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Rent capture in rights based fisheries Grafton, R. Q. 1992

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RENT CAPTURE IN RIGHTS BASED FISHERIESByR. Quentin GraftonB.Ag. Econ. Massey University, 1981M.S. (Agricultural Economics) Iowa State University, 1985A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF ECONOMICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAAugust 1992© R. Quentiñ Grafton, 1992Signature(s) removed to protect privacyIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of EconomicsThe University of British ColumbiaVancouver, CanadaDate October 9,1992DE-6 (2/88)Signature(s) removed to protect privacyAbstractA major issue in resource economics is the capture of economic rent. In fisheries,in contrast to nonrenewable resources, there has been a general failure by regulatorsto prevent rent dissipation or capture rent where it exists. New ways of managingfisheries such as the assignment of property rights in the form of individual harvestingrights have been introduced in Canada and other countries and have proved successfulin improving economic efficiency. Despite such success, there remains no detailedstudy of the implications of rent capture from such fisheries. The thesis addressesthis important problem in both a theoretical and empirical framework.The theoretical model assumes a fishery regulated by an individual transferablequota scheme where there are two representative fishers that differ oniy with respectto their harvesting functions and fixed costs. The short-run quota equilibrium in thefishery is compared to a first-best solution where a resource owner can determine thenumber of fishers of each type, their individual harvests, and the biomass. Assumingrisk averse behaviour by fishers, it is shown that with uncertainty the expected rentin the fishery will be equal to or less than the equilibrium with no uncertainty. Sucha result is not the case in an open access fishery. An implication of the work is thatreducing the uncertainty faced by all fishers for a given total allowable catch will notdecrease the expected rent from the fishery and in general will increase it. Decreasingthe risk costs of certain fishers and not others may, however, increase or decrease theexpected rents.Using the theoretical model, different methods of rent capture including a quotarental charge, profit charge, net cash flow charge, ad valorem royalty, auction of11the harvesting rights, iump sum fee, and a. quota transfer charge are compared andevaluated. The criteria for assessing the different methods of rent capture includetheir effect upon the profits of different fishers, efficiency, costs of rent collection, andrisk sharing and flexibility. It is shown that with no uncertainty a quota transfercharge and lump sum fee are both capable of distorting the Pareto efficient quotaequilibrium while still capturing less than the estimated resource rent. Assumingvariability in the output price, it is shown that a profit charge, net cash flow charge,and an ad valorem royalty cannot decrease and will in general increase the expectedrent at any charge rate whenever the quota price is positive. Comparisons betweenthe rent capture schemes also reveals differences in the burden of the rental paid bydifferent fishers.The empirical study examines the effects of rent capture in a rights based fisheryusing data from the British Columbia sablefish fishery. The first part of the studyestimates the rent in the fishery using a 1988 costs and earnings survey of individualfishers. Estimates of the rent in 1990 are obtained from simulations using a normalisedquadratic and a translog restricted profit function. Using the simulations, the differentmethods of rent capture are examined with respect to the burden they impose onfishers and implications for the fishery.The thesis provides several contributions to the literature. It provides an originalframework for examining different methods of rent capture in a rights based fisherywith heterogeneous fishers with and without uncertainty. Using this model, the thesisdistinguishes between short and long-run phenomena and presents the importantdifferences between the several methods of rent capture. Using data from the BritishColumbia sablefish fishery, the thesis also provides the first empirical study of theeffects of rent capture in a rights based fishery.inTable of ContentsAbstract iiList of Tables viiList of Figures xAcknowledgement xi1 The Problem, Objectives, Literature Review, and Overview 11.1 The Problem 11.2 Objectives 41.3 Review of the Literature 61.4 Overview 112 The Nature of Rent 152.1 Classical View of Rent 152.2 Modern View of Rent 172.3 Resource Rents and Quasi-rents in Fisheries 193 Conceptual Framework 263.1 Introduction 263.2 The Model 273.3 Fishery Rent 493.4 Overview 54iv4 Rent Capture Methods Reviewed4.1 IntroductionQuota Rental ChargeProfit ChargeNet Cash Flow ChargeAd Valorem Royalty ChargeLump Sum FeeAuction/tendersQuota Transfer ChargeDiscussionProfits of FishersDistortions to EfficiencyCosts of Rent CaptureRisk Sharing and FlexibilityOverview5858596162646465686970808994975 Rent and the BC Sablefish Fishery5.1 Introduction5.2 Description of The Fishery and Data5.2.1 Background5.2.2 Data Sources5.3 Direct Approach5.4 Licence Values Approach5.5 Profit Function and Other Approaches5.6 Overview4.24.34.44.54.64.74.84.94.104.114.124.134.14Sources106106109109110111116118132V6 Rent Capture Methods and the BC Sablefish Fishery 1436.1 Introduction 1436.2 Fisher Profits 1456.3 Distortions to the Fishery 1496.4 Overview 1557 Summary and Conclusions 1627.1 Summary of Contributions 1627.2 Suggestions for Further Research 165Bibliography 166Appendices 174A Partial Derivatives of the Quota Price 174B Description of the Data 176viList of Tables3.1 Short-run annual profits of El and F2 fishers prior to rent capturegiven risk neutrality 563.2 Annual fishery rents with no rent capture given risk neutrality . . . 564.1 Short-run profits of fishers with collection of 100% of the annual valueof quota-holdings and given risk neutrality 1014.2 Short-run profits of fishers with collection of 50% of the annual valueof quota-holdings and given risk neutrality 1024.3 Cost/return from quota trading assuming rent capture of 50% of theannual value of quota-holdings and risk neutrality 1034.4 Short-run quota equilibrium before and after a lump fee charge is imposed on the fishery that collects an amount equal to 100% of theannilal value of quota-holdings 1044.5 Short-run quota equilibrium before and after a 100% quota transfercharge is imposed on the fishery 1055.1 1988 Summary Statistics of Fishers 1345.2 Estimates of 1988 Mean Net Returns and Profitability Ratios using theSurvey Data Directly 1355.3 Predicted Mean Sablefish Profit for Non CES Vessels in 1988 ($) usingSablefish Landings and Age of Vessel Data 1365.4 Direct Estimates of Total Sablefish Profits in 1988 ($) using SurveyData and Sablefish Landings and Age of Vessel Data 136vii5..5 Nonlinear Parameter Estimates of the Normalised Qiladratic Unit ProfitFunction 1375.6 R-Square Values for Normalised Quadratic Profit hinction 1385.7 Parameter Estimates of the Translog Unit Profit Function 1395.8 R-Square Values for Translog Unit Profit Function 1405.9 Estimated Mean 1988 Sablefish Profits ($) for Profit Functions . . 1415.10 Estimated Total 1988 Sablefish Profits ($) for Profit Functions . . . 1415.11 Predicted Mean 1990 Sablefish Profits ($) for Profit Functions . . . 1425.12 Predicted Total Sablefish Profits in 1990 ($) for Profit Functions . . 1425.13 Predicted Total Sablefish Profits in 1990 ($) from the Unit Profit Functions and Accounting for Structural Change 1426.1 Predicted 1990 Profits of Fishers at Different Levels of Rent Capture with a Quota Rental Charge using a Normalised Quadratic andTranslog Profit Functions ($) 1576.2 Predicted 1990 Profits of Fishers at Different Levels of Rent Capturewith a Profit Charge using a Normalised Quadratic and Translog ProfitFunctions ($) 1586.3 Predicted 1990 Profits of Fishers at Different Levels of Rent Capture with a Net Cash Flow Charge using a Normalised Quadratic andTranslog Profit Functions ($) 1596.4 Predicted 1990 Profits of Fishers at Different Levels of Rent Capturewith an Ad Valorem royalty using a Normalised Quadratic and TranslogProfit Functions ($) 160viii6.5 Predicted 1990 Profits of Fishers at Different Levels of Rent Capturewith a Lump Sum Charge using a Normalised Quadratic and TranslogProfit Functions ($) 161ixList of Figures2.1 Short-Run Rent in an ITQ Fishery 253.1 Cost Curves of Fl and F2 Fishers 57xAcknowledgementMany thanks go to members of the thesis committee, Paul Bradley, John Cragg,Gordon Munro, and Phil Neher for helping to see this work to fruition. My thanksalso to Erwin Diewert, Ashok Kotwal, Bill Schworm, Tony Scott, Margaret Slade,Russell Uhier, Casey Van Kooten, Carl Walters, Ken White, and N.J Wilomovskyfor their help and encouragement. The support of fellow students Keir Armstrong,Benoit Delage, Kevin Fox, Greg Flanagan, Ann Holmes, Hisafumi Kusuda, HarryNelson, Tim Sargent, Stephane Vigeant, and Liz Wakerly is also warmly appreciated.Many thanks also to Anton IVleister of Massey University and Peter Calkins, formerlyof Iowa State University, in stimulating in me an interest in economics and providingthe encollragement to pursue further studies. The author is also grateful for financialassistance and data supplied by the Economics, Program and Planning Division ofthe Department of Fisheries and Oceans, Pacific region. In particular, the adviceand assistance of Bruce Turns and Michelle James of Fisheries and Oceans Canadais much appreciated.Special thanks are very warmly given to family and friends and in particular toBill and Molly Grafton for their support and encouragement over many years. Finally,the thesis is dedicated to Carol-Anne. Without your inspiration and constant supportthis thesis would never have been written.xiChapter 1The Problem, Objectives, Literature Review, and OverviewThe land is the principal of the natural agents which are capable ofbeing appropriated, and the consideration paid for its use is called rent.John Stuart Mill (1806-1873), Principles of Political Economy, Chapter 16, p. 422.1.1 The ProblemIt has long been recognised that in an open-access fishery [Warming (1911), Gordon(1954), and Scott (1955)] there may arise a divergence between private and social costssuch that total fishing effort exceeds the level that maximises the net returns in thefishery. The externality arises from the fact that one fishing vessel’s harvest reducesthe total stock available to other vessels which in turn can increase their harvestingcosts. In Gordon’s static analysis, the open-access fishery tends to reach a bionomicequilibrium where the total fishing cost equals total revenue. A level of fishing effortbelow the equilibrium would mean fishers were earning above normal profits and ina competitive environment would attract additional fishing effort. A level of fishingeffort above the equilibrium would mean total costs exceed total revenue such thatsome fishers would be obliged to leave the fishery. The result is the dissipation of thepotential rents from the fishery and excessive depletion of the resource.In regulated fisheries, the externalities evident in an open-access fishery may continue to exist where there are controls on the total harvest but there are ineffective1Chapter 1. The Problem, Objectives, Literature Review, and Overview 2restrictions upon fishing effort. In such fisheries, the incentive remains for fishers tocompete for the limited harvests leading to excess effort and capacity above that necessary to harvest the total allowable catch (TAC). Iii turn, excess fleet capacity mayalso result in a crowding externalities whereby fishers impede each others harvestingefforts.’ The result, with or without crowding externalities, is again the dissipationof potential rents [Munro and Scott (1985), 657-664].A type of management that attempts to improve economic efficiency and reducethe externality problem in fisheries is the assignment of property rights to harvestersof the resource [Scott (1986)]. These property rights may take the form of outputcontrols such as territorial user rights in fisheries (TURFs) and individual transferablequotas (ITQs). The assignment of such rights may be defined as rights based fisheriesmanagement. In the case of TURFs, resource users are assigned harvesting rights tospecific locales. For sedentary species [Beddington and Rettig (1984)] and whereTURFs are exclusive and enforceable, fishers can operate more as sole owners ratherthan competitive harvesters of the resource. In turn, this can reduce harvesting costsand increase the net returns from the fishery.Improvement in efficiency may also arise with the use of ITQ’s which allocatea total allowable catch (TAC) among fishers in the form of individual harvestingrights. By providing fishers with a greater assurance of harvesting a certain share ofthe resource, such quotas may reduce racing behaviour between fishers to “catch thefish before someone else does” and allow quota-holders to harvest the resource in aless costly manner. Evidence from Australia [Geen and Nayar (1989)] and Canada[Crowley and Palsson (1990)] suggest that ITQs and rights based management haveindeed improved economic efficiency in fisheries. Rights based management has also‘A review of the externalities prevalent in fisheries including stock, crowding, and mesh externalities is given by Smith (1969).Chapter 1. The Problem, Objectives, Literature Review, and Overview 3been successfully introduced into several other countries. Such management is evidentin Canada’s Pacific [Canada Fisheries and Oceans (1990a)] and Atlantic fisheries[Fraser and Jones (1989), Gardner (1989)], in Iceland [Arnason (1986)], in some ofthe commercial fisheries of the Great Lakes, Australia’s southern blue fin tuna fishery[Geen and Nayar (1989)], and in most of the coastal and offshore fisheries of NewZealand [Clark et al. (1989), Muse and Schelle (1988)]. Rights based management inthe form of ITQ’s can, however, create new problems for resource owners. A reviewof these issues is provided in Copes (1986).Allowing transferability of quota can also enable more efficient operators to acquirea greater share of the total harvest. By setting a TAC in a quota management systemsuch that harvesting rights are scarce, the resource owner can allow for the existenceof a resource or scarcity rent. This rent, which reflects the difference between theoutput price and marginal cost of production, should be reflected in the marketprice of quota. In the case where quota is allocated gratis to fishers and there isno attempt to collect the resource rent, returns in excess of normal profits accrue tothe first generation of quota-holders. Where, however, the resource owner wishes tocapture a share of this rent there is little guidance available on the consequences ofrent collection. Despite a great deal of literature on the subject of rent capture innonrenewable resources, there are very few papers [Waugh (1987), Grafton (1992)]that compare different methods of rent capture in fisheries. To date, there has alsobeen no empirical investigation that compares different methods of rent capture inrights based fisheries.The problem of how one may capture resource rent from a rights based fishery andthe consequences of different methods of rent capture is examined in the followingchapters. The contribution of this work is two-fold. First, it addresses an importantissue in resource economics that has received little attention. Second, the implicationsChapter 1. The Problem, Objectives, Literature Review, and Overview 4of rent capture in both a theoretical and empirical framework may aid resource ownersin the practical collection of rent. Given that rights based management is now beingintroduced into fisheries on a world-wide basis, this has become an important policyissue.1.2 ObjectivesThe principal objective of the thesis is to evaluate several systems of rent collection ina theoretical and empirical framework so as to rank different methods of rent captureunder different criteria and circumstances.The conceptual framework in chapter 3 provides the basis for studying a number ofrent capture methods in a hypothetical fishery regulated with individual quotas. Thetheoretical environment is that of a fishery where management is vested in a regulator.In place in the fishery is an ITQ management scheme, where quota was originallyallocated gratis to fishers, trades at a positive price and is denominated in quantityof fish that may be harvested per unit of time. Initially operating in the fisheryare two types of fishers each maximising their expected utility of economic profitsand who differ only with respect to their fixed costs of production aild harvestingtechnology. Using this framework, the effects of uncertainty on the quota equilibriumand expected rent in the fishery are examined. A comparison is also made betweenthe short-run quota equilibrium and a first-best situation.Using the conceptual framework, chapter 4 examines several methods of rent capture with respect to their effect upon the profits of fishers, distortions imposed uponthe fishery, costs of rent collection, and risk sharing and flexibility. Using the specified criteria, each of the methods of rent capture is given a relative ranking undereach item. No attempt is made to construct a criterion or social welfare function ofChapter 1. The Problem, Objectives, Literature Review, and Overview 5fishers under the different rent collection devices. Use of such a device would requireattaching weights to an objective function that would vary according to the resourceowner and the specific conditions in a fishery. The rent capture schemes examined inthe thesis include:• Quota rental charge based on the market price of quota in leases and/or sales.• Profit charge on a proportion of the pre-tax net revenue of fishers.• Net cash flow charge.• Ad valorem royalty based upon quota-holdings and the landed price of fish.• Lump sum fee/charge.• Auction of individual quotas valid for a given period of time.• Quota transaction charge payable whenever quota is traded.These methods of rent capture do not exhaust the possible choices available toa resource owner but are a selection that have been proposed in fisheries or appliedelsewhere. In particular, a profit tax is a common approach in taxing individuals andenterprises, a net cash flow charge has been proposed in some of Australia’s commonwealth fisheries [Campbell and Haynes (1990)], an auction is a common method ofcapturing rents in exhaustible resources, a lump sum or fixed fee charge is a usualmethod of charging fishers to help cover regulatory costs, a quota rental charge is anatural method of capturing rent from ITQ fisheries, and an ad valorem royalty hasbeen proposed as a means of correcting externalities in open-access fisheries.The empirical study in chapters 5 and 6 is complementary to the theoreticalanalysis and compares different methods of rent capture in the British ColumbiaChapter 1. The Problem, Objectives, Literature Review, and Overview 6(BC) sablefish fishery.2 This fishery has been managed with a licensing system since1981 which restricted the gear used by fishers and the total number of vessels to 48.Since 1990, the fishery has been managed with a form of ITQ’s called individual vesselquotas (IVQ’s). This management system was implemented for an initial two yeartrial period with the support of fishers in the industry. The IVQ’s were assigned gratisto fishers on the basis of past catches and vessel length, denominated as a proportion ofthe TAC, and made transferable only among licence-holders for amounts no less thanthe initial quota allocations [Canada Department of Fisheries and Oceans (1990b)}.The purpose of the empirical study is to address the problem of rent capture inan actual fisheries environment. Such a study is necessary because there are insightsand implications that can be obtained from a specific fishery that may not be possiblein a theoretical framework.1.3 Review of the LiteratureMuch has been written on the issue of rent and its capture. Some of the earliestwritings on the subject are proposals to capture ground rent from land by JohnStuart Mill (1848) and Henry George (1879). Other notable economists who proposedcapturing land rent include both Wairas and Wicksteed [Blaug (1986), 85].Today, the issue of rent capture refers to more than just land but can include allrenewable and nonrenewable resources. The major issues addressed include efficiency,or how to extract rent with the least distortion possible to optimising behaviour, andequity, or the effect on the after-tax distribution of net returns [Garnaut and Ross(1979), Boadway and Flatters (1983), and Conrad and Gillis (1985)]. In the general2The sablefish is commonly known as the black cod although it is not a member of the cod family.It is known scientifically as, Anoploma fimbria, and is an important commercial species found inwaters from Britol Bay, Alaska to southern California.Chapter 1. The Problem, Objectives, Literature Review, and Overview 7taxation literature, the concepts of equity are divided into horizontal equity (theburden of tax across individuals of the same means) and vertical equity (the burdenof tax across individuals of different means).3In measuring efficiency and rent capture from resources, the concept of neutralityis often applied with the usual assumption that the rest of the economy is fullycompetitive and efficient. In particular, a tax is preferred over another if, ceterisparibus, it distorts the extraction or production profile the least. A neutral tax isone that leaves the rent maximising production profile unchanged. In this vein, Slade(1986) has examined resource taxation in exhaustible resources at different stagesof production and from the policy goals of neutrality, increased conservation, andaccelerated depletion. Slade observes that with a tax imposed where there is resourceprocessing after extraction and before sale of the commodity, that tax will dependupon all parameters of the processing technology. In a nonhomogeneous industry,therefore, a tax that is neutral on an industry basis cannot be neutral for every firm.Other issues with respect to efficiency and rent capture include the tilting ofoutput over time, effects on exploration, optimal mix of factors, and efficiency offactor utilisation [Heaps and Helliwell (1985)]. A consideration of both equity andefficiency issues in the mining industry is provided by Church (1982). The subjectof rent capture and its effect on exploration and efficiency of factor utilisation isexamined by Garnaut and Ross (1975). In particular, they note that “... maximisingtotal government revenue involves balancing the possibility of revenue loss on highlyprofitable projects . . . against the possibility of setting rent charges so high thatthere is revenue loss through deterrence of projects which, ex ante, are not certainlyintra-marginal.” [Garnaut and Ross (1975), 273] A consideration of this issue andquestions of ex-ante and ex-post rent capture and the nature of the rent itself is given3Slemrod (1990) provides a review of taxation and tax systems in the general tax literature.Chapter 1. The Problem, Objectives, Literature Review, and Overview 8by Grubel (1979) and Cairns (1977, 1980). Garnaut and Ross also address the issuethat higher marginal tax rates reduce the incentive for efficiency thereby reducing therent available to be captured and examine the uncertainty that ex post adjustmentsin taxation place on firms undertaking investment decisions. In consideration of thesefactors, they propose a Resource Rent Tax (RRT) that is like a profit tax but includesexploration costs as an expense and oniy collects rent after a certain threshold on aninternal rate of return on total cash flow has been achieved.Comparisons of different methods of rent capture in exhaustible resources hasalso been important in the literature. A review of different methods of rent capturethat may be applied is provided by Heaps and Helliwell (1985). They include grossroyalties based on either output or value, net royalties based on profits, taxes based onhypothetical costs for a given class of operation, equity participation by the resourceowner, property taxes based upon the total value of the resource, and auction ortendering of exploration or development rights. A well known result is that a grossroyalty does distort the production profile of a mine in that the higher the tax ratethe higher the ‘cut-off’ grade of ore left in the ground.4 A comparison of the efficiencyeffects of a gross royalty compared to a profit tax is provided by Bradley et al. (1981).They find that in the BC copper mining industry the efficiency of a gross royalty isconditioned on the tax rate.In the Canadian context, rent capture in overall tax policy is reviewed by Boadwayand Kitchen (1980). The political economy of resource rents and a review of themethods and consequences of rent collection in Western Canada is provided by Guntonand Richards (1987). A summary of the major issues of mineral taxation in Canadais given by Parsons (1982).In contrast to nonrenewable resources, there has been very little published on the4Neher (1990), chapter 19 discusses the effects of a gross royalty, profit tax, and RRT.Chapter 1. The Problem, Objectives, Literature Review, and Overview 9subject of rent capture in fisheries. Much of the work has focussed upon ways ofovercoming the externality problem and avoiding rent dissipation in both open accessand regulated environments. On this issue, Crutchfield and Pontecorvo (1969), Flagg(1977) and Dupont (1988, 1990) among others have quantified the problems of rentdissipation in various fisheries. In particular, Dupont (1990) showed that a restrictivelicensing policy and government determined total catch in the BC salmon industryhas led to substantial dissipation of the potential rents. Schwindt (1987) provides areview of the public policy and issue of rent in the same industry. He notes that abuy-back scheme of vessels would reduce the overcapitalisation problem but withoutrent capture by the crown further rent dissipation would take place. De Voretzand Schwindt (1985) also provide estimates of rent in Canada’s Pacific fisheries. Inparticular, they examine the possible effects of a license auction scheme and royaltieson catches in the salmon industry.The question of capturing resource rents in fisheries has received much less attention. The literature on taxation deals almost exclusively with the issue of controllingfishing effort. In particular, Clark (1985) and others have examined a royalty or landing tax on fish which can reduce fishing effort by reducing the net price of fish tofishers. In this respect, Clark (1990, 256-260) has demonstrated that ITQ’s can beequivalent to a single landings tax in terms of economic efficiency but not in termsof distribution of returns. This equivalency will arise if fishers have identical harvesting functions and if the TAC under ITQ management is set such that the annualmarket price of quota equals the given landings tax. In actuality, fishers do differin their harvesting functions and the information requirements necessary to optimisethe level of fishing effort with landing taxes is beyond the capacity of most fisherymanagers. Recognising this problem, Arnason (1989) has recommended a minimumChapter 1. The Problem, Objectives, Literature Review, and Overview 10information management scheme that uses ITQ’s. He shows that under certain assumptions and using ITQ’s allocated as a percentage or share of the TAC, the fisherymanager can maximise the net returns from the fishery. This results from judiciousadjustments in the TAC by the manager such that the market value of outstandingquota is maximised.In practice, both landings taxes and auctions of limited entry licences have alsobeen proposed for Canada’s Pacific fisheries [The Commission on Pacific FisheriesPolicy (1982)] to deal with the problem of excess fishing capacity. New Zealand, whichhas ITQ regulations for 32 of its fisheries, is the only country that has systematicallyattempted to capture rent from its domestic fisheries. Originally, resource rentalpayments were proposed on the basis of the value of traded quota but opposition fromfishers has led to the setting of quota fees using a measure of industry profitabilityand target rates of return [Clark et al. (1988)]. The rent captured is substantialand amounted to some 10 percent of the value of domestic landings for the 1987-88fishing season. Other countries have also proposed rent capture for their fisheries.In particular, Australia has suggested auctioning and leasing of access rights, lumpsum taxes on fishers, and royalty or landing taxes on fish [Australian CommonwealthGovernment (1989)]. The issue of rent capture is also of interest in countries such asthe USA which is contemplating moving to rights based management in its fisheries.In the case of the US fisheries, the total capitalised value of introduced ITQ’s maybe as much as several billion dollars [N.Y Times (1991)].The introduction of rights based management in fisheries has now changed thequestions that economists must address. The issue is now no longer of controllingrent dissipation in open access and regulated fisheries but one of capturing rent inrights based fisheries. Despite a wide-body of work on the issues of rent and its capturein resource economics, important questions with respect to rent and its capture inChapter 1. The Problem, Objectives, Literature Review, and Overview 11fisheries still remain unanswered. They include the effect of different taxes on thedistribution of fishers’ net returns, the relative flexibility of different methods of rentcapture to adjust to changes in the fishery, their effects on efficiency, ability to collectrent, cost of collection and risk sharing between fishers and the resource owner. Thesequestions are addressed in the following chapters.1.4 OverviewChapter 2 provides a review of the meaning and significance of economic, differential,resource or scarcity, quasi, and intra-marginal rents. The purpose is to present theclassical and modern views of rent so as to better understand the nature of rent infisheries. In particular, the chapter explains why the capture of resource rent may bejustified and why the the collection of intra-marginal rents may not. The former maybe attributed to the scarcity value of the resource while the intra-marginal rents maybe attributable to other factors of production. These intra-marginal rents may betermed quasi-rents but only in the sense that there are short run rents attributableto factors of production other than the resource. In the rest of the economy it is notcustomary to capture such rents, and the retention of these earnings by fishers maybe necessary to encourage long run innovations in the fishery. In a Schumpterian viewof the world, such quasi-rents are a necessary incentive for entrepeneurs to undertakeinnovation. Their capture by the resource owner may, therefore, reduce the longrun net returns available from the fishery. Another issue addressed in the review ofthe notions of rent is the concept of management rent as applied to fisheries. Thedifference between the resource and management rent is explained as is the importanceof the notions in rights based fisheries.Chapter 3 presents the conceptual framework for examining the issue of rentChapter 1. The Problem, Objectives, Literature Review, and Overview 12capture in an ITQ fishery. The approach taken is to develop a theoretical modelof a fishery where there are two types of fishers that differ only with respect totheir harvesting functions and fixed costs. In particular, it compares a short-runquota equilibrium and a first best situation where the resource owner maximises theexpected utility of fishers net of collection costs. The difference between the short-run and a first-best optimum is demonstrated as is the effect of uncertainty upon thequota equilibrium. It is found that increasing the uncertainty in the fishery as definedby the variance of the output price will never increase the expected rent in the fisheryand in general will decrease it. Reducing the risk that is faced by a subset of fishersmay, however, decrease or increase the total expected rents in the fishery.Chapter 4 compares the different methods of rent capture using the frameworkdeveloped in the preceeding chapter. It is shown that a quota transfer charge anda lump sum fee are both capable of distorting the Pareto efficient quota equilibriumwhile capturing an amount no more than the estimated resource rent. The variousmethods of rent capture are also shown to have differential effects with respect to therental paid by the two types of fishers. For example, those fishers who earn higherprofits per unit of quota harvested will pay proportionately less with a quota rentalcharge than a profit charge than a fisher with a lower profit per unit of quota. Themethods of rent capture are also compared with respect to the cost of collecting therent by the resource owner. In addition, risk sharing between the resource owner andfishers under the various schemes is examined. Assuming variability in the outputprice, it is showii that a profit charge, net cash flow charge, and ad valorem royaltycannot decrease and will in general increase the expected rent in the fishery. Incontrast, a quota rental charge is found to leave the quota equilibrium unchangedgiven output price uncertainty and a certain quota price.Chapter 5 addresses the issue of rent capture in a specific fishery. In particular,Chapter 1. The Problem, Objectives, Literature Review, and Overview 13different approaches are used to estimate the rent in the BC sablefish fishery in 1988two years prior to the introduction of individual quota management. In one approach,using data directly from a costs and earnings survey of 28 of the 46 active fishers in1988, an estimate of a total sablefish rent of some $6.2 million is obtained. Usingthe fishers’ estimated market value of sablefish fishing licences, an annual resourcerent less a allowance for risk costs is obtained. Depending upon the assumed pay-hack period of fishers and using a discount rate set equal to an opportunity cost ofcapital assumed to be faced by fishers, the annual resource rent is estimated to bebetween $1.6 and $3.7 million. In another approach, two flexible functional form profitfunctions are estimated. These profit functions are used to provide estimates of thereturns to fishers interviewed in the costs and earnings survey. Using the estimatedcoefficients from the functions and updating prices for 1990, estimates of the rent inthe fishery for 1990 are obtained. Adjusting for the structural change in the fisherydue to quota management, an estimate of the total sablefish profits in 1990 of $8.5and $8.7 million are obtained from the two profit functions.Chapter 6 uses the predicted sablefish profits for 1990 from the two profit functionsto examine the issues of rent capture in the BC sablefish fishery. Comparisons aremade of the various methods of rent capture by comparing the rent paid by twodifferent types of vessels found in the fishery. It is found that vessels employing atrap or pot method of harvesting sablefish prefer in a descending order of preferencea lump sum charge, ad valorem royalty, net cash flow charge, profit charge and aquota rental charge. In contrast, vessels employing another harvesting method havea reverse ordering for the rent capture schemes. The relative preference for the rentcapture schemes is shown to be a function of the prices received for sablefish byfishers, the ratio of their net cash flow earnings to their profits, their quota-holdings,and profits per quantity of sablefish harvested. The chapter also addresses the issueChapter 1. The Problem, Objectives, Literature Review, and Overview 14of distortions to the short-run quota equilibrium brought about by rent capture. Itis shown that a lump sum charge imposes inefficiencies on the fishery at relativelylow levels of rent capture. An attempt is also made to separate the expected resourcerent from the intra-marginal rents of fishers in the predicted profits of fishers.Chapter 7 summarises the contributions of the thesis from both the theoreticaland empirical perspective. The chapter concludes with recommendations for furtherresearch and suggested extensions to the work.Chapter 2The Nature of Rentwe must inquire into the nature of rent, and the laws by which itsrise or fall is regulated.David Ricardo (1772-1823), Principles of Political Economy and Taxation, ChapterII, p. 33.2.1 Classical View of RentThe notion of rent, as applied to land, was the subject of great debate among classicaleconomists. It was Adam Smith who observed that “The rent of land not only varieswith its fertility, whatever be its produce, but with its situation, whatever be itsfertility.” [A. Smith (1776), Book I, 164] He also noted that rent, “... is naturally amonopoly price.” [Smith (1776), Book I, 162] Rent accrues to land, therefore, becauseof its limited supply and differences in quality and location.For expanding upon these notions and addressing ambiguities left by Smith,Ricardo1 (1817) deserves credit for the classical notion of differential rent which hedefined as the infra-marginal return to land blessed with a higher marginal productivity. In the theory, land at the extensive margin receives no rent but each unitof land of successively greater productivity receives rent at a correspondingly higher1Concurrent with Ricardo’s work were publications by West, Torrens and Maithus. Letters fromRicardo to Maithus and others in 1813 and 1814 suggest the claim for the originality of his workmay be preeminent.15C’hapter2. The Nature of Rent 16level. The existence of rent is itself explained by the scarcity of land and the existenceof diminishing returns for “... rent invariably proceeds from the employment of anadditional quantity of labour with a proportionately less return.” [Ricardo (1817),371Writing some 30 years later, J.S. Mill defended Ricardo from critics who arguedfrom the American experience that the worst land is cultivated before the more productive land. J.S Mill explained that rent reflects a scarcity price and that land differed from labour or capital in that it is “.. . not susceptible to indefinite increase. Itsextent is limited, and the extent of the more productive kinds more limited still.” [J.S.Mill (1848), 176] He also agreed with Ricardo’s notion of differential rent such that“... no land ever pays rent, unless in point of fertility or situation, it belongs to thosesuperior kinds which exist in less quantity than the demand.” [J.S. Mill (1848), 423]He further expanded upon the notion that the rent land could earn in an alternativeactivity constituted a cost that must be paid if it is used in another. This conceptis at the root of the modern notion of a transfer price for a factor of production;the minimum price that must be paid to keep the factor in its present employment.Earnings to the factor above the transfer price constitute rent.The central issue in the classical notion of rent is, therefore, that rent reflects a payment for scarcity and that the differential rents arise from diminishing returns givena fixed factor of production. In this, Ricardo may be viewed as the first marginalistalthough he presented his ideas in a proportional framework. Given identical costsper unit of input applied to land and the same output price for the produce fromthe land, competition would ensure that the value of the marginal product of thevariable input will be the same across land types and equal to its cost. At the intensive margin, therefore, the value of the last additional unit of the variable inputis the same as at the extensive margin. The return to the fixed factor, land, is thehapter2. The Nature of Rent 17difference between the total revenue and total cost produced from the different landtypes. At the extensive margin, no rent is earned as the total revenue equals the totalcost of production. For land of a higher type, each successive unit of the variable unitreduced its marginal product until the cost of an additional unit of input equalledthe value of its marginal product. The total cost represents the total number of unitsof the variable inputs applied multiplied by its price while the total revenue is thetotal product multiplied by the output price. The difference between total revenueand total costs reflects, therefore, the existence of returns in excess of costs on thesuccessive units of the variable input and may be called differential rent.Given the acceptance by classical economists of rent as an unearned residual froma gift of nature, the notion of capturing this surplus for the benefit of society became alogical deduction. Although Ricardo appears not to have favoured such rent capture[Blaug (1986), 84], J.S. Mill (1848) did propose a tax on the capital gains fromincreases in the price of land. Henry George (1880) went further hut was not alone inproposing a single tax upon land but which exempted returns from site improvements.According to George such a tax met his own canons of taxation that a tax affect theincentives for production as little as possible, be cheaply collected, be certain, providethe least advantage for tax evasion, and be applied fairly. Although never widelyapplied, a variant of the George tax, a site value tax with full or partial exemptionon improvements to land, has been adopted by some local governments in Australia,USA, and New Zealand.2.2 Modern View of RentThe classical view of rent was later shown by the marginalist school to be a residualsurplus applicable to any fixed factor and not just land. In this view, the surplusChapter 2. The Nature of Rent 18accruing to a fixed factor is determined by the gap between the average and marginalproduct of the variable factor. Despite this viewpoint, Marshall (1920) made a distinction between the surplus accruing to ‘gifts of nature’ and to labour or capital. Inseparating the two types of rent Marshall introduced a time dimension with respectto rent and defined the concept of quasi-rent as, “ ... an unecessary profit in regardto short periods, because no ‘special’ or ‘prime’ costs have to be incurred for the production of a machine that, by hypothesis is already made and waiting for its work.But it is a necessary profit in regard to those other (supplementary) costs which mustbe incurred in the long run in addition to prime costs.” [Marshall (1920), p 424]Quasi-rents, therefore, apply to factors of production temporarily fixed in supply.With respect to capital, quasi-rent is commonly defined as the difference betweentotal revenue and total variable costs or those earnings over and above that requiredto keep the firm in business in the short run.2 For other factors of production it maybe defined as those earnings in excess of what is necessary to keep the factor in itspresent use for a given period of time. In the long run, however, factors must earnquasi-rents equal to their transfer price or they will not stay in the present activity.Similarly, quasi-rents that exceed a factor’s transfer price will be eroded over time asadditional units enter into the higher value use.In a modern review on the issue of economic surplus, Currie et al. (1971) defineeconomic rent in the classical tradition as, “... payment to a factor production overand above the minimum necessary to induce it to do its work.” [Currie et al. (1971),758] They also present an alternative definition of economic rent which they attributeto Pareto stating it represents “... the excess payment to a factor over and abovethe minimum amount necessary to keep it in its ‘present occupation.’ “ [Currie et2Marshall himself never gave such a definition of quasi-rents but this has become the accepteddefinition.Chapter 2. The Nature of Rent 19al. (1971), 759] The difference between the two notions is that the classical definitionaddresses whether the factor is supplied in the economy while the latter deals withthe issue of whether it is supplied in its present activity. In both definitions, however,economic rent is a surplus that is reflected in the size of net returns that accrue tothe factor.In resource economics, it is conventional to define economic rent as including bothdifferential (Ricardian) and scarcity rent. The scarcity rent, often called the resourcerent, is defined as the difference between the output price and the marginal cost ofproduction. As such, resource rent is a function of the “... marginal conditions ofthe economic calculus” [Conrad and Gillis (1985), 35] The existence of a resource rentimplies there are restrictions placed on the supply of the factor such that there arecorresponding limitations on the produce obtained.3 In the case where resources areiii abundant supply then the output price will equal the marginal cost of productionand the net price or per unit resource rent will be zero. In this case, the economic rentconsists only of a differential rent which arises from contemporaneous exploitation ofdifferent grades of the resource.2.3 Resource Rents and Quasi-rents in FisheriesIll the case of fisheries, the setting of a TAC, often determined by biological considerations, is a restriction on the supply of fish over what would be sold in an open accessor unregulated environment. Such a restriction in conjunction with durable and enforceable property rights, can give rise to the existence of a resource rent in a fisherysuch that the net price of fish is positive. In an ITQ fishery where harvesting rightsare durable and freely transferable in a competitive market, the price of quota should3F.J. Anderson (1985), 141-142 provides a graphical explanation of the concepts of differentialand scarcity rents.Chapter2. TheI\Tatureof Rent 20approximate the resource rent attributable to the scarcity value of the fish. This isbecause the quota price will reflect the difference between the output price of fish andthe marginal harvesting cost. Assuming risk neutrality of fishers, all fishers are pricetakers in the output and factor markets, and that quota is tradeable, equilibrium inthe quota market implies that all fishers face the same marginal costs of production.For example, if a fisher faced a higher/lower marginal cost than other resource usersthen it would pay the individual to sell/buy quota until his or her own valuation ofquota equalled the market price.In addition to a resource rent, there may also exist intra-marginal rents in a fishery.These intra-marginal rents are quasi-rents in that they are essentially a short-runphenomena and are determined by the average total costs of fishers and representthe differential net earnings by resource users in a fishery. The intra-marginal rentin a fishery represents, therefore, the difference in the average profit per unit offish landed between the marginal fisher and all other fishers. Intra-marginal rents,however, should not to be confused with differential rents that arise from a differentialquality of the natural resource. With few exceptions, fishers harvest from essentiallythe same resource. The existence of intra-marginal returns is explained by differencesin human capital or fishing technology applied by fishers.One explanation for differential earnings among fishers that does not assume theexistence of intra-marginal rents is that fishing is a chancy business. For example,in one year one may be fortunate enough to land the entire quota for the season inone set of the fishing gear and hence incur a low cost of production. An individualof similar skill and with the same sized vessel and harvesting process may have themisfortune of spending many days at sea prior to catching the season’s quota. Theresult is differential net returns among fishers of similar type. Such chanciness infishing should be reflected in the quota price and any intra-marginal earnings due toChapter2. The Nature of Rent 21good luck may be necessary to compensate for losses in other periods. This descriptionof differential earnings among fishers explains away the existence of intra-marginalrents. Such ‘rents’ are merely the product of the capriciousness of nature and as suchare not attributable to any factor of prodllction in the short or long run.An alternative explanation for differential earnings among fishers that does assumethe existence of intra-marginal rents is that it arises from fishing and/or managementskill of fishing captains. Differences in skills among fishers, therefore, explains differences in average total harvesting costs. In this explanation, intra-marginal rentsare like quasi-rents in that they are temporary in nature.4 Qilality differences amongfishing captains may be further accentuated by the type of remuneration paid to crewin the fishing industry. Often crew are paid a percentage of the landed value of thecatch that is usually fixed by convention for the fishing fleet. Consequently, betterfishing captains may be in a preferred position to have first choice on the crew hiredand select for better workers. Thus according to Copes “... the differential in overall efficiency between vessels is maintained with resulting large differences between‘high-liners’ and vessels at the bottom of the efficiency scale.” [Copes (1972), 151]Another explanation for the existence of intra-marginal rents is the use of differentfishing technology among vessels. In this view, captains and crew are essentially thesame and cost differentials are explained by the use of different vessels and harvestingmethods. As older or less productive capital and gear is replaced such quasi-rentswould be eroded over time.It is conventional in other resource sectors that owners of the minerals extracted bymining operations or of the trees harvested by logging operatiois should be paid someshare of the resource rent. In this case, the resource rent paid to the resource owner4Marshall noted that “... earnings even of rare abilities are, as we have seen, to be regardedrather as a quasi-rent than as a rent proper.” [Marshall (1920), 623]Chapter 2. The Nature of Rent 22by the resource user is a payment for the right to extract or harvest the resource. Inthe case of a fishery, individual owners of ITQ’s ha.ve an exclusive harvesting rightto the resource. Where the resource owner chooses not to capture the resource rentthen this rent will accrue to the original quota-holders or those individuals fortunateenough to be allocated quota at the beginning of ITQ management. If one acceptsthe notion that the owners of a resource should be the principal beneficiaries fromothers using the resource then the capture of resource rent is an appropriate activity.The capture of intra-marginal rents of fishers by a resource owner, however, cannotbe justified on the same grounds as the collection of resource rent. If one acceptsthat intra-marginal rents are a function of fishing skill and/or the use of superiorharvesting technology, then the rents are attributable to factors of production otherthan the resource. In the case of the fishing skill of the captain, the intra-marginalrent is a reflection of embodied human capital of the individual. In the example ofa superior harvesting gear, the intra-marginal rents are attributable to the specificcapital employed. Only when differential returns among fishers is explained by goodor ill chance can such earnings not be attributed to a factor of production. Irrespectiveof the explanation, all such earnings are temporary in nature.The collection of intra-marginal rents may be tempting for a resource owner butit does impose costs that would not arise with the collection of the resource rent. Itmay be that windfall gains through good chance may be necessary to compensatefishers for being employed in a risky profession. The collection of such earnings may,therefore, lead to the exit of fishers who require the expectation of such returns toharvest the resource. Equally, if one accepts that intra-marginal rents are abovenormal returns that accrue to high-liners then the capture of such rents may drivebetter fishers out of the fishery. More importantly, the existence of intra-marginalrents may be the incentive for innovation by fishers. According to Schumpeter (1934,Chapter 2. The Nature of Rent 231950), innovation is the act by which firms attempt to collect entrepeneurial profits.In this sense, “ ... entrepeneurial profits are the prizes offered by capitalistic societyto the successful innovator.” [Schumpeter (1950), 102] The capture of intra-marginalrents from fishers may, therefore, reduce the incentive for innovation. As a result,innovations that would have led to cost reductions and increases in the total net returnin the fishery may never arise in an environment where such rents are appropriated.In addition to resource rents and intra-marginal rents, there may also exist a quasi-rent for the marginal fisher. This quasi-rent will arise when ITQ’s are allocated gratisamong fishers and there is a time lag before other fishers are able to enter the fishery.In the time period before fishers are able to acquire the necessary gear and/or vesselsto operate in the fishery, the quota price will be determined by the current quota-holders. In this period, if the marginal cost of the marginal fisher exceeds its averagecost at the short-run quota equilibrium, the marginal fisher will be earning an annualprofit in excess of the lease value of its quota-holdings. This difference may be termeda ‘marginal quasi-rent’. Over time, this quasi-rent would attract new entrants into thefishery increasing the quota price until the marginal fisher earned only a resource rent.Unlike an intra-marginal rent which is also short run in nature, a marginal quasi-rentaccrues to fishers whose only virtue were to be original participants in the fishery. Itdoes not arise from differential skill among fishers or from the use of different fishingtechnology. As such, capture of the marginal quasi-rent by the resource owner shouldnot affect the incentives for innovation by fishers. An illustration of the different typesof short-run rent in an ITQ fishery is presented in Figure 2.1. This represents a fisherywhere all fishers are earning a marginal quasi-rent. Where fishers are operating at apoint below their minimum average cost of production and given increasing marginalcosts, fisher profits will be less than the resource rent. In this scenario there will onlyexist resource and iritra-marginal rents in the fishery.C1hapter2. The Nature of Rent 24Another concept applied specifically in rights based fisheries is that of managementrent [Anderson (1989)]. In comparing a fishery in an open-access environment withone subsequently managed with ITQ’s, Anderson notes that the management rent issimply the total value of individual quotas. The management rent, in this case, isidentical to the resource rent. Recognising that most developed fisheries today arenot in an open-access situation and rights based management is often imposed onfisheries regulated with prior restrictions on fishing effort, an alternative definition ofmanagement rent may be offered. Management rent may be defined as the changein the resource rent brought about by a change in fisheries management less thedifference in management costs between the new and old policies. In this definition,it is possible for management rent to be negative if increases in the resource rentare more than offset by increased costs of managing or regulating the fishery underthe new policy. The maximum value of the management rent would, therefore, be achange in management from an open-access, zero resource rent situation, to the rentmaximising harvest level taking into account regulatory costs. The importance of thenotion of management rent is that it recognises that the costs of regulation are a truecost to society. The net benefit to society of rights based management is, therefore,the management rather than the resource rent in the fishery.25Figure 2.1: Short—Run rent in an ITQ Fisherg$mciadApricer%%%\%‘.