans actions. One case is of particular importance since it has a direct

parallel with this research. Lake trout were introduced into Lake Titicaca by the U.S. Fish

and Wildlife Service and ended up killing off the Lake Titicaca Orestias, the native species

o f the lake (Day, 1981). The end result o f the introduction o f lake trout into Lake Titicaca

was the elimination o f the native species.

Man now faces a similar problem in Yellowstone Lake in Yellowstone National

Park. Lake trout were first discovered in Yellowstone Lake in July o f 1994. Lake trout are

an exotic species to Yellowstone Lake and a predator o f the popular and native species,

cutthroat trout. Cutthroat trout are a popular species for fishermen and the main food

source for predators such as ospreys, white pelicans, river otter and an important seasonal

1


food source for grizzly bears. The expected impact from the introduction o f lake trout into

the Yellowstone Lake ecosystem is large. Some conceptual models suggest lake trout

populations will increase substantially while cutthroat decline (Stapp and Hayward, 1999).

The ecosystem impact will not end with the reduced number of cutthroat trout; ospreys,

white pelicans and river otters will see their main food source diminish which may in turn

reduce the numbers of those species found around Yellowstone Lake (Varley and

Schullery, 1995).

Mans impact on the ecosystem is not limited to introducing exotic invaders.

Humans interact with ecosystems on a daily basis and through these interactions alter

ecosystem structure and function. The ecosystem and the economic system are linked -

changes to the ecosystem will result in changes to the economic system and these changes

to the economic system will result in further changes to the ecosystem.

As a result of this interdependence, changes in the populations of species will

impact tourism in Yellowstone National Park. Several people come to Yellowstone to

fish, go bird watching, and see grizzly bears. A few visitors may stop coming to the park,

reduce the frequency of their visits or will at least have diminished enjoyment o f the park

as a result of the changing conditions within the ecosystem. Yellowstone National Park

managers may wish to control the lake trout population to help visitors enjoy the park.

In addition, Yellowstone National Park managers may wish to keep a baseline, or

minimum number, o f specific species alive including cutthroat trout. Cutthroat trout have

been proposed for endangered species protection, which might force park managers to

focus on keeping a baseline population of cutthrout trout. Even if cutthroat trout werent

up for endangered species protection, one o f the purposes o f the park is to preserve the

2


integrity of the greater Yellowstone ecosystem. Maintaining viable species populations

may be part o f that management strategy.

National Park management strategies were laid out in two crucial acts. Land was

first designated for creating Yellowstone National Park under the Yellowstone National

Park Act o f 1872 and the rules for managing the park were laid out in the National Park

Service Act o f 1916 (Executivesummary, 2000). The National Park Service Act o f 1916

specifically calls for two overriding goals o f the management o f National Parks - first, to

provide for the enjoyment o f the park by its visitors; and second, to leave them

unimpaired for the enjoyment o f future generations (NPS Act, 2000), (Preserve, 2000).

These two goals seem in at least partial conflict with each other. One stresses the

availability o f the park for the enjoyment o f visitors while the other stresses a sustainability

criterion for park managers. It is expected managers will both allow for the enjoyment of

current visitors and the enjoyment of future visitors. This conflict is further exacerbated by

the strategic plan of Yellowstone National Park, which has two main goal categories - one

to preserve the Yellowstone National Park resource so it is maintained in good

condition; the other to provide for the public use and enjoyment so visitors...enjoy and

are satisfied with (their)... opportunities (Strategicplan, 2000). The goal o f the park

managers is to simultaneously allow the current generation o f visitors to enjoy the park,

while also providing for the enjoyment of future generations.

Along these lines, park managers play a similar role as that o f a typical social

planner dealing with a common property resource (Wade, 1987). They are placed in a role

to insure the resources of the park are used at optimal levels for both current and future

generations, given their constraints. One o f those constraints with respect to National

3


Parks is a fixed budget' (Strategicplan, 2000). The managers must decide how to allocate

these limited funds across various activities to maximize the benefits to current and future

generations. One way to achieve this goal is for managers to maximize the

intergenerational utility of visitors (not helping one generation at the expense o f another)

given a fixed budget. This sets up naturally as a budget constrained utility maximization

problem.

While the details of this maximization problem are left for chapter IV, this dynamic

maximization problem has several advantages. First, this model makes explicit the links

between the economic system and the ecosystem. The two systems are connected and

changes in each system will impact the other system. Ignoring these links assumes changes

in one system will not lead to changes in the other. In order to capture the effects of the

links, these links need to be specifically modeled.

Second, dynamic modeling makes it possible to measure differences between two

specific equilibria and monetize differences that occur in the time period between those

two equilibria. A dynamic model measures the utility gained in the intermediate period

while the system is in between two equilibria. By measuring this interequilibrium behavior,

the length o f time between the equilibrium is not important. Since aquatic ecosystems in

general often take several decades and sometimes even centuries to achieve a new

equilibrium and since Yellowstone Lake is expected to take several centuries to do so, the

activity between equilibrium is of great importance in this instance.

Finally, the modeling technique is flexible enough to handle a variety o f issues.

Many of the assumptions of the model can easily be changed and the number o f species

included in the model and ways the average visitor can interact with the ecosystem is

4


flexible. This flexibility allows many potential policy problems to be handled using this

technique. While it has its limitations, this model is both unique and flexible.

This research is part o f a large project including economists and ecologists: Todd

Cherry, Tom Crocker, Rob Godby, Greg Hayward, Wayne Hubert, Chris Nations, Jason

Shogren, Paul Stapp, and John Tschirhart all contributed to both this work and the project

as a whole. Part o f this group work is my research, which creates an analytical framework

representing the management issues facing Yellowstone National Park managers. I

develop an economic model, build an ecosystem model following work done by Greg

Hayward, Chris Nations and Paul Stapp, and then integrate the two into one modeling

framework that incorporates both flows inside each system and flows between the two

systems. These links between the two systems are often underplayed in the literature, but

are important since these interactions describe how both humans and other animal species

react to changes in the ecosystem. Fully incorporating these links makes the model a more

complete and accurate representation o f the problem facing National Park Service

managers. This research answers a few key questions. First, does integrating the economic

system and the ecosystem using explicit links between the two systems yield significantly

different results than ignoring these links? Second, is there any economic reason for man

to intervene in the Yellowstone Lake ecosystem?