\%‘ ‘.‘i%\\\\\ %“ \\\%\\\\\\\\\S.%\\\\’h\\\\\\’qi quantity q2ADEF: resource rent fisher 1ACDF: resource rent fisher 2FEHO: marginal quasi—rent fisher 1FDIG: marginal quasi—rent fisher 2GIJK: intra—marginal rentr = quota priceChapter 3Conceptual FrameworkIt is not necessary to confiscate land; it is only necessary to confiscaterent.Henry George (1839-1897), Progress and Poverty, Book VIII, Ch II, p. 403.3.1 IntroductionThe issue of capturing rent in an ITQ fishery requires a number of assumptions to beable to examine the problem in a tractable framework. In developing a theoreticalmodel of an ITQ fishery, it is assumed that the initial biomass is set at a level thatwould maximise the sum of the expected utility of fishers in a first best situation andthat the harvest equals the growth in the biomass each period. Such assumptionspreclude addressing the issue of an optimal approach pa.th to an optimal biomasslevel. These questions, however, are well addressed in the literature.’The theoretical environment assumed for evaluating alternative methods of rentcapture is that of a fishery where management is vested in a resource owner and allprices are given. The question of uncertainty and risk is addressed by assuming thatthe output price is not known at the beginning of each period but there is a known andspherically symmetric probability distribution for the variable. In the first instance,the first best problem is examined where for a given amount of rent to be captured1see for example Clark and Munro (1975) and Clark, Clarke, and Munro (1979).26Chapter 3. Conceptual Framework 27the resource owner seeks to maximise the sum of the expected utility of fishers net ofcollection costs. This outcome is then compared to the short-run quota equilibriumthat arises from ITQ management under the assumptions that quota was originallyallocated gratis to fishers, trades at a positive price, and is denominated in quantityof fish that may be harvested per unit of time. In both cases, fishers are assumed toutilise one of two distinct fishing technologies.3.2 The ModelFollowing Andersen (1982), an optimal fishery under price uncertainty may be definedby maximisation of the expected rent above risk costs of the fishers. This implies thatthe resource owner is risk neutral and that risk is only considered with respect to individual fishers. The problem posed in the first-best situation is to maximise the sumof the expected utility of profits of fishers for a given amount of rent to be capturednet of collection costs. In the case where the risk costs of fishers and/or the collectioncosts are dependent upon the output of fishers this is not the same as maximisingthe expected rent in the fishery. The objective function is equivalent to maximising the general welfare of fishers defined as the simple sum of their individual vonNeumann-Morgenstern utilities.2 Provided that the random variable has a sphericaland symmetric probability distribution [Chamberlain (1983)], such a framework isconsistent with maximising the sum of the mean-variance expected utility functionsof fishers.In solving the first-best problem, it is assumed that the quantity of fish harvestedby each individual of each type, the number of fishers of each type, the biomass, andthe rent collected from each fisher is determined prior to revelation of the value of2This specification is analogous to a classical utilitarian welfare function. The axioms necessaryto generate the von Neumann-Morgenstern utility functions are presented in Hey (1978), chapter 4.Chapter 3. Conceptual Framework 28the random variable. It is assumed that the social rate of discount is zero and thatthere exists several non mutually exclusive methods of rent capture available. Thenotation used to describe the first-best problem is defined as follows:k denotes individual fisher employing the Fl technology.j denotes individual fisher employing the F2 technology.1 denotes a method of rent capture employed by the resource owner.L is the total number of rent capture methods available to the resource owner.N is the optimum number of Fl type fishers.M is the optimum number of P2 type fishers.P is the price of fish.C is the cost per unit of fishing effort.fci is the fixed cost of a El type fisher.fc2 is the fixed cost of a P2 type fisher.7rlk is the profit of individual k, Fl type fisher.qik is the total harvest of an individual k, Fl type fisher.elk is the total fishing effort of an individual k, Fl type fisher.is the catchability coefficient for Fl type fisher.r2J is the profit of individual j, P2 type fisher.q2j is the total harvest of individual j, F2 type fisher.e2 is the total fishing effort of an individual j, P2 type fisher.2 is the catchability coefficient for F2 type fisher.b is the total fish biomass.b is the maximum attainable biomass.B is a constant.Oki is the rent collected from individual k, Fl fisher using capture method 1.Chapter 3. Conceptual Framework 29is the rent collected from individual j, F2 fisher using capture method 1.v11(.) is the variable collection costs with rent capture method 1 on Fl fishers.v21(.) is the variable collection costs with rent capture method 1 on F2 fishers.K is the fixed collection costs associated with rent capture method 1.W is the total amount of rent captured from the fishery.‘ is an expectations operator.First Best ProblemMaximise with respect to [N, lvi, b, qlk, q2j, Oki, oj]N M‘{> U(-irlk) + U(ir)}k=1 jzsubject to:Pqlk — C’9 — fc1— Ok = 0 (3.1)Pq2— C-2 — fc o = K2 0 (3.2)1=1N Mq1k+q2j =Bb(b—b) (3.3)k=1 j=1L N M°kl + oj — v11(.) — v21(.) — K1) = W (3.4)1—i k=1 j=1where: if qlk, N, or 0k1 = 0 V k then v1j(q1, N, oki) = 0 and if q2j, M, or = 0V j thenv21(qj,M, o) = 0. (3.1) is the profit of an Fl type fisher after rent capturewhich must be non negative, (3.2) is the profit of an F2 type fisher after rent capturewhich must be non negative, (3.3) is an equilibrium condition that ensures that thetotal harvest equals the growth in the bioniass, (3.4) is the amount of rent collectedfrom the fishery net of collection costs.Provided that a solution exists to the first best problem for a given W then thesolution will depend on the values of the exogenous variables e{P},C,B,,fc1,fc2,Chapter 3. Conceptual Framework 30the variable and fixed costs of rent capture v11(.), v21(.) and K1, the variance of theoutput price u, and the risk aversion parameters of Fl and P2 fishers. In thismodel, the harvest functions are increasing and concave with respect to effort whereeffort is defined as some composite variable of fisher’s inputs.3 This differs from theassumption often applied in the literature of a harvesting function that is increasingbut linear with respect to effort. Concavity of the harvesting functions may arise fromgear saturation that reduces the catchability of fishing gear and congestion amongfishing vessels on fishing grounds [Clark (1990), 222-225]. The harvest is increasingwith respect to the biomass of the fishery indicating, ceteris pan bus, that a greaterstock of fish will yield a higher catch per unit of effort. The growth function of thefishery assumes a parabolic relationship between surplus production or yield and thesize of the stock. This is derived from the assumption that a fish stock produces itsgreatest harvestable surplils when it is at an intermediate and not at a maximum levelof abundance. This may be due to several causes including the fact that recruitmentof new cohorts into a fishery is often hampered by higher densities and that greaterpressure on food stocks often means a larger fraction of calories is used merely tomaintain life rather than for growth [Ricker (1987), 309-316].Under a mean-variance specification of expected utility [Just et al. (1982), Tobin(1969), and Diamond and Rothschild (1988)] with no uncertainty defined as = 0or rent capture defined as 0k1 = 0jl = 0 V k,j, the solution to the first best problemgiven by qk, N*, M*, and b* maximises the expected rents in the fishery. Underuncertainty and no rent capture, the solution to the first-best problem will maximisethe expected rent in the fishery less the risk costs of fishers. Given no uncertaintybut with rent capture, the first-best problem will maximise the expected rents inthe fishery less collection costs. In this case, the only consideration for choosing a3The harvesting function of a fisher i may be written as qj = b.Chapter 3. Conceptual Framework 31method of rent capture is the cost of rent collection. In the case of both uncertaintyand rent capture, the first-best problem maximises the expected reilt less the riskcosts of fishers and less the collection costs of rent capture. In this case, the choiceof the rent capture method is determined by both the cost of rent collection and itseffect upon the risk costs of fishers. For example, a method of rent capture may havelower collection costs for any values of N, M, qik, and q2j but may be a less desirablemethod of rent capture than another if it imposes higher risk costs on fishers.Because actual fisheries are almost never at a first-best optimum, it is useful tocompare the short-run equilibrium in an ITQ fishery to the solution in the first-bestproblem. In this respect, the analysis diverges from the traditional fisheries literaturewhich has primarily been concerned with the optimum allocation of fishing effort in afirst-best or long-run situation. The short-run is defined as the time necessary to allowfor transactions of quota among fishers already in the fishery and the long-run as thetime necessary to allow for entry and exit of all vessels. In comparing the short-runequilibrium to the first-best solution, the number of vessels fishing (including bothFl and F2 fishers) and the TAC in the ITQ fishery is set equal to the total numberof fishers and harvest level in the first-best problem given no uncertainty or rentcapture. It is further assumed that both types of fishers are operating in the fisheryupon introduction of ITQ management and that the TAC is initially allocated equallyamong all fishers at no charge.Operating in the fishery are two types of fishers; those who employ a type onetechnology (Fl) and those who employ a type two technology (F2). The Fl typefishers are assumed to have a higher catchability coefficient but incur higher fixedcosts than the F2 fishers. Such an assumption reflects the existence in a numberof fisheries of vessels with more modern search and harvesting technology operatingsimultaneously with vessels employing more traditional harvesting methods.Chapter 3. Conceptual Framework 32In trading quota, it is assumed that each fisher buys/sells or leases the quotathey desire immediately after receiving their initial allocation of quota until a marketequilibrium is achieved. Each fisher is assumed to maximise the expected utility ofeconomic profits each time period given their level of fixed costs and fishing technology. It is assumed, therefore, that fishers make their harvesting and quota tradingdecisions with sole regard to short-run economic profits and do not consider long-runinvestments. Such an assumption is reasonable in that fishers’ capital and technologyare fixed in the short-run, quota is freely tradable, and that the TAC is determinedexogenously. As a result, the current decisions of fishers will have no effect, direct orindirect, on their profits in future periods. Fishers simply maximise their expectedutility per time period by choice of their fishing effort and the quantity traded.The economic profit of fishers is defined as their total revenue less fixed andvariable harvesting costs and less the opportunity cost of owning quota at each timeperiod. A fisher’s opportunity cost is defined as the annuity that would be earnedif quota were sold/leased and the funds were invested elsewhere in the economy ata competitive rate of interest. It is best understood in the context that quota is anasset and imposes a cost on its owner whether it is bought, leased or obtained gratisfrom the regulator. The uncertainty faced by fishers is that they must undertakeharvesting and quota-trading decisions prior to knowing the output price. The fishers’belief about the output price is summarised by a probability distribution that isdefined by its mean and variance. Fishers are further assumed to be price takersin the output, input, and quota markets. Under these assumptions, the generalmaximisation problem faced by fishers at beginning of period t = 1 when quota isfirst traded is presented below.The notation used to describe the problem is as defined previously and includes:Chapter 3. Conceptual Framework 33Fkt is the economic profit of fisher k using Fl technology iii period t.jt is the economic profit of fisher j using P2 technology in period t.r is the competitive rate of interest.1kt is the quantity harvested by fisher k using Fl technology in period t.q22t is the qilantity harvested by fisher j using F2 technology in period t.ekt is fishing effort in period t by fisher k using Fl technology.e2 is fishing effort in period t by fisher j using P2 technology.Ft is the market price of quota in period t.Ak, is the initial quota allocation to fisher k, j.Wkt,jt is the quantity traded by fisher k,j in period t.6 is a discount factor equal to (1 + r).Maximisation Problem of FishersFisher k employing a Fl type technology maximises with respect to [elkt, wkt]:Tt{6tU(cIkt)}t=1subject to:qlkt(elkt; b) Ak + Wkt (3.5)where for fisher k employing fishing technology Fl:= Pqjj— Ce1k — fc1 — Fr(Ak + Wkt)Wkt > 0 if qilota is bought/leased and wj <0 if sold/leased out.Fisher j employing a F2 type technology maximises with respect to [e2t, wit]:Chapter 3. Conceptual Framework 34Tg{6tu()}subject to:q2(e2t;b) A+w (3.6)where for fisher j employing fishing technology F2:=— Ce2 — fc2— Ftr(A + w)Wit > 0 if quota is bought/leased and wjt <0 if sold/leased out.Given the separable nature of the problem faced by fishers in the short-run, onemay examine the independent maxirnisation of kt or jt for t = 1,... , T. In solvingfor the individual fishers’ quota demands, we note that if fishers face binding quotaconstraints such that quota is valuable then the harvest of fishers will not be lessthan the quota owned and/or leased provided that quota-holdings are known withcertainty. Consequently, (3.5) and (3.6) hold with strict equality such that Ak, andWkt,jt can be substituted by qlkt,2jt in the respective maximisation problem. Usingthe fishers’ harvesting functions one may also solve for the level of effort (elkt, e2t) asa function of the quantity harvested and the biomass.In addressing the issue of uncertainty, fishers are assumed to exhibit risk aversepreferences and face a fluctuating output price whose mean and variance is known.The notion of risk averse preferences for fishers is adopted by Andersen (1982) whoassumes that. fishers are risk averse and maximise the expected utility of profit. Clark(1985), however, takes a different view with respect to the short-term decision-makingof fishers and suggest fishers have “... a gambler’s taste for the daily ups and downsof their vocation” [Clark (1985), 230]. A review of the issues of uncertainty in fisheriesChapter 3. Conceptual Framework 35in general is presented in Andersen and Sutinen (1984) and uncertainty and dynamicsin Clark et al. (1985). In a particular study of the Eastern Pacific yellowfin tunafishery, Lewis (1981) has examined the question of how optimal policies change understochastic conditions. He shows that the problem of optimal management under uncertainty can be treated as a certainty-equivalent situation. Charles (1983) examiningthe issue of investment and uncertainty has shown that optimal fleet capacity withuncertainty will depend upon both the growth rate of the fish stock and the cost ofcapital.The uncertainty that fishers may face includes fluctuations in the TAC, the outputprice, price of inputs, and the quota price. For ease of analysis, the effects of uncertainty on the behaviour of fishers is examined only with respect to fluctuations in theoutput price. The uncertainty faced by fishers is that they must choose the quantityof fish to harvest and quota to be traded at the beginning of each period prior toknowing the output price. Given that the random variable is normally distributedthe expected utility of fishers can be represented by a mean-variance specification.4Under the assumption of separability across time, the specific maximisation ofproblem of fisher k using technology Fl at time period t may be defined as follows:= {S(kt)——= {q1kt — Ce(q1k; b) — fc1 ——!3l(— S(kt))2} (3.7)where is the expected price of fish, U is the utility function which is bounded fromabove, kt is the economic profit of fisher k, /3 is the risk aversion parameter for Fltype fishers, ‘(kt—8Qkt))2is the variance of economic profit, and4For a review of the appropriateness of the mean-variance specification see Diamond and Rothschild (1988), p 141. and Just et al. (1982), chapter 11.Chapter 3. Conceptual Framework 36is the risk premium associated with random fluctuations in the output price.The variance of the economic profit of fisher k may be determined by (3.8)—=—q1k fc1 — Frq1k —2(Pqlkt— C- — fc1 — Prq)}2=== qup (3.8)Similarly for a fisher j using an F2 technology the variance of economic profit is,— ‘(jt))2 = qo (3.9)Substituting (3.8) into (3.7), the maximisation problem for an Fl type fisher facingrandom fluctuations in the output price in period t becomes,= [q1kt — C ql2ki — fc1 — Firq—,31q1kP1 (3.10)Maximising with respect to 1kt we obtain the following first order condition:=— 21kt— Pr — 21q1ktu] = 0 (3.11)aq1k ?b2Solving (3.11) in terms of qlkt,* b2[F—Ptr] (3.12)qlkt= [2C + 2?bioJThe maximisation problem for an F2 fisher simplifies as follows,= [q2jt — Ct — fc2 — Frq2 — (3.13)b2Maximising with respect to q2jt we obtain the following first order condition:_______— 2t Fr — 22q2tuj = 0 (3.14)c9q2jt b2 —Chapter 3. Conceptual Framework 37Solving (3.14) in terms of q2jt,*—3 15— [2C + 2b1The short-run market equilibrium for quota can be solved by multiplying theindividual quota demands of the two types of fishers in (3.12) and (3.15), respectively,by the number of Fl and F2 fishers and then setting the product equal to the TAC.The market price of quota can then be determined from the equilibrium conditionwhich if substituted into the respective quota demands can solve for the post-tradequota distribution. This equilibrium represents the quota distribution that wouldarise given the initial conditions in the fishery. In general, this short-run equilibriumwill differ from the long-run optimum since it does not account for the possibility ofentry of additional vessels into the fishery.Defining X and Y respectively as the number of Fl and F2 type fishers initiallyallocated quota and the TAC as the total quota allocation, we obtain the followingshort-nm equilibrium condition:TAC— x1b[P— Ptr]+— Fir] 3 16)— [2C +2b14] [2C +2bu]Defining,— nt2ZQ 2a1— + ç1 Pipandr)r’l ?-2iQ 2a2— + 2c2’ /2Upone may solve (3.16) in terms of the market price of quota (Ft) and obtain,P a12TACPt =r — [X?a2 + Yai}b2r (3.17)Chapter 3. Conceptual Framework 38Differentiating (3.17), the short-run quota price is found to be increasing with respectto the price of fish, the number of fishers, the catchability coefficients, and the biomassand decreasing with respect to the cost per unit of effort, the interest rate, the totalquota allocation, the risk aversion parameter of fishers, and the variance of the outputprice.5The result may be compared to the situation where fishers are risk neutral suchthat their risk aversion parameters are zero but face the same fluctuations in theoutput price. The maximand of the Fl fisher in this case simplifies as follows,= [q1kt — C- — fc1 — Ftrqlkt] (3.18)such that,* — — Ftrjqlkt— 2C (3.19)In the case where fishers are risk averse but face no fluctuations in the output price,the maximand of an Fl fisher also simplifies to (3.18). Consequently, the demand forquota solves as per (3.19). Similarly for an P2 fisher in the case of no uncertaintyand risk neutrality*—— Pr}q23— 2C (3.20)In both the risk neutrality and no uncertainty case, the quota price solves to thefollowing,— P 2C[TAC]- r- [Xe? + Y]b2r (3.21)Addressing the issue of uncertainty, one may examine the short-run quota equilbrium given o > 0 and i3 and /12 are non-zero. In the uncertainty case with risk5see Appendix A for the partial derivatives of the quota price.Chapter 3. Conceptual Framework 39aversion, the first order condition for fishers is given by either (3.11) or (3.14). Inboth equations, the difference between the output price and the marginal cost of production does not equal the quota price. It can be seen, therefore, that the per unitexpected resource rent defined by the difference between the expected output priceand marginal harvesting cost will exceed the per unit quota price. The differencebeing accounted for by the amount by which fishers discount the expected outputprice due to uncertainty. Rearranging the first order condition of a fisher k using anFl technology the annual quota price may be written as per (3.22).—qii 2Fr = P — C —2/3qcrp (3.22)The difference between the quota price and per unit expected resource rent is, therefore, given by the last term in the RHS of (3.22). This term may be defined as themarginal risk premium of fisher k. The higher the risk aversion parameter (/3k) orthe higher the uncertainty associated with the output price (os) then the higher themarginal risk premium and the greater the difference between the per unit expectedresource rent and quota price.Comparing the case where the expected price with uncertainty and risk aversionequals the price with certainty, (3.22) suggests that in general the short-run quotaequilibrium will differ between the uncertainty and certainty case where fishers arerisk averse. Only in the special case where changes in uncertainty change the quotademands of fishers in the same proportion will increases/decreases in leave theshort-run quota equilibrium unchanged. For El and F2 fishers at the quota equilibrium it requires that,_____—_____(.a_P UPThis result is perfectly general for any ITQ fishery with a given TAC and a positivequota price. For a change in the level of uncertainty to leave the quota equilibriumChapter 3. Conceptual Framework 40unchanged it must be the case that the quota demands of all fishers must remainunchanged. In the specific fishery example, (3.23) is not implied by equality of therisk aversion parameters and is a function of both the fishers’ harvesting functionsand their levels of risk aversion. If and only if = f2 will it be true that changingthe level of uncertainty will leave the quota equilibrium unchanged. This conditionensures that the ratio of the quota demands of Fl to P2 fishers is equal to the ratioof the catchability coefficients squared of Fl to F2 fishers, i.e.,= .Under thiscondition, the quota demands are independent of the variance of the output pricesuch that the quota equilibrium is the same with and without uncertainty. Whenthis condition does not hold, the ratio of the quota demands will vary with u suchthat changing the level of uncertainty will change the short-run quota equilibrium.Consider the following result.Proposition 3.1 For a given TAC, if/3i? = /32 then = = 0.PROOF. Differentiating (3.12) by 4 and noting that al = 2C + 2?b/3iu anda2 = 2C +2b/3oj.____— (-)r?b2al— 2b431(— Ptr)3 24ãu - (al)2 (.For a given TAC, dividing the numerator and denominator of the quota price givenby expression (3.17) by (ala2) and differentiating with respect to u we obtain,2Yf3b4r().L—‘‘‘ a12 + a22 --- (Xb2r + Yb2r)2 (3.2o)Substituting (3.25) into (3.24), the numerator of the expression becomesTAC(2 1b6 + 2 2b0a1) TAC(2,Ø1b4)X2b Y2b Xb2 yc2b2 ( )( “1 . __l2__. 2 ( “1 j.