5


Chapter II: Questions That Need Answers and the State of the Current Literature

This research combines an ecosystem model and an economic model in one

framework. My motivation is the current problem facing National Park Service managers

in Yellowstone National Park with regard to management of lake trout in Yellowstone

Lake. Although this motivation is a specific issue, I build a modeling framework that is a

general approach and can be used to analyze several types of problems. Portions o f this

modeling framework have been explored at length in the literature and others have not.

Creating a model that incorporates a fishery into an economic model has been explored in

depth, however most of these models deal with a commercial fishery and only 1 fish

species is considered. My model not only explores a fishery, but a recreational fishery with

an exotic predator. Fewer models have been built that deal with recreational fisheries or

competing species. In addition, this model also deals with a specific problem in

Yellowstone National Park and builds an ecosystem model representing the interactions

between lake trout and cutthroat trout in Yellowstone Lake. For this reason, papers that

deal directly with Yellowstone National Park or deal with ecological topics related to

species in Yellowstone National Park may have already addressed issues I focus on in this

modeling framework. To guarantee that this research is both unique and productive, I

make sure that this dissertation addresses issues that have not been examined before or it

uses previous work to build a new tool for analyzing ecosystem problems.

A great deal of literature has been devoted to fisheries and recreation problems.

Issues from ownership, regulation o f the fishery and even stocking of the fishery have all

been discussed. Within this vast literature, only a few attempts at combining an economic

6


model and an ecosystem model in the same general framework have been made. Within

this class o f models, my research is unique by incorporating three important features in

one model. First, my model uses a dynamic framework that can incorporate the behavior

that takes place between two equilibria. Static models can only account for differences

between two equilibria themselves. Using a dynamic model, the activity along the path

between two equilibria can be quantified. Second, my work focuses on the direct

regulation o f an animal species. Previous attempts at regulation focused attention on

regulation o f the economic agents behavior by reducing mans impact alone. This work

allows for species to be directly controlled by allowing the park managers to kill lake trout

in an effort to alleviate pressure on cutthroat trout - A practice already being done in

Yellowstone National Park. Finally, my research allows visitors to the park to both act

myopically and to have bounded rationality of the problem facing the ecosystem - this

model does not have to assume visitors wish to maximize the intergenerational utility o f

everyone who will ever visit the park nor do they have the information to do so. Many

previous models assume fishermen have knowledge of the consequences o f their actions.

In my model, the sole person that has full information is the park manager. The park

manager is in the sole position to take action so that the average visitor to the park will

maximize his utility. Combining these three features in one model is unique in this

literature and makes this research original. In addition, this modeling technique is also

flexible and may have future applications to a variety o f ecosystem problems.

Since a great deal o f work has been done in this literature, I need to determine

what is original in my research and what has already been done. To make this distinction, I

ask 4 questions of the literature.

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1) What has been accomplished in previous attempts to integrate economic systems and

ecosystems?

2) What are the main themes already addressed in the economic fisheries literature?

3) Within the fisheries literature, have any of the features of my research been addressed?

4) Has research specific to Yellowstone National Park or ecological research touched

issues relevant to this paper?

5) What does the literature have to say about exotic invaders?

Answering these 4 questions gives insight into both the uniqueness and relevance

of my research. First, what has already been accomplished in integration of economic and

ecosystems? To see if my research is extending the literature in a fruitful direction, I need

to make sure that what I plan to do has not already been done. Second, what major

themes exist in the fisheries literature? If my attempt to integrate is heading in a fruitful

direction, I next need to see if the fisheries literature has already addressed integration or

the activity o f dynamic systems as one o f its main themes. Third, beyond integration and

dynamic activity, what themes o f my research have already been addressed? Assuming the

work is original with respect to integration and dynamic processes, I need to next see if

the other main themes of my research are as well. Finally, since the specific problem

8


motivating this research deals with a fishery in Yellowstone National Park, I need to

determine what ecological research or other research pertaining to Yellowstone National

Park has already accomplished.

What has been accomplished in previous attempts to integrate economic systems and

ecosystems?

Since this model integrates ecosystem modeling and economic modeling in one

framework, I start by discussing previous attempts to combine the two. Previous attempts

to combine the two in one model have taken modest steps forward. Integrated work

combining ecosystems and economic systems was first done by Bruce Hannon (Hannon,

1983; Hannon, 1976; Hannon, 1979). Hannons work used input-output analysis to model

an ecosystem in a similar fashion to how input-output models have been used to analyze

entire economies or sectors within those economies. The flow o f resources between the

components o f an ecosystem are fixed coefficients. No change in behavior, either by

species or humans is assumed. The interdependencies of the two systems are not modeled.

The use of input-output models to describe ecosystems has been used in other papers as

well, (Ayres and Kneese, 1969; Isard, 1972; Anas, 1988). A major challenge facing

economists is to integrate fully the ecosystem and the economic system by allowing

changes in each system to affect the other via feedback loops. A feedback loop shows how

each system will be affected by changes in the other system. These changes are an

9


important part o f system interactions not addressed with fixed coefficient input-output

models.

The challenge now is to build models that specifically account for feedback loops.

This is one o f many challenges facing economists and ecologists who attempt to work

together though. One recent paper addresses problems associated with the integration of

economics and ecology. Horst (1998) focuses on the problems o f not integrating. This

paper breaks down the most frequently used approach in the literature and discusses the

limitations and problems with this approach. In his typical model, the impacts on the

ecological system are determined in a static approach with no adaptive behavior. The links

between the economic system and ecosystem are ignored in his typical model. Ecological

impacts are translated into economic impacts to determine the expected damages from the

disturbance. This view assumes changes in the ecosystem will alter the value of the

economic system, but the economic system will not alter its actions in response to these

changes. This approach ignores the major component o f a truly integrated approach,

which is the explicit links between the two systems. In his fully integrated modeling

approach, Horst shows that intra-system relationships exist, matter, and that economic

agents will adapt to the changing environment. These feedbacks are an important and

necessary part o f a truly integrated system. While the technical model in Horst is basic, the

important issues are discussed. Horsts paper is a call for change to the typical modeling

done in this area.

This call for a change is not limited to work in economics. Other social scientists

have made a similar call. In a two-part paper, Gary Machlis and Jo Ellen Force make the

same plea for a change in the common approach to ecological problems (Machlis et al,

10


1997), (Force and Machlis, 1997). These papers do not lay out a formal model in the way

that Horst did, but they reiterate the point economic systems and ecosystems are not

distinct from each other. The two systems must be integrated to more accurately represent

an ecosystem problem.

We live in a complex world. As a result, we divide the world into smaller parts by

creating different disciplines that each study a smaller part o f the world. However, this

approach comes with a cost. That cost is a misspecified system. Reducing this

specification problem requires creating explicit links between two disciplines that allows

knowledge from multiple disciplines to be used in one model.

Still other papers show the damage that can be caused by failing to integrate the

ecosystem with the economic system. One result o f this work was to show how grossly

adjusted equilibrium outcomes can be by failing to integrate a system (Swallow, 1990;

Swallow, 1993; Swallow, 1996). Both papers indicate that equilibrium conditions are

vastly different when the ecosystem is integrated into the economic system. Failing to do

so can yield misleading results by not taking into account how changes in one system can

affect behavior and outcomes in the other.

A good model done in integration o f economics and ecology is done by Crocker

Tschirhart (Crocker and Tschirhart, 1992). Their paper, Ecosystems, Externalities, and

Economies, which builds on previous work (Crocker and Tschirhart, 1987), combines an

ecosystem model and an economic model in the same integrated general equilibrium

framework. Agents in both systems optimize a specific objective over a given choice

variable. Species maximize their stored energy while humans choose to divide their labor

between cropping different species for manufactured goods production to maximize

11


utility. An equilibrium can be achieved for both systems if they function alone. The

inclusion of both systems will also yield an equilibrium, an integrated equilibrium, and is

the way to fully describe an ecosystem problem. This paper is a fully integrated model in

the literature.

Under the umbrella o f integration o f economic systems and ecosystems, steps

forward have been achieved first using one-way feedbacks and now recognizing we need

to use feedback loops in both directions. Previous attempts use one-way feedback from

either an ecosystem to an economic system or from an economic system to an ecosystem.

The important distinction that needs to be made is the interrelationship between the two

systems. Feedbacks work both directions and those feedbacks need to be incorporated in

order to fully describe the relationship. The only paper that has completely addressed these

feedbacks thus far is done by Tom Crocker and John Tshirhart (Crocker and Tschirhart,

1992). Work addressing these feedbacks is limited and leaves much room for entry.

Research that recognizes these feedback loops are not only important, but the

explicit modeling o f these loops needs to be done. Since this research explicitly models the

feedback loops between both the economic system and the ecosystem, it extends the

literature in a positive direction.

What are the main themes already addressed in the economic fisheries literature?

The economics o f fisheries is an old field. Fisheries articles have been published for

several decades now, starting in 1954, when a basic model was developed to determine

how effort levels will be determined in a common property fishery (Gordon, 1954).

12


Already by 1957, economists were studying differences that can arise between a model

using the growth o f a single fish population (Beverton and Holt, 1957) and the growth of

a single fish biomass (Schaefer, 1957). The early literature focused on simple fishery

problems and the literature fell out o f favor for almost 20 years until a resurgence in the

1970s.

Several articles dedicated to this field can be found in the last 25 years, however

most share the narrow focus o f common property ownership of a fishery. Multiple papers

by Sandler and others are among the long list (Comes and Sandler, 1983), (Comes et al,

1986). They examined problems dealing with simple common property ownership and the

overexploitation o f fisheries, commons and the optimal number o f firms for a single

species fishery, and even introduced harvest uncertainty into the commons problem

(Sandler and Sterbenz, 1990). Elinor Ostrom has done a vast amount o f work that focuses

on the issue of commons and the problems that can arise from commons ownership

(Ostrom et al, 1994). Unfortunately, most of these papers deal with commons and how it

relates to irrigation (Ostrom et al, 1993), (Ostrom and Gardner, 1993), (Ostrom, 1992) or

how commons problems can be overcome by changing the type of ownership (Ostrom and

Walker, 1991), (Ostrom et al, 1992). Common property ownership is not tied directly to

my paper and, as such, I will not delve further into this literature.

Despite the age and breadth of the commons literature, work in the area is still

active. A recent paper has taken the problem and added a spatial component to it

(Sanchirico and Wilen, 1999). Different biological patches that have unique ecological

features within each patch and have interactions between those patches are discussed. The

biological aspects within a patch and between patches are both important. While adding

13


this spatial component is a key addition to the literature, space is not the focus o f my

research and applications o f spatial dimensions are not addressed in my work.

Commons papers are a narrow focus for the broader problem o f ownership o f a

fishery. The problem o f ownership has been studied at length in the literature and dates

back to the 1950s (Gordon, 1954). These issues include a range from open access versus

private ownership (Weitzman, 1974) to the amount o f rent able to be captured in different

ownership schemes (Grafton, 1995). Ownership issues are a main focus o f this literature,

but not my research. For this reason, I do not further explore this issue in the literature.

Optimal ownership o f a fishery is not, however, the end all to fisheries problems.

Quotas and gear restrictions have been studied as a possible solution to reach

sustainability in fisheries. Sustainability in natural resource problems, including fisheries, is

an issue that has been discussed in the literature for decades, including Ken Arrows work

(Arrow, 1974). Lee G. Anderson is a central figure in the gear restriction literature

(Anderson, 1986). Andersons work adds on to the work done by others (Allen et al,

1984), (Clark, 1985). Anderson has also contributed a large number o f papers in the field

to draw upon. His key paper on the applicability o f gear restrictions showed that gains

could be had under any cost system (Anderson, 1985). His paper described a model in

which gear restrictions would always reap positive benefits in constant cost industries,

while increasing cost industries could increase benefits given a few assumptions.

The literature on quotas is vast. Instead of dragging the reader through all the

articles, I will instead bring to light a central paper that changed the view on quotas. The

one person whose work has changed the thought o f the typical quota belief is Rognvaldur

Hannesson. His early paper, Fishery Dynamics: A North Atlantic Cod Fishery in 1975,

14


showed that constant seasonal catch may not be the first-best solution as previously

thought (Hannesson, 1975). In a controversial paper, Rognvaldur Hannesson and Stein

Ivar Steinshaan showed that constant effort quotas were preferable to the common

practice and thought that constant catch quotas could solve the problems associated w ith '

fluctuating fish populations (Hannesson and Steinshaan, 1991). Hannessons articles have

led a change to the work in fisheries models.

Many models have been developed that use dynamics or differential games to

consider optimal fishing in a dynamic setting. In a piece along the same vein as Hannesson,

Daniel Spulber created a model with a competitive firm owning a fishery (Spulber, 1983).