“ al a2 ) \ al a2Chapter 3. Conceptual Framework 41multiplying the numerator and denominator of the RHS term of (3.26) by()2±a1Yib2) the expression simplifies toTAC(21b + 2Y/3b6a1_________________al a22 1— TAC[2X1b6± 2.Y[31b6__________________________al a2 i (3.27),Xb2±(Xjb2 YE2bal a2 )al a2If ,8 = /322 it follows immediately that al = a2 = a. Simplifying (3.27) accordingly,TAC( 2Xjb6 + 2Yb6)— TAC[2 /31b6 + 2Y/31b6_(3.28)(Xb±2)2 (Xb2+a awhich solves to the followingTAC(___(3.29)X2b‘ a a /If /3i? = !32e2 it follows immediately that= 0 (3.30)04Performing similar calculations for by differentiating (3.15) with respect to 48q — ( )rb2a2 — 2b4/3(— Per) (3.31)84 — (a2)2Substituting (3.25) into (3.31), the numerator of the expression becomesTAC ( 2Xj31b6a2 2Y8b6) TAC(2,i32b4)a12 + a2___________Xb2( ai + 2)2 — 1Xb2 Y2b(3.32)al + a9multiplying the numerator and denominator of the RHS term of (3.32) by (b2 ±alYb2)and noting that al = a2 = a given !3i = /2 the expression simplifies toTAC(21b + 2Y/3b6)— + 2eYI3b61 (3.33)+(Xb+2)2a aChapter 3. Conceptual Framework 42and solves to the following(, 2 , c2’2t2v6TAC(s1F’2)“12X2b Y2b (3.34)If=it follows immediately that= 0 (3.35)such that (3.23) holds with equality DA corollary to proposition 3.1, is that if the change in the quota demands of fishersdiffer with respect to the level of uncertainty, then it must be true that the output ofsome fishers is greater and other fishers less at the new quota equilibrium. This is anoriginal result as it had previously been accepted that the quota demand of fishers inan ITQ fishery would decrease with an increase in the variance of the output price[P. Andersen (1982) p. 24]. In the fishery example, if /3i <!32 then0> >2.iUpand increasing o3 will increase (decrease) the equilibrium output of Fl (F2) fishers.Similarly, if i? > then0q0a2 < <aa_Pand increasing 4 will increase (decrease) the equilibrium output of F2 (Fl) fishers.This is an important result because it has been shown that in a competitive environment [Sandmo (1982), Ishii (1977)] that the output of a firm facing an uncertainoutput price will, cete’ris pan bus, be reduced given an increase in the variance of therandom variable. A sufficient condition for this result is nonincreasing absolilte riskaversion where absolute risk aversion is defined by (3.36) and nonincreasing absoluterisk aversion by RAFQI) 0.RA() =—_____= coefficient of absolute risk aversion (3.36)Chapter 3. Conceptual Framework 43Nonincreasing absolute risk aversion implies that the risk premium should not increaseas individuals become wealthier in terms of economic profit.A mean-variance specification satisfies the condition of constant absolute risk aversion. From proposition 3.1, however, increasing 4 in an ITQ fishery may actuallyincrease, leave unchanged, or decrease the output of heterogeneous fishers while leaving the total output of fishers unchanged. The difference between the two results isthat in an ITQ fishery it is the quota demands that determine the optimal output offishers. The quota demands are themselves a function of fishers’ harvesting functions,input and output prices, and the quota price which itself is a function of the quotademands. As a result, the effect of an increase in uncertainty on fishers is dependentnot only upon their actions but the actions of others. The effect of a change in uncertainty on the output of an individual fisher cannot be known, therefore, withoutknowing the expected utility functions of all other fishers. This will be true whetherfishers have utility functions that exhibit increasing, constant, or decreasing absoluterisk aversion. In a competitive market where firms face no constraints on their output, their optimum output is determined solely by solving the first order conditionof their expected utility functions. In this case, the affect of uncertainty on a firms’optimum output will depend unambiguously upon the absolute risk aversion of itsexpected utility function.Provided that (3.23) does not hold with equality and assuming the expected priceunder uncertainty equals the price with certainty, it has been shown that the shortrun quota equilibrium will differ between the certainty and uncertainty situations.In the certainty situation where 4 = 0, fishers maximise their individual economicprofits by choice of the quantity of fish they harvest and the quantity of quota traded.Given a competitive quota market with no externalities, it must be the case that theresulting equilibrium cannot be bettered in terms of total profits such that there canChapter 3. Conceptual Framework 44be no other quota allocation that will result in a higher profit from the fishery. Thisresult follows from the first fundamental theorem of welfare economics and impliesthat the short-run quota equilibrium with no uncertainty maximises the short-runrent in the fishery. Consider the following result.Proposition 3.2 Provided that private costs equal social costs, there exists a competitive quota market, and fishers maximise economic profits then for a given numberof fishers of all types and a given TAC, the short-run ITQ quota equilibrium with nouncertainty and/or risk neutrality will maximise the expected short-run rent in thefishery.PROOF. The expected short-run rent in the fishery may be written as follows6{H} = [Qit -___- Xfci] +[(TAC- Qu) - C(TAC-Q12- Yfc2] (3.37)where = Xq1k, Q2t = Yq2 = (TAC— Qii) and X and Y are given. Maximisingwith respect to we obtain the following first order condition_______—— 2CQt— 2C(Qit — TAC)— 3 38aQ1— ?b2X b2Y (.Solving (3.38) with respect to Qit*— TAC(?X) 3 39— x+y (.To show that the total rent in the fishery is at a unique global maximum at Q it issufficient to show thatO2S{flt(Qi;.)} — 2C 2C o 3 40— ?b2X b2Y < (.Chapter 3. Conceptual Framework 45Dividing (3.39) through by X, the number of Fl fishers, we obtain* — TAC(?) 3 41kt—which can be shown to be identical to (3.19) or the quota demand of a El fisherat the short-run quota equlibrium with no uncertainty. Similarly, solving for q2jt bysubstituting (3.39) into the expression Q2i = TAC—*— TAC TAC(X)-— TAC(Y)3 42—Dividing through by Y, the number of F2 fishers, we obtain*— TAC()3 43—( . )which can be shown to be identical to (3.20) or the quota demand of a F2 fisher atthe short-run quota equilibrium with no uncertainty DProposition 3.2 is proved for the specific fishery model but applies generally toany ITQ fishery where there is a competitive quota market, no externalities, nouncertainty, and where the marginal cost curves of fishers are increasing with respectto output. In the case where u, > 0 and the expected output price equals its valuewith no uncertainty, fishers maximise the expected utility of economic profits. In amean-variance specification this is equivalent to fishers maximising expected economicprofit less risk costs. By proposition 3.2 or the first fundamental theorem, ceterispan bus, the resulting equilibrium with oj > 0 must generate an expected short-runrent equal to or less than the equilibrium with no uncertainty. Such a result is notthe case in an open access fishery where the existence of a positive risk premiummay reduce the difference between optimal effort and equilibrium effort and therebyChapter 3. Conceptual Framework 46increase the expected rents in the fishery.6 The difference between the equilibriumwith and without uncertainty where (3.23) does not hold with equality is explainedby the marginal risk premium of fishers. In the case where fishers are risk neutralor where the resource owner bears the entire risk, the expected rent from the quotaequilibrium where > 0 will be the same as the equilibrium with no uncertaintyirrespective of whether (3.23) holds with equality. In the case where (3.23) does holdwith equality, it has been shown that an ITQ equilibrium with uncertainty and riskaversion will maximise the expected short-run rent in the fishery. This is an originalresult as it had previously been believed that a fixed producer price system, wherethe resource owner bears all the risk of output price fluctuations, was the only schemecapable of maximising the expected rent in a fishery.As a corollary to proposition 3.2, if the rent in the fishery is a strictly concavefunction of the quota allocation to fishers then reducing the level of uncertainty asdefined by c4 cannot decrease and will in general increase the expected rent from thefishery. This result is perfectly general because if the short-run rent is strictly concavein the quota allocation the quota equilibrium with no uncertainty must be a uniqueglobal maximum. Consequently, ally change in the equilibrium must reduce the short-run rent. In the specific fishery model, if (3.23) does not hold with equality, the higherthe value of u the greater will be the divergence from the short-run rent maximisingquota equilibrium and hence the lower will be the expected rent. It follows, therefore,that a resource owner concerned with maximising the expected rents in a fishery ormaximising the expected rents less the risk costs of fishers, a reduction in the levelof uncertainty at zero cost will, ceteris pan bus, unambiguously increase its objectivefunction. Reducing uncertainty, ceteris pan bus, will also increase the expected utility6llannesson (1984) made this observation while addressing the issue of fisheries managementunder uncertainty in an open access fishery.chapter 3. Conceptual Framework 47of fishers and will in general increase the expected rent in the fishery. Consider thefollowing result.Proposition 3.3 Provided that the total expected rent in an ITQ fishery is strictlyconcave in the quota allocation then increasing uncertainty cannot increase the expected rent and will in general decrease it.PROOF. Prom proposition 3.2, the rent maximising quota allocation is defined asfollows*— TAC(X)— 2v c2 (3.44)1dkDefining Qit = Xj as the short-run quota equilibrium with uncertainty then from(3.12)- TAC(?X)-Q it = c2y (3.4o)aa2Given that al = 2C + 2?b8iu and a2 = 2C + 2b it follows immediatelythat if = !32 then al = a2 andQ *it— itif/3i? > /3 then al > a2 and< Q (3.47)and if <B9 then al <a2 and> Q (3.48)Differentiating (3.45) with respect to 4ôQu — TAC(?X)[(/3i? — ,@2)4Cb’YJ (3 49)— (?X + Yai )2Chapter 3. Conceptual Framework 48It follows from (3.49) that if /j== 0 (3.50)If !3i? > I32aQit< 0 (3.51)and if i3? </32aQ1> 0 (3.52)Given that the expected rent is strictly concave in the quota allocation then it followsimmediately from (3.46-3.48) and (3.50-3.52) that increasing uncertainty will decreasethe expected rent in the fishery provided that Q Q and leave the expected rentunchanged if Q = QitFrom proposition 3.3., given that the expected rent in the fishery is strictly concavewith respect to the quota allocation, increasing a cannot increase the expectedrent. Similarly, reducing the uncertainty faced by fishers will not decrease and ingeneral will increase the expected short-run rent. From the objective function offishers, irrespective of whether the expected short-run rent is maximised, reducing theuncertainty faced by fishers will always increase their expected utility. An implicationof proposition 3.3, therefore, is that given a risk neutral resource owner and risk aversefishers it is advantageous to reduce the uncertainty faced by fishers. Such risk sharingcould take the form of a fixed output price payable to fishers at price equal to itsexpected value. Increasing the risk aversion of one or more of the fishers defined byor i@2 may, however, increase the total expected rent in the fishery. This surprisingresult arises from the fact that if (3.23) does not hold with equality then the expectedrent maximising equilibrium defined by will not arise. It follows, therefore, thatChapter 3. Conceptual Framework 49if i3? increasing or decreasing the risk aversion parameters of one or both ofthe fishers until (3.23) does hold with equality will change the quota equilibrium towhere expected rents are maximised. The implication to a resource owner, therefore,is that reducing the uncertainty faced by all fishers for a given TAC will not decreasethe expected rent from the fishery and in general will increase it. However, decreasingthe risk costs of certain fishers and not others may increase or decrease the expectedrents.3.3 Fishery RentGiven that the short-run equilibrium allows for the existence of both types of fishersand because regulators are as concerned about the short run as they are about thelong run or a first-best situation, the implications of rent capture methods are firstaddressed assuming the short-run quota distribution. To illustrate the differencesbetween the short run and first best situation a numerical example of a fishery ispresented that is consistent with the conceptual framework.In the example it is assumed u = 0 and that the exogenous variables have thefollowing values: = 2, C = 3.2, r = 0.1, B = 10, b = 20, fc1 = 80, fc2 = 40, and= 2, 2 = 1. Given no rent capture defined as 0k1 = oi = 0 V j, k, the first-bestproblem can be solved by choosing the harvest for each type of fisher and total numberof fishers of all types by solving an algorithm that maximises the sum of individualprofits at each biomass level for different numbers of fishers of the two types. Theglobal optimum is found by searching for the highest total profits over all biomasslevels. The first-best solution with no uncertainty and with no rent capture is to set= 14, N* = 6, M* = 0, = l4OVk, = OVj. This yields a total rent per timeperiod, defined as the sum of the individual profits of fishers, of 720 monetary units.Chapter 3. Conceptual Framework 50This first-best solution with no uncertainty or rent capture requires that the biomassbe 14 and that the total harvest of 840 quantity units per time period be caught bysix Fl type fishers each harvesting 140 quantity units. Given no barriers to entryand exit, a competitive quota market, and that private costs equal social costs, thefirst-best solution should also be the long-run quota equilibrium. In the case of rentcapture, the long-run quota equilibrium and first-best situation will differ because theindividual fishers’ maximisation problem will not internalise the rent collection costsof the resource owner.In comparing the short run to the first-best it is assumed that the TAC under ITQmanagement is set equal to the first-best harvest level of 840 quantity units. Further,it is assumed that the TAC for the ITQ fishery of 840 quota units is allocated equallyamong both types of fishers who in total number no more than the number of fishersin the first-best solution. The amount allocated to individual fishers, however, has noeffect on the market equilibrium and ultimate distribution of quota but does affect thecost/return to fishers from buying/selling or leasing quota. Under these conditionsand using expression (3.21), the market price of quota is found to be some 1.71/unit.Solving for the short-run equilibrium with no uncertainty, each of the three Fl typefishers are found to harvest 224 units while each of the three F2 type fishers harvest56 quota units. The marginal and average cost curves for the fishers are presented inFigure 3.1.It is asumed that the 84 quota units that were obtained by the Fl type fisherswere sold by the F2 fishers at an amount equal to the market price of quota multipliedby number of quota units. In an actual fishery, however, one would likely observeboth outright purchases and leases of quota. At this equilibrium and prior to entryof other vessels, the total fishery rent per time period equals 552 monetary units orsome 168 less than in the long-run or in the first-best situation without rent captureChapter 3. Conceptual Framework 51or uncertainty. Merely setting the TAC equal to the harvest level and allocatingquota to the same total number of fishers as in the first-best solution is insufficientto ensure that the rent available in the short run will be the same. Putting asidethe effects of uncertainty or the costs of rent capture, the rents in the short run andfirst-best solution will only coincide if the number and type of vessels at the timequota is first allocated in the fishery is the same as in the first best solution. Forexample, if the fishery at implementation of ITQ’s had only six Fl type fishers thenthe first-best optimum would arise immediately since there would be no adjustmenttime required for entry and exit of vessels. On the other hand, if the initial conditionswere such that there were three Fl and P2 type fishers, as in the above example, thenthe short-run and first-best equilibrium will differ.Given the potential increase in welfare in moving from the short-run to the first-best, one may expect the distribution of quota to change over time as some vesselsare retired and others added to the fishery. Provided there are perfect markets, nobarriers to entry, and private and social costs are identical, then the first-best isachievable in the time necessary to allow for the entry and exit of all vessels. ‘Where,however, market imperfections exist such as capital constraints on fishers wishing tobuild or buy new vessels or quota, the first-best optimum may never arise. Givensuch imperfections, the initial conditions of the fishery at implementation of ITQ’swill have implications for rent capture in both the short and long-run.Using the example, it is useful to present the profits, average profit per quota unit,and economic profits of fishers not including the costs/returns from buying/selling orleasing quota of the El and F2 fishers. These values are presented in Table 3.1 for eachof the El and P2 fishers in addition to a total for the fishery under the assumption= = 0. The total profits are calculated by multiplying the number of Fl and F2fishers at the short-run equilibrium by the profit for each type. The average profits areChapter 3. Conceptual Framework 52the total profits of fishers divided by their harvests. Consulting Table 3.1, it can beseen that the Fl fishers have both higher total profits and average profits. The higheraverage profits earned by Fl fishers over and above that earned by F2 fishers may beviewed as intra-marginal rents that accrue from the particular harvesting technologythat they employ. The expected per unit resource rent, assuming risk neutrality, isrepresented by the difference between the expected output price and the marginalharvesting cost of fishers at the equilibrium and is reflected in the quota price. It is,therefore, determined entirely by the marginal conditions of the optimising behaviourof fishers. In the case where fishers are risk averse, the expected resource rent willdiffer from the per unit quota price by an amount equal to a fisher’s marginal riskpremium.In examining the different rent capture methods, the maximum rent to be capturedper period by the resource owner is set to be no more than total value of quota-holdings multiplied by a competitive rate of interest. In the case of risk neutralityor no uncertainty this will equal the annual resource rent in the fishery. The intramarginal rent per quota unit in the fishery is defined as the difference in average profitper unit of fish harvested between the least and most profitable fishers. Given theassumption of identical fishing skills among fishers, intra-marginal rents in this fisheryexist because of the technology employed by Fl fishers. Over time, as other fishers areable to adopt the more profitable Fl technology, the difference in profitability amongfishers would disappear. In addition to resource and intra-marginal rents, there maybe another rent that exists in the fishery in the short run. This rent, which maybe termed a marginal quasi-rent, reflects the difference between the marginal fisher’stotal rent and resource rent. It arises because there is a time lag between when ITQmanagement is introduced into the fishery and when other fishers can enter, purchase,and use quota. In the long run, this marginal quasi-rent would disappear becauseChapter 3. Conceptual Framework 53other fishers entering the fishery would bid up the quota price until the marginalfisher was earning only a resource rent less any discounting because of risk.Under the assumption that the earnings of fishers outside of the fishery are zeroand noting that the marginal cost of production exceeds the average total costs forevery fisher, the total rent in the fishery in the short run will, therefore, include anexpected resource rent, an intra-marginal rent, and a marginal quasi-rent. The totalexpected rent is reflected in the expected total profits of fishers, the resource rentin the difference between the expected output price and marginal harvesting costs,the intra-marginal rent in the difference in average profitability between Fl and F2fishers, and the marginal quasi-rent in the difference between expected total profitsand the expected resource and intra-marginal rent. In the case where the average costof some fishers exceeds their marginal cost at the quota equilibrium then the resourcerent will exceed the total profits or total rent in the fishery. Such an equilibrium ispossible in the short run where some fishers may be earning profits and others maybe only covering their variable costs and a share of their fixed costs. The possibilitythat the resource rent may exceed the total profits in the fishery in the short runsuggests, therefore, that an estimate be made of both the total profits of fishers andthe resource rent in fishery prior to any rent capture.The magnitude of the different rents in the short and long run in the fisheryexample are provided in Table 3.2 under the assumption of risk neutrality. A definitionof the rents in the fishery with no uncertainty and positive profits for all fishers isprovided in (3.53) under the assumption that fishers are price takers in both theoutput and factor markets.Total Rent = Resource Rent + Intra-Marginal Rent + Marginal Quasi-Rent— ACq) = (P—MC) qj + [(max(AC) — AC)q] +Chapter 3. Conceptual Framework 54(MC — max(AC)) qj (3.53)where n is the total number of fishers, AC is the average harvesting cost of fisheri, MC is the marginal harvesting cost which is identical for all fishers at a quotaequilibrium given risk neutrality or no uncertainty, max(AC7)is the average cost ofthe marginal fisher.Consulting Table 3.1, Fl fishers have a higher average profit than F2 fishers at theshort-run equilibrium. Both types of fishers continue to remain in the fishery becauseat the equilibrium their marginal value of an additional unit of quota is identical. InTable 3.2, the short-run rent in the fishery is shown to include a resource rent, anintra-marginal rent, and a marginal quasi-rent. The resource rent is reflected in theper unit difference between the output price and marginal harvesting costs multipliedby the total quota-holdings and represents some 26% of the total short-run fisheryrent. The intra-marginal rents, earned exclusively by Fl fishers, accounts for some43% of the short-run rent while the marginal quasi-rent accounts for some 30% ofthe total rent. Over time, as fishers are able to enter the fishery and adopt the Fltechnology the quota price should rise to include the marginal quasi-rent. Giventhe assumption that the intra-marginal rents are due exclusively to the technologyemployed and not differential fishing skill then over time as the El technology isadopted the intra-marginal rents would also disappear. Eventually, the quota pricewould in a world of no uncertainty reflect the total rent per unit in the fishery.3.4 OverviewChapter 3 compares various methods of rent capture in a short-run equilibrium andcompares the outcome to a first-best solution where a resource owner may choosethe total harvest, number of fishers and their individual harvests per time period. InChapter 3. Conceptual Framework 55case of no uncertainty and no rent capture, the short-run quota equilibrium is notfound to be the same as the first-best solution. Merely setting the TAG equal to thefirst best harvest level and allocating quota to the same total number of fishers asin the first-best is insufficient to ensure the rent in the short run will be the same.The first-best and short run solution with no uncertainty or rent capture will onlycoincide when the number and type of vessels when quota are first allocated is thesame as in the first-best solution.The short-run rents in a fishery are also discussed and defined. It is noted thatthere may exist an intra-marginal rent defined on a per quota unit basis as the difference in average profit per unit of fish harvested between the least and most profitablefishers. A resource rent per quota unit represents the difference between the priceand marginal cost of fishers at a quota equilibrium and is reflected in the quota price.A marginal quasi-rent which accrues to all fishers may also exist in the short run andon a per unit basis is the difference between the marginal fisher’s total rent per unitand resource rent per unit.Addressing the issue of uncertainty, it is found that, in general, changing the levelof uncertainty as defined by o will change the short-run quota equilibrium. It is alsoshown that the optimal output of fishers will change depending upon how the quotademands of fishers change with respect to 4 and may increase, stay the same, ordecrease. In a related result, is demonstrated that reducing the uncertainty faced byfishers for a given TAG will not decrease the expected rent from the fishery and ingeneral will increase it. However, contrary to what one might expect, decreasing therisk costs of certain fishers and not others may increase or decrease the expected rentin the fishery.Chapter 3. Conceptual Framework 56Table 3.1: Short-run annual profits of Fl and F2 fishers prior to rent capture givenrisk neutralityDescription Profit Quota-Holdings Average Profit Economic ProfitFl 163.2 224 0.73 139.2P2 20.8 56 0.37 11.2Total 552 840 0.66 451.2Table 3.2: Annual fishery rents with no rent capture given risk neutralityPeriod Resource Rent Intra-marginal Rent Marginal Quasi-rent TotalShort Run 144 240 168 552Long Run 720 0 0 72057Figure 3.1: Cost Curves of Fl and F2 Fishers350431020 86 152 218 284QuantityChapter 4Rent Capture Methods ReviewedA pity only that the rent on land goes into private handsJens Warming (1873-1939), History of Political Economy, vol 15(3), 1983, p 124. Atranslation of Jens Warming’s 1911 article “On rent of fishing grounds” by PederAndersen.4.1 IntroductionUsing the fishery model developed in chapter 3, seven methods of rent capture arereviewed including a quota rental charge, profit charge, net cash flow charge, an advalorem royalty, lump sum fee, an auction/tender, and a quota transfer charge. Eachmethod of rent capture is first examined individually along with a description of itsprincipal features. A comparison is then made of the various methods by assessingtheir differential impact on fisher profits, distortions to efficiency, collection costs, andthe risk costs of fishers. A discussion is also provided on the effects of rent captureunder uncertainty.To aid in the exposition, the