Introducing uncertainty and using a dynamic approach, Spulber finds that under specific

conditions, pulse fishing is optimal. Pulse fishing involves no fishing at certain times and

high levels of fishing at others. Further research in dynamic games has provided both some

intuitive results and some surprising results. Using the Nash and Stackelberg concepts of

equilibrium in a differential game, the firm with the cost advantage can induce a higher

catch rate and elicit a higher profit than his competitor (Dockner et al, 1989). While using

a two-country dynamic game with whaling ships in international waters, jointly used

strategies can result in Pareto-efficient solutions (Ehtamo and Hamalainen, 1993). While it

can be shown that a portion o f these strategies rely on credible threats, some restrictions in

the model are severe. These three previous models rely on assumptions o f constant and

enforceable property rights. This may not always be the case. One paper that addresses

this issue is a fishery model with poaching developed by Crabbe and Van Long (Crabbe

and Van Long, 1993). It is not surprising that the optimal stock level under open access

poaching is greater than under exclusive ownership. The ability of poachers to drive down

15


the stock of fish, will cause the owner to overexploit the fishery and extract more rent

early. It is surprising that entry deterrence by the rightful owners o f the fishery is more

successful under open access poaching than under a system o f restricted entry. The harder

it is for the poachers to enter the fishery, the harder it also becomes to deter illegal entry

into the fishery. Other work addresses the optimal harvesting o f single species, but ignores

interactions with other species (Clark, 1990), (Hartwick and Olewiler, 1998).

All of these previous articles address several main themes in the fisheries literature.

However, none o f the aforementioned articles address two important issues. First, fish

species interact with each other. Many fish species that are wanted in commercial fisheries

or for recreational fishing, are predators to other fish species who are wanted themselves.

Second, commercial fisheries are an important part of fisheries literature and generate

significant monetary gain, but recreational fisheries also generate a great deal of human

utility in addition to monetary gain and should not be overlooked. A good deal of work

has been done in recreational fisheries discussing non-market valuation o f a recreational

fishery, but not much modeling o f a recreational fishery has been done. The issues of

ownership, the use of quotas to elicit first-best behavior and the ability o f owners to elicit

rent from a fishery are all explored at length in the commercial fisheries literature.

Ownership of the fishery is not of great importance in the case o f Yellowstone Lake

though. Yellowstone Lake is a recreational fishery with competing fish species. The next

section looks into recreational fisheries papers and papers that deal with competing fish

species.

Within the fisheries literature, have any o f the features o f my research been addressed?

16


To see if utility derived from recreational fishing is explored in the literature, I now

turn to models that deal directly with recreational fisheries and models that specifically

incorporate competing species. As compared to commercial fishery models, relatively few

models have been developed that either focus on recreational fisheries or have competing

fish species. Even within this sparse literature, few papers focus on recreational fishing in

lakes or streams. This is a developing literature. While none o f the papers in this section

are a direct parallel with my work, several o f them use similar techniques.

The first paper written on competing fish species was Flaaten (1983). His work fits

nicely into the previous work on open access fishing, the one new tweak added to the

literature was the introduction o f competing fish species in one model. This new tweak

does not change the results that open access creates overexploitation of fish, which has

been shown extensively in the commercial fisheries literature. The new twist was adding

competing fish species into the open access literature.

This theme o f competing fish species focusing on the optimal harvest o f one of the

species has been continued in many other papers (Hannesson, 1983), (Ragozin and

Brown, 1985), (Flaaten, 1991), (Flaaten and Stollery, 1996), (Wacker, 1999). Ronald

Fisher and Leonard Mirman compile a summary article in The Compleat Fish Wars:

Biological and Dynamic Interactions (Fisher and Mirman, 1996). They cover articles on

dynamic externalities and biological externalities. Dynamic externalities are competition

between countries (or between two fishing boats in a simple example) while biological

externalities are competition between two fish species. The article combines the two

externalities from (Levhari and Mirman, 1980) and (Fischer and Mirman, 1992) into one

17


model. The model shows explicitly when both types o f externalities are present, catch

rates will be set too high and overexploitation o f the fishery will occur. While this deals

with competing fish species, the necessity of competing countries for fish is not found in

my research. This work also does not deal with the introduction o f an exotic fish species

into an ecosystem.

Two books in the literature delve into the issue o f competing species as well,

(Clark, 1990), (Hartwick and Olewiler, 1998). While both o f these contain sections on

multiple species, the specific technique used and the focus o f the work is different from

this paper. The introduction o f exotic species and the optimal management o f a

recreational fishery with an exotic is not explored in their work.

One paper that does have an explicit link with my work is a paper by Kenneth

McConnell, who developed the first simple biological model for a recreational fishery

(McConnell and Stinen, 1979). McConnell took the modeling approach that catch rates

depend on stocks of fish and future stocks of fish depend on current catch rates. The

results from this paper are threefold. First, this paper shows the now well-known result

that when a recreational fishery is open access, the fishery is overexploited. This result

supports previous work from the commercial fisheries literature. Additionally, the paper

explores the optimal regulation o f a fishery when it is jointly used for both commercial and

recreational fishermen. The final and most interesting result when compared to my work is

in the last section of the paper. McConnell explains that when a small portion of

recreational fishermen (highly skilled fishermen) are responsible for the majority of the

catch, direct regulation on only that small portion of fishermen can result in the first-best

outcome. This last result needs to be taken with caution. It may be difficult to distinguish

18


skilled fishermen from all other fishermen at the time when regulation needs to be set

forth. Even if it is the case and it is possible to selectively regulate specific individuals, it

could very well be politically costly to do so. The modeling approach that catch rates

depend on stocks o f fish and future stocks o f fish depend on todays catch is one o f the

most important ideas used in my research. Tracking the population o f species is necessary

in my model. The use o f variables that directly account for changes in populations is a

critical aspect o f both my research and McConnells work.

The second crucial paper is a piece by Anderson. Anderson developed a full model

o f a recreational fishery with stock enhancement (Anderson, 1983). Anderson showed the

conditions when stock enhancement could improve the welfare o f fishermen as well as

when it could not. Only under certain restrictions would pure stock enhancement (straight

stocking of the fish) result in welfare gains. Anderson instead finds that improving the

habitat o f fish would be much more likely to increase the welfare o f fishermen than

stocking fish would.

By studying the recreational fisheries literature, work closer to my research can be

found. This literature does deal with humans deriving utility from recreational fishing.

While most o f these papers still have little in common with the specific model I use, some

similar approaches are taken. I use the competing fish species approach from Flaaten, the

dynamic approach from Fisher and Mirman and the concept that current catch rates

depend on current fish populations and that future fish populations are at least partly

determined by current catch rates from McConnell and Stinen. Parts o f each o f these three

papers are used in the ecosystem portion o f my model.

19


In addition to the insight into the ecosystem model I use, two papers directly lay

out concepts used in my economic model. The two papers most closely linked to my work

are Theory and Estimation o f the Household Production Function for Wildlife

Recreation by Nancy E. Bockstael and Kenneth E. McConnell and Toward a Complete

Economic Theory o f the Utilization and Management o f Recreational Fisheries by Lee G.

Anderson. One essential idea is taken from each o f these papers and used in my model.

Bockstael and McConnell build a theoretical model to describe the interaction

between the households behavior and... wildlife recreation. (Bockstael and McConnell,

p. 199). An important relationship is discussed in the paper, but is not fully explored; the

interrelationship between government decisions and individuals decisions on how to

allocate time in national parks or other wildlife refuges, In the chain o f causation, public

actions affect the stock of wildlife, which in turn influences success per day on which net

benefits depend. (Bockstael and McConnell, p.200). Bockstael and McConnells paper

brings this issue to light but does not fully explore its relationship on any specific case.

Their paper does not fully allow the National Park Service managers control over

decisions in the same way as my work, however many useful ideas in my work w ere

initially examined in their paper. The framework of Bockstael and McConnells model is a

static theoretical model of inputs {both public (exogenous) and private (endogenous)}

into household production functions to provide final goods to consumers. Specifically, a

relationship between the public agencys choice variable, A (newly purchased wetlands)

and the stock o f a particular species (fish) S is explicitly written as, S = S(A). A s the

public agency increases expenditures on A the stock of the species increases. In this

model, two environmental goods are desired, both the quantity of species caught, x and

20


the quality o f the experience, q. This framework is used with a constrained utility

maximization problem for the individual. The end result is a set o f structural demand

functions for catch and quality, which shift with changes in public agency actions

(Bockstael and McConnell, p.203). Bockstael and McConnell go on to derive welfare

improving results under different scenarios for quantity (catch) and quality o f

environmental goods. The necessary conditions for which cost and preference functions

can be identified increase when both quantity and quality are endogenous.

Bockstael and McConnells 1981 paper takes a different approach from my work.

While not a direct parallel to my research, some common threads exist between the two

papers. Both of these models: 1) Use household production functions in the theoretical

model for private wildlife recreation; 2) Have individuals spending resources (time in my

model and intermediate goods in Bockstael and McConnells) to produce final

environmental goods; 3) Have a public agency choosing the level o f a choice variable to

help the desired species. While these themes are common between the two models, the

approach taken is very different. Regulatory control is different in the two models.

Household production uses different inputs to create a final good in each model. The type

o f regulator and the type of regulations in the model are different. And finally, and most

importantly, my research has dynamic interactions and links between the ecosystem and

the economic system.

Anderson builds a model to describe the optimal management o f a recreational

fishery (Anderson, 1993). Anderson acknowledges the work done in fisheries literature

has ... for the most part, been developed in the context o f commercial fisheries.

21


(Anderson, p.272). The main purpose o f this paper is to derive the conditions for optimal

utilization o f a recreational fishery.

Anderson sets up a static model to represent the recreational fisherman. He sets up

a benefit function, which depends on the number o f days spent fishing, the landings per

day and the catch per day (Anderson, p.274). This benefit function is used to form a

Lagrangian constrained maximization problem (Anderson, p.277). The maximization

shows the optimal number o f days spent fishing and the optimal number of landings using

Kuhn-Tucker analysis. Anderson uses a key assumption in his model; the harvest or

Catch Per Day (CPD) is the control variable o f the regulatory agency. The agency can

limit the number o f fish that leave the lake to each person fishing. He then develops his

model under several scenarios: CPD is a function o f stock size only, CPD is used in

conjunction with a tax per day spent fishing, The CPD constraint is binding for some

people and non-binding for others.

The focus of Andersons paper is similar to the focus of my model. Both try to

develop the optimal actions taken by the regulatory agency overseeing the recreational

fishery. Even though the focus of Andersons paper and my paper are similar, the models

take a very different approach. Anderson sets up a static model. I set up a dynamic model.

Anderson uses both taxes per day and CPD as a regulatory tool. I use direct actions on

one of the species as a regulatory tool. Anderson focuses his model on a single fish species

with no biological interactions. I focus on the interactions of several species. While the

focus is similar, the paths taken to the end are very different.

Few models incorporate dynamic interactions in a fishery or competing fish species

in a fishery. Fewer still deal with specific issues related to my research. Anderson has

22


modeled the behavior o f individuals when a regulatory agency has control over the fishery.

The regulatory agency plays a similar role in his model as the park manager does in my

model. While the focus is the same, the path taken to this end is very different. Anderson

focuses in on catch per day as both a regulatory tool and an outcome. Regulation in my

model deals with directly impacting fish species.

While few models have a direct link with my work, two papers use some similar

modeling techniques. Both Anderson and Bockstael and McConnell have direct parallels

between their work and my research. These common techniques create a link between

their work and mine, but the while the tools are the same, the problems analyzed with

those tools vary greatly.

Has research specific to Yellowstone National Park or ecological research touched issues

relevant to this paper?

I also searched the literature dealing with Yellowstone National Park. Since the

specific problem studied in my research is an ecosystem problem in Yellowstone Lake, it is

necessary to find out what previous research in Yellowstone National Park has been done.

I need to ensure that the focus o f my research has not already been done in either

economic work or ecological work.

Several papers in economics have some facet of Yellowstone National Park as the

focus. This research has a long history, with the valuation and protection o f species as a

main focus. This literature is divided into two main groups, valuation and management.

The valuation literature primarily uses either travel cost or contingent valuation as the

23


method o f valuation. Management papers focus on limiting behavior of visitors to the park

in order to reduce their impact on either species in the park or other visitors to the park.

A problem when using a travel cost model to determine willingness to pay is

heterogeneous visitors (Smith and Kopp, 1980). A group of travel cost models have been

developed that separate on-site costs from long-distance travel costs, called on-site cost

models (McConnell, 1975). This approach has been used for a variety of topics (Shaw,

1991), (McConnell, 1992), (Larson, 1993). The on-site cost model is a popular way to

estimate economic values o f environmental goods. It has been used to calculate the

economic value of Yellowstone National Parks fishery (Kerkvleit and Nowell, 1998).