fishery example provided in chapter 3 with givenvalues for the exogenous variables is used to compare the effects of rent capture onfishers’ profits. In the comparison, it is assumed the resource owner captures rent at100% and 50% of the total annual value of quota-holdings as measured by the quotaprice multiplied by the TAC and the interest rate. A rate of rent capture equal to58Chapter 4. Rent Capture Methods Reviewed 59100% of the total value of quota-holdings is, however, not a recommended practicesince it may be desirable for the resource owner to have quota trade at a positiveprice.14.2 Quota Rental ChargeA quota rental charge imposes a rental payment equal to some proportion of thequota price multiplied by a competitive rate of interest, i.e.,Annual Rent Captured from Fisher i,t =where c is the quota rental charge rate, F is the market price of quota per unit attime t, r is the competitive rate of interest, and q is number of quota units ownedat time t by fisher i.The quota rental charge attempts to collect a rental equal to a share of the annuitythat would be earned if all quota owned were sold and the amount was invested outsidethe fishery at a competitive rate of illterest. In a perfect quota market where fishersare price takers, have perfect foresight, the same planning horizon, a rate of timepreference equal to the competitive rate of interest, and there is no uncertainty, a100% quota rental charge should over time capture the entire resource rent in thefishery. In fisheries where such conditions do not exist, a quota price will not be atrue reflection of the resource rent in the fishery. In the case of risk aversion anduncertainty the quota price will be less than the expected resource rent. Where thereexists an uncompetitive quota market, the quota price will also be less than the perunit resource rent. Such a quota market may arise from oligopsonistic behaviour andbarriers to entry into the fishery which penalises both sellers and lessors of quota. It‘Arnason (1989) has showii that under certain assumptions maxinhising the total value of quotain an ITQ managed fishery where quota is denominated as a share of the TAC will mañmise thetotal fishery rent.Chapter 4. Rent Capture Methods Reviewed 60may also arise from an uneven distribution of risk costs among fishers. In such cases,the resource owner may capture less rent than desired from the fishery.A feature shared by the quota rental charge with an auction or tender is thatit is an ex-ante method of rent capture. Because it is based upon the expectationsof future net returns of fishers, it is possible for a quota rental charge to collectrent even when fishers are facing short-run losses due to adverse fluctuations in thefishery. Consequently, a quota rental charge can place a considerable burden on fishersin that short-run fluctuations in the fishery not reflected in the quota price are borneexclusively by fishers. In this sense, the quota rental charge fails to reduce the costof risk faced by fishers. If it is the case that fishers are risk averse and the resourceowner is risk neutral then there are potential welfare benefits from the sharing of riskbetween fishers and the resource owner.In imposing a quota rental charge, the resource owner faces the choice of basing therental on the pre-rental quota price or on the quota price following the announcementof rent capture in the fishery. If imposed on the pre-rental price then the resource rentcollected each time period will not reflect any changes or fluctuations in the fishery. Ifimposed on the current quota price, the quota rental charge will vary with changes inthe market’s expectation of future net returns in the fishery. Given that the currentprice would reflect the marginal profit to fishers net of the rental charge, the chargerate would necessarily have to be greater than if it was imposed on the pre-rentalqilota price. For example, a 100% quota rental charge assessed on the quota priceafter announcement of rent capture by the resource owner would collect the sameamount of rent as a 50% rental charge assessed on the pre-rental quota price. Thequota rental charges examined in this and other chapters assumes that the rental isimposed on the pre-rental price.Another feature of a quota rental charge is the assignment of a “competitive rateChapter 4. Rent Capture Methods Reviewed 61of interest” and a market price of quota in setting the rent charged. In deciding uponan appropriate rate of interest, the regulator must take care to avoid a rate that is toohigh such that more than the resource rent is collected and setting a rate too low suchthat less rent than desired is captured. If a resource owner wishes to reduce the risk ofcapturing more than the resource rent then assessment of the rental at a risk free rateof return may be desirable. In determining a quota price, it should be realised thatprices can vary significantly over a fishing season and between bids [Lindner et al.(1989)]. On a practical basis, if quota prices are subject to considerable fluctuationssome weighted average of quota prices on a regular basis may be desirable in termsof determining the rental charge.4.3 Profit ChargeA profit charge captures rent at a fixed proportion of fisher profit and would beapplied prior to any standard company profit taxes, i.e.,I pOj if8 >0Annual Rent Captured from Fisher i,t =( 0 otherwisewhere p is the profit charge rate and &j is the profit of fisher i at time t.The profit charge proposed above would collect rent whenever profits are positive.Whenever profits are negative, the losses are borne exclusively by the fishers. It doesnot, therefore, represent a full loss offset profit charge where the resource owner paysout to fishers at the given charge rate whenever profits are negative. In determiningthe profit of fishers, the lease or purchase costs or interest payments on quota shouldnot be treated as a deductible expense. This would ensure all fishers were treatedequally in terms of their rental payments and avoid the possibility of fishers whowere initially assigned quota gratis from selling their quota to a third party and thenChapter 4. Rent Capture Methods Reviewed 62leasing it back thereby reducing their tax liability.The profit charge, unlike the quota rental charge, does not face the problem ofdeciding upon an appropriate rate of interest or quota price. It does, however, requirethat the resource owner know the individual earnings of fishers. Such informationmay be difficult and/or expensive to obtain. Further, in environments where thereexist legal allowances such as accelerated depreciation or investment write-offs, theaccounting profit of fishers may differ markedly from actual profits. There is also apotential problem that may arise out of the treatment of interest payments in thecalculation of profits. If interest payments are deductible then those fishers who havepurchased vessels or quotas with borrowed funds are relatively favoured over thosewho have financed such expenditures out of their own equity. The profit charge may,therefore, not be uniform in its effect across fishers.The setting of an appropriate profit charge in multi-species fishery may also proveproblematic. This is especially true in a multi-species fishery where a profit chargemay collect rent from a subset of the species harvested. In such fisheries, separatingexpenses such as fixed costs among species would require arbitrary judgements by theregulator.4.4 Net Cash Flow ChargeA net cash flow charge captures rent as a proportion of the net cash flow of fishers,i.e.,TNCFt given AlAnnual Rent Captured from Fisher i,t T[NCF + >Ej NCF(l + r)x} given A20 otherwiseAl : NCF > 0 and D11NCF(l + r)x > 0.Chapter 4. Rent Capture Methods Reviewed 63A2 : Ej NCFj(1 + r)x 0 and NCF + NCF(1 + r) > 0.where T is the net cash flow charge rate and NCF is the net cash flow of fisher i attime t, 1jNCF(l + r) is the capitalised value of fisher i’s net cash flow untilperiod t.The net cash flow of a fisher is defined as the total revenue from harvesting lesscash expenditures excluding interest payments. Interest should not be considered asa deductible item since it would favour the operations of fishers with lower equityand higher debt load. Although similar to a profit charge, the net cash flow chargehas some important differences. In keeping with Garnaut and Ross (1975) and theirresource rent tax, positive cash flows would be charged at a predetermined rate whilenegative cash flows would be increased by a specified interest rate. Any capitalisednegative cash flows would be substracted from positive cash flows before any rentcapture would take place. In proposing such a rental charge, Campbell and Haynes(1990) suggest that the rates of interest used to capitalise negative cash flows varyacross fisheries. The greater riskiness of the fishery as measured in terms of uncertainty with respect to future returns and stock fluctuations then the greater theinterest rate applied.One problem with a net cash flow is its treatment of capital costs. In the case ofvessels and gear already in the fishery, the net cash flow charge does not provide anallowance for depreciation or an opportunity cost for the value of the assets employed.Only when fishers purchase new gear or equipment is the net cash flow reduced by thecapital expenditure. One way of addressing this problem is to allow for depreciatedcapital as a one off expense when the rental scheme is first introduced [Campbelland Haynes (1990)]. Without such an allowance those fishers who undertake capitalinvestments after the charge is imposed will be better off in terms of their rentalChapter 4. Rent Capture Methods Reviewed 64payments than identical fishers who purchased their vessel and gear before the chargewas imposed. Another problem with a net cash flow charge, shared with a profitcharge, is the separation of costs for individual species if fishers pay only a resourcerent in a sub-set of the species. Imposing a net cash flow charge or a profit charge ina single species fishery may also prove difficult as unlike other rent capture methods,both require detailed cost and earnings information from individual fishers.4.5 Ad Valorem Royalty ChargeThe ad valorem royalty charge collects rent as a set percentage of the landed price offish multiplied by the quota-holdings of fishers, i.e.,Annual Rent Captured from Fisher i,t =where [L is the ad valorem charge rate, P is the landed price of fish at time t, and qjjis number of quota units owned at time t by fisher i.In an ITQ managed fishery where each fisher faces a binding quota constraint,assessment of the royalty on quota-holdings should approximate the actual landingsof fishers. An advantage of imposing a royalty on quota-holdings rather than onlandings is that it gives less incentive to fishers to misrecord their catches. Oneadvantage with an ad valorem royalty is that it is relatively easy to implement andrequires less information than a profit or net cash flow charge. In the case wherefishers are risk averse and there exists random fluctuations in the output price, an advalorem royalty also provides a means for risk sharing with the resource owner.4.6 Lump Sum FeeA lump sum fee collects rent from fishers by dividing the total amount of rent to becaptured in the fishery by the number of fishers. The annual rent captured by theChapter 4. Rent Capture Methods Reviewed 65resource owner is, therefore, identical over all fishers, i.e.,Annual Rent Captured from Fisher i,t = R/nwhere R is the total amount of rent collected by the resource owner and nt is thetotal number quota-holders at time t.A feature of the lump sum fee is that each fisher pays the same rental to theresource owner irrespective of the quota-holdings and resource rent of fishers. Itsprincipal advantage is the relative ease with which it may be applied in a fishery. Itis for this reason that is a common method of cost recovery in a number of fisherieswith limited entry or restrictive licensing.4.7 Auction/tendersAn auction or tender of quota collects rent by selling a share of the TAC to individualfishers. An auction may allow quota-holders harvesting rights in perpetuity with fullrights of resale or the resource owner may impose restrictions such as limiting thetenure to a given period of time with a subsequent auction/tender in future periods.A feature of an auction of individual quotas in a fishery is that the bidder would berequired to specify both a price and quantity to be purchased. To aid in the biddingprocess, the bidders would be required to submit a minimum and maximum desiredquantity of quota and a price that would be paid for the various quantities in between.In auctioning quota, a resource owner faces the choice between a number of different types of auctions. These include an English, Dutch, first price sealed-bid,and second-price sealed bid auctions. Under the following assumptions, [McAfee andMcMillan (1987)] the choice of the auctioii type will have no effect on the averagerent captured.Chapter 4. Rent Capture Methods Reviewed 661. Bidders are risk neutral.2. Bidders appear the same to each other and the seller.3. Bidders determine the value of their bids independently.4. Payment is a function of the bid alone.This revenue equivalence proposition is dile to Vickrey (1961). Under these assumptions and given perfect forsesight by fishers, an individual will bid an amountequal to the net present value of quota for the tenure of the quota, i.e.,TRent Captured from Fisher i =t=1where 5 is a discount factor, 8 is the profit for fisher i in period t for a given levelof quota, and T is the tenure of the quota.In an actual fishery, however, the assumptions for revenue equivalence are unlikelyto hold. Fishers may be risk averse with respect to quota purchases and there may beconsiderable uncertainty with respect to the true value of the net returns in the fishery.In the case of uncertainty and risk averse individuals with competitive bidding, fisherswill pay an amount in monetary terms no more than the discounted sum of theexpected utility of their future profits for a given quantity.TRent Captured from Fisher i=e{ 6’U(O,,)}where 5 is a discount factor, U(8) is the utility of profit for fisher i in period t fora given level of quota, and T is the tenure of the quota.The difference between the certainty and uncertainty cases is that in the formerfishers can bid up to the discounted sum of their future profits, while in the latter theywill bid up to discounted sum of their expected profits less risk costs. In the certaintyChapter 4. Rent Capture Methods Reviewed 67case, an auction has the potential of capturing the present value of any future resourcerent, intra-marginal rent, and marginal quasi-rent. The capture of intra-marginal rentshould, however, have no efficiency implications because any returns from innovationafter the auction would accrue directly to the fisher. In a mean-variance specificationand assuming the mean of the random variable equals the value with no uncertainty,the difference between the certainty and uncertainty cases would be entirely reflectedin the discounted sum of the risk premium of fishers.A concern common to all auctions is the up front costs and burden that such anex-ante method of rent capture may impose on fishers. In the case of quota thatis being auctioned in perpetuity, the bids may be several times greater than theexpected annual profit of fishers. This may, in turn, penalise those fishers who face agreater borrowing constraint due to a high debt burden or little collateral. Similarly,companies who own several vessels or have more diversified interests may be better inovercoming any borrowing constraint and have an advantage in the auction process.In such cases, the successful bidders need not be those individuals with the highestvaluation of the quota. To overcome this difficulty, auctions of quota may be givenon a time limited tenure basis. In moving to time limited quotas, however, the natureof the property right is diminished. Uncertainty about future success in an auctionmay also limit investment that might otherwise take place. Another alternative toimposing high up-front costs on fishers is to impose both ex-ante and ex-post rentcapture. In such a system, an additional method of rent capture, such as an advalorern royalty, could be announced prior to the auction thereby reducing the netprofits to fishers and their bid prices.Another issue with an auction is that if fishers are risk averse, increasing uncertainty will reduce the bid price for quota. The greater the degree of risk aversion fora given level of uncertainty, the lower will be the price bid for quota by a fisher inChapter 4. Rent Capture Methods Reviewed 68an auction. Similarly, the greater the uncertainty for a given level of risk aversionthe lower will be the bid price. In the absence of capital constraints, the successfulbidders for quota will, therefore, be those fishers with the highest expected profitsless the costs of risk. Such fishers need not necessarily be individuals who earn thehighest expected profits. Indeed, fishers who are highly specialised in a particularfishery may face greater risk costs reflected in a higher risk aversion parameter thandiversified companies with interests in other economic activities. In using an auctionto capture rent from a fishery, the less uncertainty faced by fishers, ceteris pan bus,the greater will be the amount of rent collected. In this sense, it may be worthwhilefor a risk neutral resource owner to take on the risk that would otherwise be faced byfishers. In the case of uncertainty with respect to the output price, this could takethe form of auctioning the quota and arranging to pay fishers a fixed output priceequal to its expected value.4.8 Quota Transfer ChargeThis method of rent capture imposes a burden only upon the seller or lessor of quotaand collects rent equal to a share of the quantity of quota traded multiplied by theprice at which it traded. It represents, therefore, a direct transfer from the seller orlessor of quota to the resource owner.Annual Rent Captured by Resource Owner, t= riPb + C7twtwhere F is the average price paid for quota in perpetuity, L’ is the amount of quotasold, ‘y is the average lease price of quota, and Wt is the amount of quota leased inperiod t, while and are the transfer charge rates, respectively, on quota sold andleased.Chapter 4. Rent Capture Methods Reviewed 69The amount of rent captured with a quota transfer charge is dependent on thecompetitiveness of the quota market and the number of transfers. It shares a featurewith the quota rental charge in that it is based on the quota price but differs inthe respect that it is imposed only when quota is traded and leaves the returns inthe fishery unchanged. A quota transfer charge, therefore, reduces the incentive formarginal fishers to exit the fishery but not the profits they may earn. Such a methodof rent capture may, consequently, prevent more profitable operators from harvestinga greater share of the TAG. In the extreme, where i = = 1.0, there is no incentivefor a marginal fisher to trade quota such that individual quota management will notlead to the Pareto efficient quota equilibrium. Such a situation is equivalent to havingnontransferable individual quotas. Another problem with a quota transfer charge isactually collecting the rent with such a charge. In many fishery environments, itwould he difficult to police the reported sale or lease price and relatively easy for abuyer and seller to agree to unreported payments to their mutual advantage.4.9 DiscussionThe seven methods of rent capture are assessed according to their effect upon the post-rent capture profits of fishers, their distortions upon the efficient operations of thefishery, their costs of rent collection and ability to capture rent, their ability to sharerisk between the resource owner and fishers, and their flexibility to adjust to changesin the rent. These issues are examined separately and where possible each methodof rent capture is ranked according to the respective criteria. An overview of thedifferent methods of rent capture according to the different criteria is then providedat the end of the chapter. To aid in the exposition, the fishery example presented inchapter 3 with defined values for the exogenous variables is used to compare the rentChapter 4. Rent Capture Methods Reviewed 70capture methods with respect to the burden they impose on different fishers.4.10 Profits of FishersAn important consideration to a resource owner in selecting a method of rent capture is the differential effects on the profits of different fishers. Some methods maypenalise smaller but not necessarily less profitable operators while others may collectproportionately less rent from one group of fishers than another.To illustrate the issues, Tables 4.1 and 4.2 detail the profits and rent collectedfor various rent capture schemes for the Fl and F2 fishers assuming risk neutralityfor all fishers and using the fishery example presented in chapter 3. The post-rentalprofits are calculated by subtracting from fisher profits the rental payment associatedwith the different methods of rent capture. In determining the rental payment fora net cash flow charge, it is assumed that the net cash flow of fishers equals theirtotal revenue less variable costs. Under this assumption, the fixed costs of fishersmay be viewed as an interest payment on capital employed in the fishery. It is furtherassumed that all quota is purchased/sold and that transactions take place at thepost-rent capture price after announcement of the method and rate of rent capture.Table 4.1 compares the post-rental profits of fishers given 100% collection of theannual value of quota-holdings while Table 4.2 compares post-rental profits of equivalent rent capture schemes under 50% rent capture.2 Observation of Tables 4.1 and4.2 reveals that a quota rental charge imposes the same burdeii on Fl and F2 fishersas an ad valorem royalty and a net cash flow charge. In all three methods of rentcapture and assuming risk neutrality, the El and F2 fishers are left, respectively, withannual profits of 124.80 and 11.20 given 100% capture of the resource rent. Under2Any two or more methods of rent capture are said to be “equivalent” if they capture the sametotal amount of rent from the fishery.Chapter 4. Rent Capture Methods Reviewed 7150% rent capture, the three schemes leave Fl and F2 fishers with profits of 144 and16 monetary units.Provided that fishers face the same output price, an ad valorem royalty on thequota-holdings of fishers can be shown to always leave fishers with the same profitsas an equivalent quota rental charge with or without uncertainty. This proposition istrue for any fishery and not just for the specific model used in the thesis. Considerthe following result.Proposition 4.1 At a short-run quota equilibrium if fishers face the same outputprice and charge rates then a quota rental charge and an equivalent ad valorem royaltyon quota-holdings will leave fishers with identical profits.PROOF. Equality of the rent captured by an ad valorem royalty and quota rentalcharge requires that= crFrq (4.1)Given that fishers face the same charge rates, output price, quota price, and mterestrate (4.1) simplifies toiPt =It follows immediately= V i (4.2)where the LHS of (4.2) is the rent paid with an ad valorem royalty and the RHS isthe rent paid with a quota rental charge DEquivalency between the net cash flow charge and quota rental charge as shownin Table 4.1 and 4.2, however, is not a general result and arises from the specificChapter 4. Rent Capture Methods Reviewed 72characteristics of the harvest functions given in the fishery example. In the specificfishery example with no uncertainty, it can be shown that the ratio of the output ofthe El to F2 fishers at the quota equilibrium is the same as the ratio of their variablecosts and equals the ratio of the catchability coefficients squared. It follows, therefore,that the ratio of the net cash flow of fishers will equal this same ratio and will alsoequal the ratio of the value of quota-holdings of the Fl to F2 fishers. This impliesthat the proportion of the value of quota-holdings to net cash flow is the same foreach fisher. Consider the following result.Proposition 4.2 At the short-run quota equilibrium without uncertainty, the ratioof the quota demands of Fl and F2 fishers equals the ratio of the variable costs of Fland F2 fishers and equals the ratio of the catchability coefficients squared of Fl andF2 fishers. It follows that the ratio of the value of quota-holdings to net cash flow isthe same for Fl and F2 fishers.PROOF. The quota demands of Fl and F2 fishers with no uncertainty are as follows— ?