Using the on-site cost model, the value of fishing in and around Yellowstone National

Park is calculated.

However, the on-site cost model approach has its own problems. One such

problem is parameter instability. Parameter estimates are sensitive to the sample

composition. A recent paper used a new approach to get around this issue and estimated

benefits from visiting Yellowstone National Park (Kerkvleit and Nowell, 1998). The

approach used in this paper is to separate the visitor days and vacation itinerary from

actual travel costs. When used, this eliminated the parameter instability for the data. This

work needs to be addressed if travel cost models are used to calculate non-market values

for environmental goods. I do not use travel cost models though and thus do not need to

worry about these problems.

Two issues key to the introduction o f lake trout are discussed in separate papers.

First, questions about congestion in Yellowstone are discussed (Wilkinson, 1995). This

paper asks two key questions; is congestion currently a problem at National Parks? And

24


can these congestion issues be controlled? The determination o f whether or not crowds

are a problem at each individual park is left for further research. Instead the issue of

congestion is discussed more on a philosophical level in Wilkinsons paper. The issue o f

congestion being a problem in the specific case o f Yellowstone Lake is discussed further in

later work. Controlling congestion is discussed and multiple methods of limiting visitors

are used. The second key problem the literature discusses is that o f intra-use conflicts.

Certain uses of parks are in conflict with each other. For instance, a fishery has two uses;

It can be used as an intermediate good in the production o f other species in the ecosystem

or it can be used as a final product for fishermen who enjoy catching fish. The two uses

interfere with each other. While the specifics are left to a case-by-case basis, the issues

surrounding this topic are discussed in the literature (Jacob and Schreyer, 1980). Intra-use

conflicts are important since they are used in my research, while the issue o f congestion is

not of central interest in my research11.

Another key issue facing park managers is the use o f regulations to achieve park

goals. Park managers have several tools to achieve their goals. They can restrict visitation,

restrict gear use, increase the cost of a yearly pass, or increase the cost of a single visit. A

few of these specific tools and their use in Yellowstone National Park in particular are

discussed in the literature (Kerkvleit and Nowell, 1998). Two key results are found that

directly affect this research. First, while congestion is an issue to fishermen, the number o f

fish caught per hour is a much greater determinant in fishermens behavior than any other.

Second, the increase in the cost o f annual fishing permits and per day permits both have a

problem associated with them. Direct regulation o f the fishermen is not a first-best policy

for Yellowstone National Park. This is an important result for my work. My research

25


allows no direct regulation o f fishermen, but instead direct regulation o f species

populations through using money to kill lake trout. Since direct regulation o f fishermen is

already being used in Yellowstone National Park, using direct control o f lake trout as a

further control on the ecosystem is a reasonable way to model the problem o f lake trout in

Yellowstone Lake.

The results from Kerkvleit and Nowells 1998 paper alleviate the questions studied

in other work. Since the number o f fish caught per hour mainly concerns fishermen, human

congestion within a fishery will not need to be the main focus of my research. Previous

works have studied congestion at length (Anderson, 1980), (Deyak and Smith, 1978).

Kerkvleit and Nowells results suggest my current modeling technique can be used

without major concerns about congestion or the use o f direct regulation of fishermen.

Although the focus of this paper is on species interactions, research in ecosystem

management has not been limited to species. Ecosystems have been valued in previous

papers as both insurance and as human capital (Crocker et al, 1996), (Agee and Crocker,

1997). The same modeling approach used in my research is also used in Agee and

Crocker. They also use household production functions in their analysis. While household

production functions are used in both Agee and Crockers work and my research, research

papers using household production functions outside the realm of species production will

not be discussed at length since their focus is different than the current research.

The most comprehensive research done on the Yellowstone Lake ecosystem was

done by the director of research at Yellowstone National Park, John Varley (Varley and

Schullery, 1995). This paper is the single best written work on the lake trout problem in

Yellowstone Lake and it is also the best collection o f all different types of work done by

26


both biologists and economists on the introduction o f lake trout into Yellowstone Lake in

Yellowstone National Park. The work starts out with a description o f the problem facing

park managers and the potential consequences from the introduction o f lake trout to the

ecosystem. Varley and Schullery combine previous work on contingent valuation studies'

on fishing (Duffield et al, 1987) and the value o f a fishery (Varley et al, 1983) plus travel

cost surveys on the value o f grizzly bears (Swanson et al, 1994) and wolves (Duffield,

1992). These surveys were compiled to not only estimate the overall value o f the

Yellowstone Lake ecosystem, but also to estimate the damages that might be caused by

the introduction o f lake trout. In addition, various ways to reduce the lake trout

population are discussed. The total elimination of lake trout is seen as impossible unless

the entire lake was treated chemically to kill all trout species including both lake trout and

cutthroat trout and then cutthroat trout were introduced at some point in the future to

return the ecosystem to its original state. Using previous estimates o f the value o f the

cutthroat trout fishery, a benefit-cost ratio was developed to show the potential for

economic gain from killing lake trout.

The work done by Varley and Schullery suggests that the introduction o f lake

trout into Yellowstone Lake is a risk that can be reduced but not completely eliminated.

The benefit-cost ratios suggest money would be well-spent killing lake trout to alleviate

pressure on cutthroat trout. This work is good motivation for the importance o f my

research. If the money is well spent, then how much money should be spent and if the

National Park Services budget is fixed, what is the true cost o f killing lake trout?

27


Once you broaden the focus to include ecological and biological papers, the

literature on Yellowstone becomes massive. To keep focused, I work with research that is

crucial to either this research directly or the research done by the ecologists on the grant.

Ongoing research indicates which o f the species in the Yellowstone Lake

ecosystem will be most affected by a decline in the cutthroat trout population.

Consumption estimates show that although a great deal o f research has been done on the

potential effect on the grizzly bear population, they will not be affected nearly as much as

birds of prey will (Stapp and Hayward, 1999). Other research indicates that a particular

age class o f cutthroat trout is o f the greatest importance (Stapp and Hayward, 1999). The

juvenile fish are more important to the survival of cutthroat trout than are adult spawning

age fish. Since lake trout feed primarily on juvenile cutthroat trout, their impact is

expected to be great.

Research devoted to Yellowstone National Park and ecological research on the

lake trout problem in Yellowstone Lake have addressed issues close to this topic. Some

research gives insight into what issues are important in regulation o f Yellowstone Lake.

Some research, including work on this project, deals with issues specific to the ecology of

the ecosystem in and around Yellowstone Lake. While the research touches issues dealing

with Yellowstone Lake, none o f this work is describing the type of activity described in

this research.

What are the potential problems and how large is the risk o f exotic invaders?

28


In this particular problem an exotic invader, lake trout, have been introduced into

an ecosystem and are threatening the native species, cutthroat trout. What does the

literature have to say about exotic invaders in general? Is this a widespread phenomenon?

Is this an isolated incident?

We have already seen exotic invaders being responsible for the extinctions of

species. The Dodo is now extinct, largely in response to exotic species introduced by man

into the Dodos ecosystem (Day, 1981). We also know exotic invaders were responsible

for the extinction of the Lake Titicaca Orestias and the culprit responsible was lake trout

(Day, 1981). Current research is being done to determine how much o f a problem lake

trout are expected to cause in Yellowstone Lake. We know exotic invaders have caused

extinctions in the past. We know lake trout have caused extinctions in the past. This is not

an isolated incident. But how far reaching is this problem?

Evidence does exist showing that exotic species being introduced into a foreign

ecosystem does not always end up in ruin. Often times the introduced species does not

even survive in the new surroundings (Kareiva, 1996), (Mack, et al, 2000). If invaders do

not always become a problem, information about the specific case needs to be determined.

If the problem does exist, we have options about how to handle the problem as well.

Mitigation and adaptation can both be done to reduce the effect o f an exotic invader

(Shogren, 2000).

An overriding assumption made in this ecosystem problem is that cutthroat trout

are facing significant pressure from the introduction of lake trout. This assumption is given

great credibility by a key paper in the fisheries science literature (Lassuy, 1995). The

damage caused by species introduction is the focus of Lassuys work. The results show

29

with permission of the copyright owner. Further reproduction prohibited without permission.

that 68% o f North American native fish species extinctions were a result o f introduced

exotic fish and that 70% o f the 69 listed species for Endangered Species protection with

adequate information about their listing were caused by introduced fish species.

Further evidence shows neglecting the potential damage o f introduced fish species

can cause extinction. Several species o f fish have become extinct as a result of introduced

species, including the Lake Titicaca Orestias, the Ash Meadow Killifish, and the Pahroup

Kiilifish (Day, 1981). Since lake trout are an introduced species to Yellowstone Lake and

are threatening the native cutthroat trout population, this work suggests the potential

impacts of lake trout should be studied to determine the extent o f expected damage from

the lake trout introduction.

Further work suggests this particular exotic invader will cause immense damages if

left alone. Projections of the amount o f damage lake trout could do to cutthroat trout

suggest the cutthroat trout population could fall by as much as 90%, from its current size

o f 2,500,000 to 250,000 (Varely and Schullery, 1995).

It appears fish species in general are some of the most damaged o f all species

facing exotic invaders. Of those, not only do lake trout have a history o f causing

extinctions, but in this particular case they are expected to seriously threaten the survival

o f cutthroat trout. This particular exotic invader is of serious concern.

Overview

This literature review has given insight into my research. Previous work in

integration o f economic systems and ecosystems has shown that my specific dynamic

30


approach that combines links between both systems is unique. My work uses a dynamic

ecosystem-economic system model incorporating feedbacks between the two systems to

analyze a specific problem. That problem is an exotic invader in Yellowstone Lake

expected to make a large impact on the native fish population. The manager wishes to

maximize the intergenerational utility o f visitors to the park who use household production

functions using time to produce goods. None of the specific work in the fisheries literature

addresses all the main issues that my model incorporates. Some work has been done on

recreational fisheries and papers that use a dynamic model to represent a fishery have been

developed. Within this narrow range, however, no one model has incorporated all o f the

main themes of my work. This insures my research is both unique and productive, adding

new aspects to the current literature.

Chapter in lays the groundwork for the general modeling technique used

throughout this paper. Chapter IV takes the general modeling technique and applies it to a

specific problem - the introduction o f lake trout into Yellowstone Lake. Chapter V

explains the internet experiment used to gather data for valuation o f the goods in

Yellowstone National Park. Chapter VI explains the simulation model in parts, as a whole

and gives the simulation results across a variety o f possible scenarios. Chapter VTI

concludes the paper.

31


Chapter HI: Explanation of General Modeling Technique

Before laying out the full Yellowstone Lake model, we first motivate the

integrated modeling technique using the simplest case, a 2 species model. This general

model has two interacting species. These two species need not be animals, but any species

interacting with each other for survival. A simple predator-prey model is the least

complicated of this type. The predator species (denoted as species Z) eats the prey species

(species Y) for survival and the prey species tries to survive the predator species. I further

assume humans (an average visitor) derive utility from a household production function,

using time to consume the two species. The model also allows the average visitor to

derive utility from enjoying the rest o f the park in the form o f a park public good. All other

attractions at the park are subsumed in the park public good (denoted as X). All notation

used in this paper is given in a notation sheet on the back o f the dissertation.

This type of model can easily be adapted to include non-consumptive uses as well.

Instead of harvest functions, the same functions can be thought o f as viewing functions for

species (either bird watchers or other wildlife viewing). Time and the species population

would still be the inputs to the household production functions, however human

consumption would result in no decline o f the species populations for true non

consumptive uses. If human consumption resulted in either a decline in the species

population (by killing the species) or a decline in the population o f the species in the area

they are viewed (perhaps driving the species into the woods by viewing them), the

production function would still be consumptive in nature. Since consumption o f the

species (viewing the species) would reduce the number o f species later visitors could see,

32


that would drive down the population o f viewable animals. Even though the average

visitor is not directly killing the animal, he is reducing the viewable population and thus

reducing the relevant population. This model is also not limited to either consumptive or

non-consumptive uses. Both could easily be incorporated in the same model. In addition '

to non-consumptive use, existence values could also be easily incorporated in this model.

The addition of existence values would apply directly in the average visitors utility

function. The species populations would appear, possibly as a binary variable: 1 if the

population is positive, 0 if it is not. The use of a binary variable assumes existence values

do not fluctuate with different levels of the species population. If the species has not

become extinct, the existence value exists and is constant. If the species has become

extinct, the existence value is zero. Thus, if the species is alive, the existence value is

positive. If the species is not alive, the existence value is zero1".