(TAC)qlkt—(4.3)— (TAC)44q23t—. )The variable costs of Fl and F2 fishers are as followsVC1 = (4.5)= Cq2 (4.6)Dividing (4.3) by (4.4) and dividing (4.5) by (4.6)T7f1kt — VL’l—ci 47q2tVC2Chapter 4. Rent Capture Methods Reviewed 73From (4.7), the net cash flow of Fl and F2 fishers may be written as followsNCF1 = Pq1k - VC1 (4.8)2NCF2= [q1kt — VC1]- (4.9)From (4.7), the annual value of quota-holdings of Fl and F2 fishers is as followsAnnual Value Quota-Holdings Fl = Firqlkt (4.10)Annual Value Quota-Holdings F2 = [Ftrq1kl] (4.11)It follows immediately from (4.8-4.9) and (4.10-4.11) that the ratio of the value ofquota-holdings to net cash flow is identical for both fishers DIf the value of quota-holdings to net cash flow is the same for all fishers, irrespectiveof the harvesting functions of fishers, then the rent paid in either a net cash flow chargeor quota rental charge will be identical. Consider the following result.Proposition 4.3 If the individual value of quota-holdings of fishers as a proportionof the net cash flow is the same for all fishers then a net cash flow charge and anequivalent quota rental charge will leave fishers with identical profits.PROOF. Equivalency of a net cash flow charge to a quota rental charge requires that— C(q1)J = [Ftrqt] (4.12)Rearranging (4.12)r—Frq1N,‘•jii —Provided that the value of quota-holdings as a proportion of net cash flow is the samefor every fisher then the following must holdr—Frq Frq1 (4 13— fL1(Pq — C(q)) (Pq — C(q))’Chapter 4. Rent Capture Methods Reviewed 74which implies— C(qt)) = V i (4.14)where the LHS of (4.14) is the rental paid with a net cash flow charge and the RHSis the rental paid with a quota rental chargeIn general, if the value of quota-holdings as a proportion of net cash flow for a fisheris higher than the average for the fishery then an individual will pay proportionatelymore with a quota rental charge than an equivalent net cash flow charge. Similarly,if the value of quota-holdings as a proportion of the net cash flow is less than theaverage for the fishery, a fisher will pay proportionately more with an equivalent netcash flow charge. The net cash flow charge will, therefore, tend to be preferred bythose fishers whose net cash flow earnings per quota unit are less than the average forthe fishery. Conversely, those fishers with higher than average net cash flow earningsper quota unit will prefer a quota rental charge. To the extent that net cash flowearnings per quota unit are a measure of average profitability, so-called highliners willprefer a quota rental charge over a net cash flow charge.In the fishery example, the post-rental profits of fishers are the same with a quotarental charge, net cash flow charge, and ad valorem royalty if all three schemes collectthe same total amount of rent from the fishery. Such a result, however, does not holdfor a profit charge or a lump sum fee. Observation of Tables 4.1 and 4.2 reveals thatfishers who earn higher average profits per unit of fish harvested (Fl) will prefer aquota rental charge over a profit charge. For example, at 50% rent capture of theannual value of quota-holdings, Fl fishers pay 21.29 with a profit charge and 19.20monetary units with a quota rental charge. In comparison, F2 fishers pay, respectively,2.71 and 4.8 monetary units under a profit and quota rental charge. Consequently, F2fishers pay proportionately more rent with a quota rental charge than an equivalentChapter 4. Rent Capture Methods Reviewed 75profit charge while Fl fishers pay proportionately less rent with a quota rental chargethan a profit charge. This result is completely general: provided that a fisher earnsa higher profit per quota unit than another, the fisher will pay proportionately lessrent with a quota rental charge than with an equivalent profit charge than a fisherwith a lower profit per quota unit. Consider the following result.Proposition 4.4 Fishers with a higher average profit per unit of quota will pay proportionately less with a quota rental charge than with an equivalent profit charge incomparison to a fisher with a lower average profit per unit of quota.PROOF. Equality of the rent captured by profit charge and quota rental chargerequires that= (4.15)Defining the average profit per quota unit by fishers which satisfies (4.15) as>qij 2t ntMultiplying bypcFrwe obtainP8it P6ntcq1Frwhere the numerator is the rental paid with a profit charge and the denominator isthe rental paid with a quota rental chargeConsulting Tables 4.1 and 4.2, it can be seen that the Fl fishers pay the leastamount of rent with a lump sum fee than with any other method of rent capture.Chapter 4. Rent Capture Methods Reviewed 76Conversely, F2 fishers pay the greatest amount of rent with a lump sum fee. Thisdifference arises from the proportion of the total quota owned by the respective fishersrelative to the proportion they represent of the total fleet. For example, the proportionof the total quota owned by individual Fl and F2 fishers is, respectively, 0.267 and0.067. Each El and F2 fisher, however, represents 0.167 of the total number of fisherssuch that El fishers would pay less with a lump sum fee than a quota rental chargewhile F2 fisher would pay more. This result is completely general and applies to anyfishery. Consider the following.Proposition 4.5 Individual fishers who own a share of the TAC that exceeds theproportion of the rent paid per fisher with a lump sum fee will pay proportionately lesswith a lump sum fee than with an equivalent quota rental charge.PROOF. The rent paid, as a proportion of the total rent captured, by fisher i with aquota rental charge isit= E1 qtThe rent paid, as a proportion of the total rent captured, by fisher i with a lump sumfee iswit=where n is the number of quota-holders or those persons liable for a lump sum feecharge at time t. It follows immediately that if V > T’V then a fisher i will prefer alump sum fee over an equivalent quota rental charge 0A lump sum fee can also be shown to be preferred over a profit charge by thosefishers who have a higher than average level of profits. Such fishers would pay rentin the same proportion as fishers with low average profits with a profit charge butChapter 4. Rent Capture Methods Reviewed 77would pay proportionately less in an equivalent rent capture scheme that chargesevery fisher the same amount.A lump sum fee by forcing every fisher to pay the same rental irrespective ofquota-holdings or profits, has the ability, therefore, to capture more than just rentfrom certain fishers. Consulting Table 4.1, it can be seen that a lump sum fee thatcollects an amount equal to 100% of the annual value of quota-holdings leaves P2fishers with after-tax losses of 3.20 monetary units. At this same rate of rent capture,Fl fishers retain some 38% of the annual value of their individual quota-holdings.A method of rent capture not presented in Tables 4.1 and 4.2 is the quota transfercharge. An equivalent comparison with such a rent capture method is not possiblebecause it is unable to collect the same total amount of rent from the fishery as theother schemes. The imposition of a quota transfer charge has the effect of changingboth the quota equilibrium and the quota price. For example, noting that Fl (P2)fishers are buyers (sellers) of quota, one may use (3.19) and (3.20) to solve for thequota demands of fishers with a quota transfer charge rate and i3 = /32 = 0:2b[P— Ptr]qlkt= 2C (. )——_______________q2jt— 2C (4.17)where and are, respectively, the quota demands of Fl and P2 fishers facinga quota charge rate of = in the interval (0 — 1). Assuming risk neutrality or nouncertainty the quota price solves to the following:— P[X + Y]b2 — 2C(TAC) (4 18- [Xe? + (1- )Y]b2rSubstituting (4.18) into (4.16) and (4.17) and differentiating with respect to theChapter 4. Rent Capture Methods Reviewed 78charge rate reveals that the quantity harvested by Fl (F2) fishers is decreasing (increasing) with respect to the charge rate. Consider the following result.Proposition 4.6 An increase in the quota transfer charge rate in the closed interval[0 — 1] will increase (decrease) the output of F2 (Fl) fishers.PROOF. Given Fj > 0 it follows from (4.18)—Yjb2r[P(X+ Y)— 2C(TAC)]0 4 19- (X?b2r+ (1- C)Yb2r) > (.It follows from (4.16)____2br(-)kt = —2C <0 by (4.19) (4.20)It follows from (4.17)_— b2r[(( l)(t) + Pt] (4 21)2Csubstituting (4.18) and (4.19) into the expression [( — 1)() + P] we obtain[(C -1)(OFt) += X +(1-C)Y >0 (4.22)Substituting (4.22) into (4.21) it follows immediately that > 0 DAt any quota transfer charge rate greater than zero, therefore, the quota equilibrium will differ from the Pareto efficient quota equilibrium. In the extreme case wherethe charge rate is set at 100% of the quota price, the F2 fishers would optimise bysetting their marginal cost plus a marginal risk premium equal to the expected outputprice. In the case of risk neutrality for all fishers, the quota equlibrium would haveeach F2 fisher selling 78.75 quota units aild harvesting 61.25 quota units. Assumingthe quota traded was sold by F2 fishers at the quota price given by (4.18), the quotatransfer charge would collect in total some 506 monetary units. At this equilibrium,Chapter 4. Rent Capture Methods Reviewed 79each F2 fisher would earn profits of 21.25 monetary units per time period and theoutput price would equal their marginal cost. Correspondingly, Fl fishers would harvest only 218.75 quota units and earn profits of 162.19 monetary units. The totalrent in the fishery in the short run would be 550.31 monetary units, a reduction of1.69 monetary units over the equilibrium without a quota tranfer charge.The final method of rent capture to be examined is an auction of quota. Givenrisk neutrality, an auction under certain conditions is able to capture the presentvalue of expected profits. In an annual auction of the entire TAC of 840 quota units,an auction should capture 552 monetary units, an amount equal to the total profitin the fishery. This is substantially more than the 144 monetary units captured witha 100% quota rental charge, an amount equal to the expected resource rent in thefishery. Only in the case where marginal cost equals average cost for every fisherwould a quota rental charge and an auction capture the same amount of rent fromthe fishery. In general, this condition will only arise in the long run after the passageof sufficient time to allow for full adjustments in the fishery and entry and exit of allvessels.In reviewing the effects of rent capture on fishers it is important to considerboth the annual profits and gain/loss from quota trading of fishers. To aid in theanalysis, Table 4.3 presents the gain/loss from quota trading assuming all quota issold/purchased in the first period after announcement of the type and rate of rentcapture. In comparing the gains/losses from quota trades, it is useful to examine thedifferent impacts of different methods of rent capture on the quota price.The methods of rent capture that affect the quota price the most for a givenamount of rent collected are a quota rental charge and an ad valorem royalty. Ina quota rental charge, each percentage increase in the charge rate on the pre-rentcapture quota price reduces the quota price by one percent. Provided that an adChapter 4. Rent Capture Methods Reviewed 80valorem royalty collects the same amount of rent as a quota charge, it will also havethe same affect upon the quota price. In the case of a profit or net cash flow charge,the quota price after rent capture is, respectively, (l-p) and (1-T) multiplied by thepre-rent capture quota price. Whenever the annual value of quota-holdings is lessthan the total profits or total net cash flow of fishers, then the charge rate for a quotarental charge will be greater than that for an equivalent profit charge or net cash flowcharge. It follows, therefore, that if p or r are less than the quota rental charge ratec, the post-rent capture quota price will be higher than with a quota rental charge.The rent capture method that does not change the quota price is a lump sum fee.This is because a lump sum fee will be treated as a fixed cost by fishers and would notbe accounted for in a quota price that reflects the marginal conditions in the fishery.Those methods of rent capture that reduce the quota price the least will, therefore,tend to benefit those fishers who sell or lease out their quota. Consulting Table 4.3,therefore, a lump sum fee is the least (most) preferred method of rent capture in termsgains/losses from quota-trading for Fl (F2) fishers. In descending order of preferencein terms of quota trading only, Fl fishers would prefer a quota rental charge and advalorem royalty, profit charge, net cash flow charge, and lump sum fee. F2 fisherswould have a reverse ordering, preferring the lump sum fee the most and quota rentalcharge the least in terms of the gains from quota-trading.4.11 Distortions to EfficiencyA fundamental feature of ITQs given a competitive quota market, zero transactionscosts, private costs equal social costs, perfect information, and no restrictions on exitor entry or on the sale or lease of quota is that the resulting equilbrium allocationChapter 4. Rent Capture Methods Reviewed 81should be Pareto efficient for the given TAC’.3 If this was not the case, it would implythat at a quota equilibrium there would be gains to be made from trade. An importantconsideration in capturing rent, therefore, is to ensure that the Pareto efficient quotaallocation does not change and that no distortions are introduced into the fishery.In comparing the different methods of rent capture where the annual value ofquota-holdings is equal to or less than the total profit of fishers, it can be shown withthe specific fishery model that a lump sum fee charge and a quota transfer chargecan alter the Pareto efficient allocation while still collecting an amount no more thanthe total value of quota-holdings. In the case of the lump sum fee applied uniformlyto all fishers, the rental paid by each fisher is unrelated to their individual earningsor quota-holdings. It has the potential, therefore, of penalising fishers who haverelatively small quota-holdings but who may be no less profitable than other fishers.In the specific fishery example, a lump sum fee that collects in total 144 monetaryunits, an amount equal to the annual value of quota-holdings, would charge a rentalto each fisher of 24 monetary units. At this charge rate, however, F2 fishers wouldface losses of 3.2 monetary units per time period. Such fishers would, therefore, beobliged to exit the fishery resulting in a new short-run quota equilibrium. The totalrent in the fishery and quota-holdings of fishers before and after the introduction ofsuch a lump sum fee are presented in Table 4.4.At the new equilibrium with a lump slim fee, each Fl fisher would harvest 245quota units and earn a pre-tax profit of 165 monetary units. Assuming the sameamount of rent is collected from the fishery then each of the El fishers upon thedeparture of the F2 fishers would pay 48 monetary units per time period for theprivilege of leasing the quota from an F2 fisher. In total, the rent in the fishery at the31t should be noted that ITQs can deal with the problem of stock externalities but not withexternalities that arise from the “... interference of each vessel with other vessels’ fishing operations”[Clark (1980)].Chapter 4. Rent Capture Methods Reviewed 82new equilibrium would be some 495 monetary units or a reduction of 57 monetaryunits over the Pareto efficient quota equilibrium. Observation of Table 4.4 also revealsthat at the new equilibrium, 105 units of quota would be unused such that the TACwould no longer he binding on the fishery. Over time with no barriers to entry orcapital constraints on fishers, additional Fl fishers should enter the fishery attractedby the positive profits. Eventually, the total rent in the fishery should rise to thelong-run equilibrium level.A quota transfer charge may also change the optimal allocation of quota. Theeffects of a 100% quota transfer charge in the specific fishery model are provided inTable 4.5. It can be seen that by eliminating the gains from trade to fishers butnot the returns from the fishery, those fishers (F2) that would otherwise have sold orleased their quota-holdings may choose to use the quota themselves. For example,in the absence of a quota transfer charge each fisher will maximise their expectedutility given a mean-variance specification by setting the annual quota price equal tothe expected output price less marginal harvesting costs and less the marginal riskpremium. Under a 100% quota transfer charge, however, F2 fishers no longer attachan opportunity cost to owning quota and will maximise their profits by setting theexpected output price equal to the marginal cost plus the marginal risk premium.Given increasing marginal cost, this implies F2 fishers will harvest more with a quotatransfer charge than without. The result is a change to the Pareto efficient quotaallocation and consequently a reduction in the total expected rent in the fishery.Under risk neutrality, a quota rental charge, profit charge, net cash flow charge,and ad valorem royalty will not change the Pareto efficient quota equilibrium providedthat no more than the expected resource rent is collected from the fishery and thatfishers exit the fishery when they face negative economic profits. In the case ofuncertainty and risk averse behaviour by fishers this may not be true such that aChapter 4. Rent Capture Methods Reviewed 83change in the charge rate may indeed change the short-run quota equilibrium. Beforeaddressing the problem of charge rates and their effect on optimal output levels, itis useful to present some results in the literature. Assuming that fishers maximisethe expected utility of economic profits and that their utility functions are boundedfrom above and twice differentiable then the following types of risk aversion may bedefined.4RA(1) = = coefficient of absolute risk aversion (4.23)RR(’1) = —IUii()/UiQ) = coefficient of relative risk aversion (4.24)where UQ) is the utility of economic profit, decreasing (increasing) absolute riskaversion is defined by RA’() < 0 (R’() > 0), decreasing (increasing) relative riskaversion is defined by RR!() <0 (RR’() > 0).In the literature, the concepts of absolute and relative risk aversion are normallyapplied to individuals whose utility functions are a function of their wealth. Arrow(1984) has argued that individuals have increasing relative risk aversion and decreasing absolute risk aversion. The former implies that persons willingness to accept a betwill decrease if the size of the bet and their wealth increase in the same proportion.There is conflicting evidence whether this is observed empirically although Arrow argues there are theoretical reasons for making this assumption. Decreasing or at leastnonincreasing absolute risk aversion implies that as individuals become wealthier therisk premium defined as the difference between the expectation of the return and itscertainty equivalent should not increase.A result due to Sandmo (1971) is that increasing the tax rate of a full loss offsetprofit tax rate under uncertainty will cause a firm’s output to increase, stay constant,or decrease according to whether relative risk aversion is increasing, constant, or4Arrow (1984), chapter 9, provides a review of the theory of risk aversion.Chapter 4. Rent Capture Methods Reviewed 84decreasing. In the case of an ITQ fishery, a change in any charge rate on the outputof fishers is dependent upon both its direct effect on quota demands and indirecteffects on the level of uncertainty and quota price. As a corollary to proposition3.1, provided that the change in the quota demands of fishers from a change in thecharge rate is the same for all fishers then for a given TAC the quota equilibrium isunchanged with a change in the charge rate. This requires that= Oq(.)= k, (4.25)0c1where qj is the quota demand of fisher i which is a function of the charge rate c1,the level of uncertainty which may itself be a function of c1, the harvesting functionof the fisher, expected input and output prices and the quota price which is itself afunction of the charge rate and level of uncertainty. Provided that (4.25) holds withequality irrespective of the level of relative risk aversion, a change in the charge ratewill not change the outputs of fishers at the equilibrium.In the mean-variance specification, the condition that ensures a change in thecharge rate of any of the methods of rent capture will leave the quota equilibriumunchanged is given by (4.26).= (4.26)In the case of a quota rental charge, irrespective of whether (4.26) holds with equalityor not, a change in the charge rate will leave the quota equilibrium unchanged. Thisis because with a quota rental charge the quota demands are not a function of thecharge rate and the level of uncertainty is the same whatever the charge rate.Given positive profits and net cash flows, the risk costs of fishers under the differentcharge rates can be solved for a profit charge and net cash flow charge as per (3.8).It can be shown that under this condition, with uncertainty with respect to outputChapter 4. Rent Capture Methods Reviewed 85and input prices, the risk costs of fishers are reduced to the square of one minus thecharge rate multiplied by the variance of economic profit. In the case where fishersface uncertainty only with respect to the output price, an ad valorem royalty will alsoreduce the risk costs of fishers. VvThere the uncertainty faced by fishers is not withrespect to the output price, an ad valorem royalty will leave the risk costs of fishersunchanged. In this case and provided that the quota price remains positive, the quotaequilibrium will be unchanged for any ad valorem charge rate. This is because thequota demands of fishers with an ad valorem charge rate will only change if the levelof uncertainty changes with the charge rate.In the case where (4.26) does not hold with equality and the uncertainty is withrespect to the output price, a change in the rate of a profit charge, net cash flow charge,and an ad valorem royalty will change the quota equilibrium. Given positive profitsand net cash flow each period then, if i3i? > /32, an increase in the charge rate willincrease (decrease) the output of Fl (F2) fishers. In the case where i3i? < /3 anincrease in the charge rate will decrease (increase) the output of El (F2) fishers. Itcan also be shown that increasing the charge rate if (4.26) does not hold with equalitywill increase the expected rents in the fishery provided that the expected rents arestrictly concave in the quota allocation. Consider the followingProposition 4.7 Given that the expected rent is strictly concave in the quota allocation, the uncertainty faced by fishers is only with respect to the output price, andthat /3 = !2 then increasing the charge rate of a profit or net cash flow chargewill leave the output of all fishers and the expected rent in the fishery unchanged. If> /32 then an increase in the charge rate will increase (decrease) the output ofFl (F2) fishers and increase the expected rent in the fishery. If </2 then anincrease in the charge rate will decrease (increase) the output of Fl (F2) fishers andChapter 4. Rent Capture Methods Reviewed 86increase the ezpected rent in the fishery.PROOF. The quota demands of El and F2 fishers with a profit charge of p in theclosed interval [0, 1] are as follows,?(TAC)qlkt= Y2d (4.27)x?+ ‘(TAC)q2J= X 2d (4.28)2where d1 = 2C(1—p) + 23(1 —p)2acb and d2 = 2C(l—p) + 2/32(1 — p)2ub.Replacing the profit charge rate p by a net cash flow charge rate r in (4.27) and (4.28)will yield the quota demands with a net cash flow charge. From proposition 3.2, thequota demands of Fl and F2 fishers without rent capture and without uncertaintymaximise the short-run rent in the fishery for given number of Fl and F2 fishers andare as defined follows*— (TAC)1kt—(4.29)*— (TAC)—(4.30)It follows tl1at if /3? = /32& then d1 = d2 and= q1k (4.31)=(4.32)If ,@ > /3 then d1 > d2 and‘jt <q (4.33);t > q (4.34)If i3? </32 then d1 <d2 and> qikt (4.35)ãit (4.36)Chapter 4. Rent Capture Methods Reviewed 87Differentiating (4.27) and (4.28) with respect to the charge rate=— (TAC)() (Up (X?+jd1)2-2fmAri\1DW2\Uq2 = (438)Up (X?d2 +Y)2whereUW1 — Y[(/32—!31?)4C(1 — p)2ab] 4 39Up c1 (.)91472— X?[(81—,82)4C(1 — p)24bj (4 40Up d?It follows immediately that if i3i? = /2 then___—___— 0 (4 41)Up UpIf 8? > thenUq1k> 0> (4.42)Up Up/‘? <!2 then<0< (443)Up UpGiven that the expected rent is strictly concave in the quota allocation (see proposition 3.2) then the quota demands given by (4.29-4.30) provide a unique globalmaximum. From (4.31-4.32), it follows that the quota equilibrium with rent captureand uncertainty is identical to that with no uncertainty and no rent capture providedthat (4.26) holds with equality. From (4.41), this equilibrium is unchanging withrespect to the charge rate provided that the quota price is positive. If (4.26) doesnot hold with equality then from (4.33-4.36) the equilibrium with uncertainty andrent capture will yield a lower rent than the maximum. Combining the results fromChapter 4. Rent Capture Methods Reviewed 88(4.33-4.36) and (4.42-4.43), it follows that increasing the charge rate will increase theexpected rent in the fisheryUsing the same approach as in proposition 4.7, identical results can be derivedfor an ad valorem royalty. Proposition 4.7 is proved for the specific fishery but it hasgeneral implications for ITQ fisheries. Provided that the short-run rent is strictlyconcave with respect to the quota allocation it can be shown from proposition 3.2that under specific conditions the quota equilibrium without uncertainty is a uniqueglobal maximium. Proposition 4.7, therefore, leads to an interesting and importantconclusion. If the resource owner is concerned solely with maximising expected rentsand the uncertainty is with respect to the output price, increasing the charge rate ofan ad valorem royalty or profit and net cash flow charge may actually increase theexpected rents in the fishery. This result comes directly from the fact that certaintypes of rent capture can reduce the uncertainty faced by fishers. In reducing the levelof uncertainty, the quota equilibrium approaches the quota allocation that maximisesthe expected short-run rent in the fishery for the given number of fishers and TAC.The cost of increasing the expected rents in the fishery with a higher charge rate,however, is to reduce the expected economic profit of fishers.Another issue in comparing the methods of rent capture is their affect on fishers’incentives for innovation. Under a quota rental charge, ad valorem royalty or auctionthe benefits of individual innovation accrue directly to the quota-holder. Because thefisher pays a rental based only upon the market price of quota multiplied by quotaholdings, any extra returns that arise from individual risk taking or innovation arekept by the fisher. In contrast, with a profit charge or net cash flow charge the benefitsof innovation are shared with the resource owner. If one accepts the Schumpeteriannotion of intra-marginal rents5 as being both a payment and incentive for innovation5Schumpeter (1950) discusses this notion in detail.Chapter 4. Rent Capture Methods Reviewed 89then a quota rental charge, ad valorem royalty or auction may be preferred methodsof rent capture. In a dynamic sense, therefore, by providing greater inceiltive forfisher innovation such methods of rent capture may stimulate more innovation andmay give rise to greater rents from the fishery in the long run.In assessing the effects of efficiency of the different methods of rent capture, itwould seem that a lump sum fee and a quota transfer charge are the least desirablechoices. These two methods are both capable of changing the Pareto efficient allocation even with no uncertainty. In comparison, a quota rental charge, ad valoremroyalty, and profit and net cash flow charge will not change the quota equilibriumprovided that no more than the annual value of quota-holdings is collected from thefishery. A quota rental charge, ad valorem royalty, and auction have the added advantage that they can allow fishers to capture the full benefits of innovation. In the caseof uncertainty, a quota rental charge will also leave the quota equilibrium unchangedirrespective of the charge rate provided that the quota price is known with certainty.This is also true of an ad valorem royalty if the uncertainty facing fishers is not withrespect to the output price. In the case of output price uncertainty, a profit charge,net cash flow charge, and an ad valorem royalty will change the quota equilibriumthat maximises the expected rent less risk costs. Increasing the charge rate for allthree rent capture methods will reduce the uncertainty with respect to fluctuationsin the output price and in general will bring about an equilibrium with higher totalexpected rents.4.12 Costs of Rent CaptureThe costs of rent collection are likely to depend upon various characteristics of afishery including the magnitude of the rent to be collected, the number of fishers andChapter 4. Rent Capture Methods Reviewed 90their catches, the authority vested in the resource owner, and the human resourcesavailable to the resource owner. In certain fisheries, rent collection costs may proveto be a substantial proportion of the total rent captured and hence are important indetermining the choice of a particular method of rent capture.Determining the collection costs of different methods of rent capture requiresintimate knowledge of the fishery where it is to be imposed. In a world where theprofit and economic profit of each fisher is costlessly and perfectly known, therewould be little difference in the collection costs across the different methods. Theresource owner could simply determine an appropriate charge for each fisher with dueconsideration for the risk costs of fishers and collection costs. Unfortunately, suchinformation is rarely if ever available to the resource owner and the choice of themethod of rent capture is as much a reflection of the information constraints facingthe regulator as the costs of rent collection and the effect upon efficiency, equity, andrisk costs in the fishery.One approach to compare different methods of rent capture is to contrast theinformation required for each and the fixed and variable costs associated with rentcapture. In this sense, an auction of the quota imposes up-front costs on the resourceowner that bears little relation to the size or the rent available from the fishery. Theseup-front costs may be considered a fixed cost of rent collection. Other methods of rentcapture including a quota rental charge, ad valorem royalty, profit charge, and netcash flow charge would require on going expenditures to function effectively. Theseon going costs may be considered as variable collection costs and could be a functionof the number of fishers obliged to pay the rental and in the case of a royalty or quotarental charge the quantity harvested per fisher.For a resource owner choosing an optimal TAC for a fishery, the variable collection costs of rent capture are an important consideration. In the choices available toChapter 4. Rent Capture Methods Reviewed 91the resource owner, a method of rent capture that is a function of the total quantityharvested may reduce the optimal TAC if the resource owner wishes to maximise therent in the fishery less the costs of rent capture. More generally, however, the TAC infisheries is determined by biological factors and historical factors. In most fisheries,therefore, the issue with respect to collection costs is to minimise the expenses incapturing rent for a given TAC. The method(s) of rent capture that minimise collection costs, however, need not necessarily be the most desired method of rent capture.For example, the collection costs associated with a lump sum fee may be relativelysmall but such a method of rent capture may change the Pareto efficient quota equilibrium. In addition, some methods of rent capture such as a profit charge, net cashflow charge, and ad valorem royalty that may have higher rent collection costs mayreduce the risk costs of fishers.In comparing the different methods of rent capture, it may be noted that only anauction of the quota in perpetuity does not impose on going costs of rent collection onthe resource owner. The bidding process itself reveals the total expected rent in thefishery less risk costs as well as providing a ready means of collecting the rent. Thereis essentially, therefore, no information burden imposed upon the resource owner andlittle or no enforcement costs required to determine any fraud in terms of the rentalpayments. A quota transfer charge shares this feature with an auction in that it toodoes not requiie information on the total rent, resource rent or individual earnings offishers to collect rent for the resource owner. Unfortunately, a quota transfer chargecreates an incentive for sellers of quota to misrecord their sale price so as to reduce therental paid. To be an effective method of rent capture, therefore, it may be necessaryto have a method for verifying the price at which quota traded. Such verificationcould only be achieved at additional cost to the resource owner.Another method of rent capture that may have relatively small collection costs isChapter 4. Rent Capture Methods Reviewed 92a quota rental charge. If the resource owner wishes to capture an amount equal to orless than the annual value of quota-holdings, the appropriate charge would be to setthe quota rental as some percentage of the quota price multiplied by some defined rateof interest. The informational requirement would include, therefore, an estimate ofthe market price of quota and the quota-holdings of fishers. The quota price should,however, be readily available in a competitive quota market and the quota-holdingsof fishers should be known to the resource owner in a well functioning ITQ fishery.A particular advantage of a quota rental charge is the relatively small informationalburden it imposes on the resource owner. Changes in the value of the resource rentin the fishery should be reflected in the quota price and hence in the amount of rentcaptured. A quota rental charge would also require little policing or enforcement toensure that the appropriate rental was paid by each fisher as the rental would bebased on the quota-holdings of fishers.An advantage of a lump sum charge is that it does not require an estimate of theprofits of individual fishers to capture rent from the fishery. Provided there existsan estimate of the total profit in the fishery, a uniform lump sum charge is set equalto the desired rent to be captured divided by the number of quota-holders. Thisamount would then simply be charged to each of the fishers. Because the individualquota-holders would be known to the resource owner, the lump sum fee would provideno opportunity for tax evasion. Consequently, no costs would be incurred in policingfishers so as to prevent tax fraud. A draw-back with a lump sum fee is that it wouldrequire regular updating to ensure that an amount no more than a desired share ofthe resource rent was captured from the fishery. Another consideration with the lumpsum fee is that it may leave certain fishers with after-tax losses even when capturingan amount no more than the estimated resource rent. If a resource owner wishes toavoid such a potentially distorting outcome then an estimate of the after-tax profitsChapter 4. Rent Capture Methods Reviewed 93of fishers would also be required. In this, a trade-off between reducing the risk ofimposing distortions in the fishery would have to be balanced against the extra costsof obtaining individual financial information from fishers.An ad valorem royalty shares a common feature with a quota rental charge andlump sum fee in that it does not require data on the individual profits of fishers.It would, however, require information on the landed price of fish, quota-holdings offishers, and the rent in the fishery. Where the value of landings are already recorded bythe resource owner, as is the case in most of Canada’s fisheries, such information couldbe obtained at very little extra cost. A problem may arise, however, in obtaining anaccurate landed price per fisher if the rental paid was based on the value of landings.Fishers may find it in their interest to reduce the recorded landed values so as to reducetheir rental payments. To address this difficulty, a system of policing or verificationof the landings may be required at an additional cost. To the extent that changesin the value of the rent are brought about by changes in the price of fish then anad valorem royalty would be a flexible method of rent capture. Where changes inthe rent are brought about by changes in the biomass or costs, some updating of theestimate of the rent in the fishery would also he required.Both a profit charge and net cash flow charge share the feature that they requireindividual costs and earnings information from fishers to be made operational. Suchinformation is likely to be much more costly to obtain and verify than a generalestimate of the rent in the fishery. For this reason, both the net cash flow and profitcharge are likely to cost more than the other methods of rent capture in collecting anequivalent amount of rent. Because of the incentive to inflate costs or reduce revenuesso as to reduce the rental payable, a system of checking or verifying the profit or cashflow statements would also be required. Iii fisheries with a large number of vesselsharvesting multiple species this may prove to be a considerable cost burden to theChapter 4. Rent Capture Methods Reviewed 94resource owner.Ranking the various rent capture schemes according to their costs of collection, itwould seem that an auction would be the least costly method while a profit chargeand net cash flow charge may prove the most burdensome. The collection costs fora quota transfer charge and lump sum fee may also prove to be less than a quotarental charge or ad valorem royalty which should impose similar costs on the resourceowner.4.13 Risk Sharing and FlexibilityThe issue of risk sharing between the resource owner and fishers is important if oneaccepts the notion that fishers are risk averse. In the case where the resource owneris risk neutral and fishers are risk averse there may be a benefit to both parties fromthe sharing of risk. The same characteristics that allow for risk sharing betweenthe resource owner and fishers, however, also make a method of rent capture moreresponsive to fluctuations in the value of the rent. For example, a rent capture schemeat a given charge rate that reduces the fluctuations and the risk costs of fishers willalso adjust to changes in the rent brought about by such fluctuations.In the case of a profit charge and uncertainty with respect to the output price,the risk cost of a fisher before and after rent capture may be determined in the samemanner as (3.8). Assuming positive economic profits in every period, the risk costof a fisher i before rent capture is /3qoj while with rent capture the risk cost isreduced to ,8q?(1— p)2oj. Similarly, ceteris paribus, in periods where P > E{P},the rent captured by the resource owner will, therefore, be greater than in periodswhere P < E.’{P}. A profit charge is, therefore, able to reduce the risk cost of fishersand is a flexible method of rent capture. This feature of flexibility and risk sharingChapter 4. Rent Capture Methods Reviewed 95is shared with a net cash flow charge with uncertainty with respect to the outputand input prices. In the case of a net cash flow charge, however, the reduction in therisk cost in any period is complicated by the fact that risk may not only be sharedwithin a time period but that negative cash flows can be capitalised and subtractedfrom future positive cash flows. Assuming fishers always have positive net cash flows,irrespective of the fluctuation in the output price, the risk cost faced by a fisher i isgiven by j3q(1 — r)2u. The risk premium is also reduced over what it would bewithout rent capture with a net cash flow charge when fishers incur both positive andnegative net cash flows.An ad valorem royalty is also shown to reduce the risk costs of fishers but only ifthere is uncertainty with respect to the output price. It differs from the profit andnet cash flow charge, therefore, in that it does not reduce the risk costs of fishers dueto uncertainty with respect to input prices. Assuming uncertainty only with respectthe output price, the risk cost of fisher i after imposing an ad valorem royalty is givenby ,8q(1 — Although an ad valorem royalty does reduce the risk cost of fisherswhen there are fluctuations in the output price it does have the feature of collectingrent from fishers when they face losses. Where fishers view a marginal increase inlosses as less desirable than a marginal decrease when profits are positive, it maybe desirable to have a tiered royalty. In a tiered ad valorem royalty, the resourceowner would set a floor and ceiling price. Whenever the output price was below thefloor price no rental would be paid by fishers, in between the ceiling and floor price afixed royalty rate would apply, and above the ceiling price a higher royalty rate wouldapply. The tiered ad valorem royalty would have the effect, therefore, of reducing theprobability of capturing rent when fishers face temporary losses due to a low outputprice. Conversely, it would capture more rent when the output price was particularlyhigh.Chapter 4. Rent Capture Methods Reviewed 96The quota price in an ITQ fishery where there is uncertainty only with respect tothe output price is shown to be function of the expected output price, the varianceof the output price, and other variables. For a given variance of the outpllt priceand provided that the quota price is known with certainty, a quota rental charge willnot change the variance of the economic profit of fishers. As a result, it is unableto reduce the risk costs of fishers. If the quota price varies with changes in fishers’expectations of the input and outpllt prices and biomass, however, it will be a flexiblemethod of rent capture. This is because as the quota price changes with changedexpectations in the fishery so too will the rent captured for a given charge rate.A lump sum fee and auction are shown to leave fishers with the same risk costswith or without rent capture. In the case of the lump sum fee, subtracting a constantterm or the rental paid to the resource owner, will leave unchanged the variance of theeconomic profits of fishers. In an auction, the risk faced by fishers is dependent uponthe uncertainty with respect to the output and input prices and the TAG. Providedthat the bid and auction process leaves unchanged the variance of the economic profitsthen an auction will also leave unchanged the risk costs faced by fishers.A feature of a lump sum fee shared with a quota rental charge and ad valoremroyalty is that it requires that a rental be paid each period by each fisher whetheror not fishers incur a profit or loss. If it is the case that a dollar increase in losses isviewed as less desirable than a dollar decrease when profits are positive, such methodsof rent capture may place an extra burden of risk on fishers. Such is not the casewith a profit charge or net cash flow charge.In summary, it would seem that a profit and net cash flow charge are the mostcapable of reducing the risk costs of fishers while a lump sum fee, auction, and quotatransfer charge do so the least. An ad valorem royalty is shown to reduce the riskcosts of fishers provided that there is uncertainty with respect to the output price.Chapter 4. Rent Capture Methods Reviewed 97Imposition of a tiered ad valorem royalty may also be advantageous where fishers viewa marginal increase in losses as less desirable than a marginal decrease when profitsare positive. A quota rental charge is not found to reduce the risk costs of fishers butis a flexible method of rent capture in that changes in the expected output and inputprices, biomass, and level of uncertainty will be reflected in the rental paid.4.14 OverviewAn important question addressed in the thesis is how rent capture may affect thetotal rent in the fishery. It has been shown that a lump sum fee that collects no morethan the annual value of quota-holdings may chailge the Pareto efficient allocationof quota. A quota transfer charge is found to alter the efficient quota equilibrium atany positive charge rate. A profit charge, net cash flow charge, ad valorem royalty,and quota rental charge do not chailge the quota equilibrium given no uncertaintyor risk neutrality by fishers. Given uncertainty with respect to the output price,changes in the charge rate of an ad valorern royalty will, in general, change the quotaequilibrium that maximises the expected rents less the risk costs of fishers. In thiscase, increasing the charge rate has the effect of reducing the risk costs of fishers andmay move the quota equilibrium closer to the rent maximising quota allocation at thecost of reducing the expected utility of fishers. Changes in the charge rate of a profitcharge and net cash flow charge will also, in general, change the quota equilibriumgiven uncertainty and risk aversion. As with the ad valorem royalty, increasing thecharge rate can move the quota equilibrium closer to the allocation that maximisesthe expected rents in the fishery. A quota rental charge, however, will not alter thequota equilibrium with or without output price uncertainty provided that the quotaprice is known with certainty.Chapter 4. Rent Capture Methods Reviewed 98Another issue with respect to efficiency is the effects that rent capture may haveupon the incentives for innovation in the fishery. A net cash flow charge and a profitcharge imposed at high rates reduce the benefit for individual innovation by sharingany future intra-marginal rents with the resource owner. A quota transfer charge andquota rental charge do allow an individual to recover the full benefits of innovationthat is not reflected in the quota price. An auction, ad valorem royalty, and lumpsum fee allow fishers to fully recoup such benefits without reservation.An important concern to a resource owner is the differential effects of rent captureon different fishers. It is shown that those fishers who earn a higher average profit onthe fish harvested will prefer a quota rental charge over a profit charge that collectsthe same amount of rent. To the extent that net cash flow earnings per quota unit area reflection of intra-marginal rents in the fishery, it is shown that highliners will alsoprefer a quota rental charge over a net cash flow charge. A lump sum fee is favouredin terms of annual economic profits over a profit charge or quota rental charge bythose fishers who earn higher than average profits or have higher than average quota-holdings. An ad valorem royalty is shown to be equivalent to a quota rental chargeif fishers face the same output price and the rental is assessed on the quota-holdingsof fishers. A quota transfer charge imposes burdens only upon those fishers selling orleasing quota.The different methods of rent capture also differ with respect to the costs ofcollection. It is suggested that an auction may be the most cost effective methodof collecting rent from the fishery. Those methods of rent capture not requiringindividual costs and earnings information from fishers including a lump sum fee,quota rental charge, ad valorem royalty, and quota transfer charge may also be costeffective methods of rent collection. A net cash flow charge and profit charge thatdo require individual data. from fishers aloig with a system for verifying returns areChapter 4. Rent Capture Methods Reviewed 99likely to be the more expensive methods of rent collection.Another distinguishing feature among the rent capture methods is their ability toreduce the risk costs of fishers. It is shown that a lump sum fee, auction, and quotatransfer charge do not reduce the risk costs faced by fishers. A profit charge and netcash flow charge do reduce risk costs if the uncertainty faced by fishers is with respectto the output and input prices. An ad valorem royalty is also capable of reducingthe risk costs of fishers provided a source of uncertainty is with respect to the outputprice. A profit, net cash flow charge, and an ad valorem royalty are shown to havesome flexibility to adjust the rent captured with the actual rent in the fishery.One other important factor to consider in choosing any method of rent capture isthe ability to implement any given rent capture scheme in a fishery. The ability toimplement a given method of rent capture is governed by a number of factors includingthe management skills and resources available to the resource owner, traditional andhistorical fishing rights, the spatial size and number of fishers in the fishery, and theexpected value of the rent to be collected. For instance, a profit charge may be adesirable method of rent capture with a relatively small number of fishers but mayprove too burdensome in terms of a collection costs in a much larger fishery. Similarly,an auction and a quota rental charge may not be possible in a small fishery wherethere may not be a competitive bidding process or competitive quota trading but mayfunction well in a fishery where there are a large number of fishers.In implementing a rent capture scheme, traditional fishing rights or access is alsoan important consideration. Where fishers have been given access to a fishery in thepast, the introduction of ITQs and the auctioning of quota could lead to considerableprotest from fishers. If such protest took the form of sabotaging gear of successfulbidders, quota-busting, and poaching it could put at risk the potential benefits ofITQs. In many cases, therefore, it may be appropriate to allow for at least someChapter 4. Rent Capture Methods Reviewed 100“grandfathering” in of quota on the basis of historical catches. This has certainlybeen the practice in countries such as New Zealand, Canada, Australia among others.If historical rights are recognised in the initial quota allocations by the resource ownerthen any method and rate of rent capture should be announced prior to any quotatrading. If no such announcement is made and there is no expectation of rent capturethen the resource owner faces the prospect of collecting resource rent from fishers whohave already paid the expected resource rent to the previous quota-holders.Chapter 4. Rent Capture Methods Reviewed 101Table 4.1: Short-run profits of fishers with collection of 100% of the annual value ofquot a-holdings and given risk neutralityScenario Profit Rent Captured100% Quota Charge:Fl 124.80 38.40F2 11.20 9.6Total 408.00 144.0026.09% Profit Tax:Fl 120.63 42.57F2 15.37 5.43Total 408.00 144.0015.79% Net Cash Flow Charge:Fl 124.80 38.40F2 11.20 9.60Total 408.00 144.008.57% Ad Valorem Royalty:Fl 124.80 38.40F2 11.20 9.60Total 408.00 144.00Lump Sum Fee:Fl 139.20 24.00F2 -3.20 24.00Total 408.00 144.00Chapter 4. Rent Capture Methods Reviewed 102Table 4.2: Short-run profits of fishers with collection of 50% of the annual value ofquota-holdings and given risk neutralityScenario Profit Rent Captured50% Quota Charge:Fl 144.00 19.20F2 16.00 4.80Total 480.00 72.0013.04% Profit Tax:Fl 141.91 21.29F2 18.09 2.71Total 480.00 72.007.89% Net Cash Flow Charge:Fl 144.00 19.20F2 16.00 4.80Total 480.00 72.004.29% Ad Valorem Royalty:Fl 144.00 19.20P2 16.00 4.80Total 480.00 72.00Lump Sum Fee:Fl 151.20 12.00F2 8.80 12.00Total 480.00 72.00Chapter 4. Rent Capture Methods Reviewed 103Table 4.3: Cost/return from quota trading assuming rent capture of 50% of the annualvalue of quota-holdings and risk neutralityRent Capture Method Cost/Return Quota Trades50% Quota Charge:Fl-72.0F2 72.013.04% Profit Charge:P1-125.2F2 125.27.89% Net Cash Flow Charge:Fl-132.6F2 132.64.29% Ad Valorem Royalty:Fl-72.0P2 72.0Lump Sum fee of 12 units/fisher:Fl-144.0P2 144.0Chapter 4. Rent Capture Methods Reviewed 104Table 4.4: Short-run quota equilibrium before and after a lump fee charge is imposed on the fishery that collects an amount equal to 100% of the annual value ofquota-holdingsScenario Profit Rental Paid Quota-HoldingsPre Rent Capture:Fl 163.20 0 224P2 20.80 0 56Total 552.00 0 840Lump Sum Fee:Fl 165 48 245F2 0 0 0Total 495.00 144 735Chapter 4. Rent Capture Methods Reviewed 105Table 4.5: Short-run quota equilibrium before and after a 100% quota transfer chargeis imposed on the fisheryScenario Profit Quota-HoldingsPre Rent Capture:Fl 163.20 224F2 20.80 56Total 552.00 840100% Quota Transfer Charge:Fl 162.19 218.75F2 21.25 61.25Total 550.32 840Chapter 5Rent and the BC Sablefish FisheryIt will appear, I hope, that most of the problems associated with thewords “conservation” or “depletion” or “overexploitation” in the fisheryare, in reality, manifestations of the fact that the natural resources of thesea yield no economic rent.H. Scott Gordon, Journal of Political Economy vol 62, 1954, p 124.5.1 IntroductionThe problem addressed in a theoretical framework in chapters 3 and 4 is examinedempirically with reference to the BC sablefish fishery. Prior to comparing differentmethods of rent capture in the fishery, it is necessary to have an estimate of therent that accrues to the individual vessels. This chapter uses several approaches forestimating the rent before and after the introduction of ITQs into the fishery. Theseestimates are used in chapter 6 to simulate the effects of rent capture in the fishery.Empirical estimates of the rent in fisheries are common in the resources literature. One of the best known works is by Crutchfield and Pontecorvo (1969) whoestimated the potential rent in the Alaska Bristol Bay and Washington Puget Soundsalmon fisheries. Flagg (1977), using a Schaefer model of fishery exploitation examined the difference between a maximum sustainable yield (MSY) and maximum106Chapter 5. Rent and the BC Sablefish Fishery 107economic yield (MEY) in the eastern tropical Pacific tuna fishery. More recently, Devoretz and Schwindt (1984) have examined the rent that may be collected from someof Canada’s Pacific fisheries. Using the Royal Commission on Pacific Fisheries Policy(1982) as a starting point, they analyse the returns from a royalty per ton on thequantity harvested and an auction of commercial fishing licences by the Governementof Canada in the salmon and roe herring fisheries. The traded value of commercialfishing licences has also been used by Schwindt (1986) to estimate the rent in the BCsalmon industry. Using the licence values as a proxy of the capitalised rent in thefishery, Schwindt (1986) applies several different discount rates to obtain an estimateof an average annual rent.More recent empirical studies by Dupont (1988, 1990) and Squires (1984, 1987)have attempted to measure the rent in fisheries through the use of restricted profitfunctions. Both these approaches use duality theory to address regulatory problems infisheries. In particular, Squires uses a restricted translog profit function to show thatregulations may be improved by regulating several inputs in multi-species fisheries.In this manner, inefficient product and factor proportions may be avoided allowingthe total rent in the fishery to increase. Dupont (1988, 1990) uses a normalisedquadratic restricted profit function to estimate the effects of rent dissipation in arestricted access fishery. The profit function is then used to estimate the costs of rentdissipation from input substitution, fleet redundancy, and fleet composition.The general thrust of these studies has been to examine the issue of rent dissipationand the effects of inappropriate regulation in fisheries. Only with the introdllctionof rights based management in the past decade has the issue of estimating the rentin a fishery with a view to rent capture become an issue. One of the first studies toexamine the question of rents with ITQ management was by Geen and Nayar (1989)in reference to the Australian southern bluefin fishery. Using a model developedChapter 5. Rent and the BC Sablefish Fishery 108specifically for the fishery they investigate the total rent with free entry and withITQ management. They find that economic rents of $A 10 million/year can be earnedby fishers owning quota rights. In a study using New Zealand data, Lindner et al.