Human activity is not limited to the consumption of the species by the average

visitor. In addition to the direct effect that the average visitor has on the ecosystem, the

park manager is engaged in activity to ensure that the average visitor maximizes his utility.

The park manager must determine how to best use the limited park funds to help the

visitor maximize his utility. He decides how much money to spend relieving pressure on

the prey species (mz) and how much money to spend improving the rest o f the parks

public good (mx). We presume the park manager spends money on either improving the

rest of the park public good or relieving pressure on the prey species. This does not mean

the park manager only spends money on these two activities, rather he has a limited

budget to spend on them and must decide how to allocate those limited funds across both.

In one specific case, the park manager may relieve pressure on the prey species by killing

33


the predator species. In this case, the money spent relieving pressure is used to reduce the

population of the predator species. It must be noted this is by no means the only way

money can be spent to reduce pressure on the predator species. Often times a park

manager has other options at his disposal. A manager can restrict or change the behavior

o f the average visitor to relieve pressure on the prey species. An example would be a

fishery, which changes its gear restrictions. I f more harmful gear use is disallowed, a catch

and release fishery will result in fewer o f the fish being killed. The manager changes a

policy to increase a species survival rate. A manager can also improve the habitat o f the

prey species to help reproduction. Any activity costing money to help the prey species can

be done within this framework.

Use o f Household Production Functions

In this model, humans allocate their time across different activities. The average

visitor must choose how much time to spend doing each activity. He can either spend time

trying to catch species Z, trying to catch species Y, or trying to see all the other

attractions of the park, X. More time spent at each activity will produce more of the good

(either species Z, species Y or the park public good X). In addition to time spent doing

each activity, the level o f the good (species populations for Z and Y or the level o f the

public good X) also helps determine how much of the good will be produced. A larger

population or higher level o f the good will lead to a larger number of individuals being

caught or viewed by the average visitor. The average visitor has control over the amount

o f time he spends doing each activity. Unlike with a market economy, the average visitor

34


does not trade money for goods, he instead gives up time to produce goods. This is why

household production functions are used to represent the production o f goods for the

average visitor.

In the household production functions, humans use time and the species

population as inputs to produce the final good - catching or seeing species or enjoying the

public good. I call these household production functions harvest functions since humans

catch the species for enjoyment. The subscript on the harvest functions denotes the

species. In this model, there is a harvest function for the predator species (hz) and one for

the prey species (hy). Tz is the amount of time spent by the average visitor attempting to

catch the predator species. Ty is the amount of time spent by the average visitor

attempting to catch the prey species. Once again it is important to note humans need not

consume either o f the species. These production functions could be non-consumptive in

nature where the visitor simply sees the species in its environment. The example outlined

in this chapter has consumptive use. The last household production function, Sx, also uses

time as an input, but uses a level o f the public good as its second input in place of a

species population.

These production functions are similar to those built by Bockstael and McConnell,

however time enters into the function differently (Bockstael and McConnell, 1981). They

assume time is multiplied by a catch per day function. The catch per day function depends

on effort and the stock of the species. My harvest functions depend on time and the

species population. Another similar production function is done by Anderson (Anderson,

1993). His production also depends on the species populations and aggregate effort,

however the catch per day is a direct regulatory tool by the manager o f the ecosystem.

35


Other catch functions in the literature have catch as a linear function o f species

populations (McConnell and Sutinen, 1979), (Fischer and Mirman, 1996), include biomass

instead o f species populations (Dockner, et al, 1989), or relate biomass and species

populations (Spulber, 1983). Each o f these production functions have species population

or species biomass as an argument in catch rates. As a species population or the biomass

of a species increases, the harvest increases. The three production functions are listed

below.

hz = hz(Tz, Z) - harvest function for the predator species (1)

hy = hy(Ty, Y) - harvest function for the prey species (2)

Sx = SX(TX, X(mx)) - viewing function for the public good (3)

where dhz/dZ > 0, dh/dY > 0, dSx/dX > 0, dhz/dTz > 0, dh/dT y > 0, and dSx/dTx > 0

The first two functions are set up to be harvest functions. These represent the

number of the particular species caught either in hunting or fishing (consumptive use). The

final household production function (Vx) is a non-consumptive use function (viewing

function) for the park public good. The park public good is a pure public good

representing all non-species related activities, such as enjoying any other attraction at the

park other than the two species.

36


State Variables fo r Species Populations

Species populations play a vital role in this model. The larger a population o f a

particular species is, the larger the catch o f the average visitor on any particular visit to the

park. A change in species populations either reduces or increases the productivity o f time

spent at that activity. A higher population o f a species would result in a higher harvest of

the species for a fixed amount of time spent trying to catch the animal (since dh/dY > 0,

dhz/dZ > 0 ). In this manner, a higher population corresponds to a lower productivity and

a lower population corresponds to a higher productivity where productivity is denoted by

the amount of time it takes to catch a particular number of individuals. With lower species

populations, more time must be spent to catch the same number of a species.

Species populations are used in this model as state equations. The population

(state) of the species next period is a function of its own population the current period and

the population o f other species the current period. For instance, the change in the

population of the predator species is a function of its own population, since a larger

population will spawn a larger number of offspring each year than a smaller population,

and the population o f the prey species since they are the main food source of the predator

species and get consumed by them.

(4)

ddf = 1 - (k)(Z)/(Y) (5)

37


Y = Y {Y ,Z ,h y ) (6 )

X = X (X ,m x) (7)

The above equations show the relationships between the two species populations

and the growth function for the park public good. The change in predator population (Z )

is a function of the current population o f the predator (Z), the number o f predators

harvested (caught) by the average visitor (hz), the amount o f money spent by the park

manager killing the predator species (mz) and the prey species population through a

density dependence factor (ddf).

A density dependence factor relates the population of the predator species that can

be sustained from a specific population o f the prey species. In the equation (5), (1/k) is the

amount of predators that can be supported by one prey species. The density dependence

factor is shown as an indicator for how many predators can be sustained by a population

of the prey species. Within a formal model, the density dependence factor can be

subsumed in the first equation by directly relating the predator species to the prey species

as in equation (8).

This modeling technique that assumes current populations o f a species depends on

previous populations and previous levels o f harvest comes from McConnell and Sutinen

(McConnell and Sutinen, 1979). As harvesting o f a species increases, the population

lted1hq4oalpwsji 4 y 5. integration of economic systems and ecosystems a dynamic

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