(1989) compare traded quota prices to estimates of profitability in the industry usingaggregate industry revenues, costs, and asset values. On the basis of the industrystudy, they conclude that in aggregate the fishing industry was incurring losses in1987/88 while expectations of future profits were positive as reflected by positivequota prices.The focus of chapter 5 is to present estimates of the rent in the BC sablefish fisheryin two periods; 1988 when only restrictive licensing was in place, and in 1990 whenindividual quota management was first introduced into the fishery. Three approachesare employed to estimate the rent in the fishery. All approaches make extensive useof a Canadian Department of Fisheries and Oceans’ (DFO) 1988 costs and earningssurvey (CES). In a direct approach to estimating the resource rent in the fishery, theprofits of fishers are obtained directly from the 1988 CES under suitable assumptionswith respect to the allocation of implicit and indirect costs among species. In asecond approach, the market values of sablefish licences in 1988 are used to estimatethe expected annualised resource rent in the fishery. In another approach, two profitfunctions are estimated using 1988 data. Estimates of individual profits for 1988 arethen obtained directly from the estimated functions. Using updated prices for 1990,the profit functions are used to predict the profits of fishers in 1990. These predictedprofits are then compared to estimates calculated using the price of quota tradedin an open market and the remuneration system employed in the sablefish fleet forpaying the crew and the vessel owner.Chapter 5. Rent and the BC Sablefish Fishery 1095.2 Description of The Fishery and Data Sources5.2.1 BackgroundThe fishery chosen for the study of rent capture issues is the BC sablefish fishery. Thisresource generated a gross landed value of some $CDN 18 million in 1990 and hasbeen managed with limited entry licensing since 1981. This licensing system restrictedthe use of gear by fishers and the total number of licence-holders to 48. Under amanagement system that existed until the end of 1989 fishers faced a restricted fishingseason for sablefish. In 1988, all fishers were restricted to a 20 day fishing season whichthe fishers could choose themselves out of a possible seven choices determined by theCanadian Department of Fisheries and Oceans (DFO) in consultation with the fishers.By comparison, the fishing season in 1981 with a similar TAC was 245 days. In early1990, individual vessel quotas (IVQs) were introduced into the fishery with support ofthe industry for a two year trial period. This trial period was subsequently extendeduntil the end of 1992. The PiQs were assigned gratis to fishers on the basis of pastcatches and vessel length, denominated as a proportion of the total allowable catch,and made transferable only among licence-holders for amounts no less than the initialquota allocations [Canada Department of Fisheries and Oceans (199Db)].A general feature of the sablefish fishery is that it has had a relatively stablebiomass and total allowable catch [Saunders and McFarlane (1990)]. Almost theentire catch is exported to Japan [Longva (1990)]. Harvesting the resource are twotypes of vessels employing different gear. A trap or pot harvesting method is generallyemployed by larger vessels and involves the setting of baited traps at depths of 250-600metres. These traps, attached to each other and buoys at the surface, are generallyleft to “soak” for 12 to 24 hours before recovery. An alternative method of fishingis to use bottom longline gear in which baited hooks lie on or near the sea bottomChapter 5. Rent and the BC Sablefish Fishery 110and are maintained in position by anchors attached to buoys at the surface. Longlinegear is generally left to soak for approximately 1 and a half to three hours prior torecovery by fishers. Because of the depth at which the gear-types are often used bothlongline and traps are capable of being highly selective for targeting sablefish.In the first year of IVQ management in 1990, there were 15 trap and 15 longlinevessels operating in the fishery. The trap vessels accounted for 75% of the totalharvest of 4,260 MT while the longline vessels caught the remainder. In contrast, in1988 with total landings of some 4,600 MT there were some 21 trap and 25 longlinevessels actively operating in the fishery. Many of these fishers also operated in otherfisheries such as halibut and salmon.5.2.2 Data SourcesThe different approaches to estimating the rent in the BC sablefish fishery makeextensive use of a DFO costs and earnings survey for 1988 and/or DFO catch statisticsdata. In the survey, 17 longline fishers and 11 trap fishers were interviewed includingsome of the smallest and largest vessels in the sablefish fleet. The survey obtainedinformation on fishing revenue and direct fishing costs per species, financial payments,repairs and maintenance, and the value of assets employed by fishers. In addition tothe costs and earnings survey, data was obtained on marine fuel prices from ChevronCanada, catch statistics by species per vessel from DFO, and the tonnage of vesselsfrom the Vancouver ship registry. Summary statistics from the survey and othersources are presented in Table 5.1. The table provides minimum, maximum, mean,and the coefficient of variation of various variables including the estimated profits offishers, landings of sablefish and other species, vessel size, sablefish revenue and directand indirect expenses of fishers.Chapter 5. Rent and the BC Sablefish Fishery 1115.3 Direct ApproachUsing the CES data, a direct measure of the profit of vessels may be obtained for1988. Total sablefish profits are calculated as the total sahiefish revenue per vesselless direct fishing costs attributable to sablefish such as fuel and labour and less aportion of indirect and implicit fishing costs. Total vessel profits are calculated in asimilar manner by subtracting from total revenue of vessels the total direct fishingexpenses and total indirect and implicit fishing costs. The indirect and implicit costsattributable to sablefish fishing include a portion of the opportunity cost for the assetsemployed by the vessel, a share of the total vessel depreciation, and a portion of theopportunity cost wage for the skipper in owner operated vessels.The factor used for apportioning overhead to sablefish and other species for eachvessel equalled the ratio of direct fishing expenses from sablefish alone to total directfishing expenses. This ratio averaged 56% over the complete sample and varied from21% to a 100% for individual vessels. For vessels where the ratio was less than 100%its value was increased by 10, 20, and 30%, where applicable, to assess its sensitivityon the estimated profits of fishers. This had the effect of reducing the mean sablefishprofit of vessels by 4, 9, and 13%.The direct fishing costs per species were obtained directly from the CES. In thesurvey instrument, fishers were asked to provide their total income from various fisheries along with labour costs, fuel, bait and other expenses. Separating sablefishrevenue from other species and subtracting the direct expenses associated with sablefish provided a measure of the variable sablefish profits per vessel. To obtain anestimate of the sablefish profits, an implicit cost or an opportunity cost wage forthe skipper was determined for all those vessels where the captain was the owneroperator. This opportunity cost wage on an annual basis was calculated using anChapter 5. Rent and the BC Sablefish Fishery 112estimate of the average weekly earnings of fishers using a methodology described inAppendix B. Where applicable, this opportunity cost wage and the total depreciationon vessel and gear as given in the CES were multiplied by the ratio used for allocatingoverhead to sablefish and subtracted from sablefish revenue. In addition, a measureof the opportunity cost of the assets employed per vessel was obtained by using thefishers’ own esimate of the assets employed including the value of the vessel and gear.This estimated value was obtained by asking fishers what price they would expect fortheir vessel if they sold it that day and the value of their nets and gears as the first ofJanilary, 1988. acquisitions less losses/sales. The estimated value of assets was thenmultiplied by an interest rate equal to 11.83%, or the mean prime lending rate onbusines loans plus 1%, to obtain an annual cost per fisher. This annual cost of theassets employed was then multiplied by the ratio for allocating overhead to sablefishand subtracted from the estimated variable sablefish profits as per (5.1) to obtain ameasure of the sablefish profits. This estimate of the sablefisli profits uses data exclusively from the CES. An alternative measure for the indirect costs of fishers usingsecond-hand vessel prices is provided in the profit function approach to estimatingthe rents in the fishery.Sablefish Profit = R3—C — i[T + + rA] (5.1)where: R3 is total revenue from sablefish, C. is the direct fishing expense associatedwith sablefish, ic is the ratio for allocating indirect and implicit costs to sablefish, T isthe opportunity cost wage associated with the skipper in owner-operated vessels, z istotal depreciation associated with the vessel, r = 0.1183 is the mean prime businesslending rate plus 1% for 1988, and A is the value of the assets employed by fishers.The estimated sablefish profits for the vessels included in the CES by gear-type isChapter 5. Rent and the BC Sablefish Fishery 113presented in Tables 5.1 and 5.2. Consulting Table 5.2, the mean sablefish profits forlongline and trap vessels respectively was some $79,000 and $211,000. These estimatesof the profits of fishers may, however, be biased downwards. This is because the valueof assets provided by fishers in the CBS may overestimate their true value. Forexample, the mean value of vessels from the CBS is some $465,000 while comparablesecond-hand values of vessels based on discussions with a fish boat trader (K.Gaynor,pers. comm.) and advertisements in commercial fishing trade magazines for thesame period range in price from $50,000-$150,000. A possible explanation for thediscrepancy lies in the wording of the survey instrument. In particular, respondentswere asked to provide a market value of their vessels with fishing licences and thenlater asked to separately list the value of these licences. Separating the value offishing licences from the value of a vessel when both are normally sold together may,however, have posed problems for fishers.Using the survey estimates of vessel and sablefish profits, a number of profitabilityratios may be collstructed. These ratios are presented in Table 5.2 and are useful forcomparing relative profitability between gear-types and rates of return. ConsultingTable 5.2, trap vessels earned a mean profit of $1.20 per kilogram of sablefish landedwhile longline vessels earned some $1.38/kg. Over all gear-types, the mean ratio ofbefore-tax sablefish profits to gross revenue from sablefish was some 35% while beforetax profits from all species to the value of equity employed was some 33%. Both thesemeasures exceed the target returns for healthy fleet performance in the BC salmonfishery [DPA Group (1988), 43] of some 6% for before tax profit to gross income and15% for before tax profit to equity. In both these ratios, the mean ratio for longlinevessels exceeded that of trap vessels. It suggests, therefore, that although trap vesselshad higher mean absolute profits than longline vessels they were not necessarily moreprofitable in terms of the equity employed or sablefish landed.Chapter 5. Rent and the BC Sablefish Fishery 114Because the CES obtained data from only 28 of the 46 fishers actively fishing forsablefish, it is necessary to estimate the sablefish profits for the missing vessels toobtain a measure of the total sablefish profits in 1988. To provide such estimatesdata common to all vessels were employed. The data were obtained from DFO catchstatistics and include the age of the vessel in years and the total value of sablefishlanded for 1988. The estimates of sablefish profit for trap and longline vessels in theCES were then separately regressed on the independent variables of value of sablefishlandings (xl) and the age of vessel (X2).The estimated coefficients from these ordinary least squares regressions were thenused to obtain a mean prediction of the sablefish profits for vessels not in the CES.The results of the regressions are given in equations (5.2) and (5.3).Trap Vessels= O.3587X1 — 374.82X2 (5.2)(0.0677) (1961.2)= 0.821 df = 10 F2,10 = 23.99Longline Vessels= 0.4484X1— 694.02X2, (5.3)(0.0551) (594.81)= 0.914 df = 14 F2,14 = 74.64where r2 is the raw moment r-square, standard errors are in parentheses, * indicatescoefficient is significantly different from zero at the 10% level of significance, issablefish profit, X1 is value of sablefish landed, and X2 is age of vessel in years.Chapter 5. Rent and the BC Sablefish Fishery 115In equations (5.2) and (5.3) only the coefficients with respect to the value ofsablefish landings were significantly different from zero. The calculated F statisticstest whether collectively the coefficients are significantly different from zero. Forboth equations, the null hypothesis of zero coefficients is rejected at the 10% levelof significance. Because both equations do not have a constant term, the standardr2 value is not well defined. For this reason, the raw moment r2, which measuresthe deviation in the actual and predicted dependent variable from zero is presented.The r2 value for both equations is high considering the estimates are obtained fromcross-sectional data. It should be emphasised, however, that the performance of anequation for forecasting or prediction is quite distinct from the classical t, F, andr2 statistics. Good forecasts may come from regression models with low r2 or oneor more insignificant regression coefficients if there is relatively little variation in thedependent variable.Using the estimated coefficients from (5.2) and (5.3) and the mean values of sable-fish landings and age of vessels for the two gear-types, a mean prediction of sablefishprofits was obtained. The predicted values and 95% confidence intervals for the 18vessels not in the CES who caught sablefish in 1988 are presented in Table 5.3. Interestingly, the lower confidence interval for the mean prediction for trap vessels exceedsthe upper confidence interval for the longline vessels. In both cases, the confidenceintervals are in a positive range with the means for trap and longline vessels beingrespectively some $190,000 and $64,000. Multiplying the mean predicted sablefishprofits by the number of vessels for each gear-type, an aggregate measure of theprofits for those vessels not in the CES can be obtained. Summing this predictedaggregate value to the sum of the estimated profits of vessels in the CES, a measure of the total sablefish profits in the fishery can be determined. These values arepresented in Table 5.4. Consulting Table 5.4, it would seem that the 1988 sablefishChapter 5. Rent and the BC Sablefish Fishery 116profits in the fishery are estimated to be some $6.2 million. This provides an estimateof both the annual resource rent and the intra-marginal rents in the fishery. A lowerrange for the estimated sablefish profits can also be obtained by using the lower 95%confidence intervals given in Table 5.3. This provides a lower estimate of the totalfishery profits of some $5.2 million.5.4 Licence Values ApproachAnother approach to estimating the profit of fishers in 1988 is to use their estimatedvalue of sablefish licences. These licences, restricted to a total number of 48, are aprerequisite for being a legal participant in the fishery and are assigned to a particularindividual and vessel. To the extent that newcomers are able to purchase vesselswith sahiefish licences from fishers retiring from the fishery, such licences commanda positive price. These sablefish licences provide fishers with a legal fishing privilegeand the price paid for a licence reflects the market’s expectation of resource rents inthe fishery less an allowance for risk under the management policies in place in 1988.Employing a methodology used by Schwindt (1986) one may use the aggregatevalue of sablefish licences as a proxy of the expected capitalised rent in the fisheryin 1988. Depending upon the level of risk aversion by fishers and the perceiveduncertainty in the fishery, the expected capitalised rent in the fishery should be equalto or greater than the total value of sablefish licences. Estimates of the market priceof sablefish licences is provided in the CES. In the survey instrument, fishers wereasked to provide the price they would expect to receive if they sold their vessels withall licences and the specific price that would be paid for a sablefish licence. The pricesprovided by fishers is presented in Table 5.1. The mean price for a sablefish licencewas some $280,000 while the range was from $100,000 to $600,000. To obtain anChapter 5. Rent and the BC Sablefish Fishery 117estimate of the licence values for vessels not in the CES, a mean licence value permetre of vessel length of some $14,500/metre was calculated from the 26 vessels inthe CES where data was available. This mean price was multiplied by the remainingnumber of licences in the fishery and added to the total from vessels in the CES toobtain a total value of the licences in the fishery of some $13.3 million. This sumrepresents the expected capitalised resource rent in the fishery less any discountingby fishers because of risk.To obtain a measure of the annual expected resource rent from the fishery, theaggregate value of sablefish licences may then be multiplied by an appropriate rate ofdiscount. Using a discount rate equal to one percent above the mean prime businesslending rate for 1988 or 11.83% and multiplying the total value of licences by thisamount, an estimate of the annual resource rent in the fishery less discounting becauseof risk is some $1.6 million. In calculating this anniialised rent it is implicitly assumedthat fishers face an infinite planning horizon. In actual fact, fishers may face a muchshorter pay-back period or planning horizon. The shorter the planning period offishers the greater must be the annual rent in the fishery. For example, using thesame discount rate and assuming fishers have a pay-back period of five years and tenyears, the annual resource rent in the fishery less an allowance for risk is, respectively,some $3.7 and $2.4 million. It should be emphasised, however, that estimates of therent in the fishery using 1988 licence values reflect the expected resource rent for theperiod 1988 only. Information from a broker in the fishing industry [K. Gaynor, pers.comm.] in 1990 indicates that the value of sablefish licences with quota increasedsome three to four fold with the introduction of IVQs. Much of this increase in valueis probably attributable to the coupling of licences with individual quotas which inturn give fishers a much more secure fishing privilege than licences alone. It is alsopossible that the profits in the fishery are higher today than in 1988. This may beChapter 5. Rent and the BC Sablefish Fishery 118due to efficiency improvements due to IVQ regulations and an increase in the priceof sablefish since 1988.5.5 Profit Function and Other ApproachesThe third approach to estimating the rent in the fishery is to predict individualprofits per vessel using two restricted profit functions. Unlike the other approachesto estimating rent in the fishery, the estimated profit functions may also be used topredict the profits of fishers in 1990 using updated prices and data. The use of a profitfunction assumes that fishers seek to maximise profit by choice of an input and outputmix. The approach is based upon duality theory [Diewert (1974)] in that the directproduction function of a firm may be estimated from a dual profit function. The dualfunctions, in contrast to direct production functions, use input and output prices asarguments instead of quantities. The profit function can also provide estimates ofthe elasticities of substitution between inputs and outputs, elasticities of intensitybetween variable and restricted inputs, and returns to scale.Choosing the functional form of the profit function to be estimated is governed bya number of issues. Theoretically, such a function should not impose a priori restrictions on the elasticities of substitution among inputs and outputs. The two functionalforms used in this thesis, a normalised quadratic and a translog variable profit function, are both flexible in this property. Estimates of the unknown parameters of theprofit functions are estimated using the CES, landing slip data, and market priceinformation solicited by the researcher. In particular, the price and catch of sablefishand other species were obtained from landing slip data obtained from DFO, fuel pricesfrom Chevron Canada, an opportunity cost wage was calculated using average weeklyearnings and unemployment insurance payments from Statistics Canada. A detailedChapter 5. Rent and the BC Sablefish Fisheiy 119description of the data used in estimation of the functions is provided in AppendixB.One of the profit functions used in estimating sablefish profits is the normalisedquadratic form. This functional form has the advantage that convexity, a necessarycondition for profit-maximisation, can be imposed as required on the profit functionwith no loss in flexibility. The function was first defined by Fuss (1977) and later ina general form by Diewert and Ostentoe (1988) and more recently by Diewert andWales (1988, 1990). A normalised quadratic profit function was first used in a fisherycontext by Dupont (1988, 1990) in a study of rent dissipation in the BC salmonfishery. Imposing linear homogeneity in prices, a variant of the function is defined by(5.4). The notation used to describe the profit function is defined as follows:’Hf? is restricted profit.c is a prespecified parameter.aik, i = 2 . . N and k = 2• N are parameters to be estimated.c, c, and d7, i = 1 N are parameters to be estimated.D is a dummy which is 1 for trap and 0 for longline vessels.Z, is the restricted input of vessel size.P, i = 1 . . . N are input and output prices.1 NNHf?(P, Z,) aZ, >: >: Ok(PPk)/Pl +i=2 k=2N N N> cPZ1 + + dPD (5.4)i1 i=1 i=1The function defined by (5.4) is a returns to scale flexible functional form [Diewertand Wales (1990)] and requires one less free parameter than a flexible functional form.‘An initial hypothesis is that the profit function defined by (5.4) assumes joint-in-inputs technology for sablefish and other species. This hypothesis may be subsequently tested econometrically.Chapter 5. Rent and the BC Sablefish Fishery 120Symmetry may be imposed on the unit profit or net revenue function defined by (5.4)by setting the coefficients a.k = ak. With symmetry imposed there are N(N-1)/2 akfree parameters, N c free parameters, N c free parametrs, and N d free parameters.Following Diewert and Wales (1988) and Dupont (1988, 1990) an a priori choice forthe prespecified parameter is 1/Z, where Z is the first observation of the restrictedinput.In order for the unit profit function to describe the underlying production technology, it is necessary that (5.4) be linearly homogeneous and convex in prices, non-decreasing in the fixed factor, and monotonic in the output supply and input demandfunctions. Linear homogeneity is a maintained hypothesis with F1, the price of labourservices, being the normalising price.Convexity in prices of the unit profit function is established globally and locallywhen the matrix defined by A with individual parameters ak is positive semidefinite.A sufficient condition for a positive semidefinite A matrix is that all the eigenvalues benonegative. Monotonicity can be verified by observing whether the predicted outputsare positive and the predicted inputs are negative.Using Hotelling’s lemma the associated net supply equations to (5.4) may bederived. For i = 2, 3,4 with symmetry imposed the net supplies are given by equation(5.5).NX = cZ ak(Fk/Pl) + cjZ1 + (5.5)k=2c + dDFor i = 1 the net supply is given by equation (5.6).1 NNX1 = —cZ ak(FjPk)/P? + cZ1 + (5.6)i=2 k=2c1 + d1DChapter 5. Rent and the BC Sablefish Fishery 121The price of labour services (Pr) is defined as the normalising price that assureshomogeneity of degree zero in the outputs and inputs while the restricted input (Z1) isdefined as the vessel length in metres. The net supplies include the input demands forlabour (Xi) and fuel (X2) and the output supplies of other species (X3) and sablefish(X4). The set of equations to be estimated include (5.5) and (5.6). By convention,inputs are defined as negative quantities and outputs as positive quantities.The price of labour services (F1) was calculated as an exj)ected average weeklyearnings of fishers. This was necessary so as to avoid a possible simultaneity problemin estimation because in the fishing industry crew are often paid a specific share ofthe landed value of the harvest. For example, in the sablefish industry fishing creware generally paid 50% of the landed value of fish after deducting operating expensessuch as bait, fuel, and provisions. The methodology used to calculate an expectedaverage weekly earning was the same as used by Dupont (1988, 1990) and involvedweighting the mean wage for different regions of the BC coast by the probabilityof being employed. This labour price index was set such that the first observationwas set equal to unity when estimating the normalised quadratic unit profit function.This procedure was followed for all prices and for the fixed factor. Dividing thelabour price index into the total labour expenditures per vessel plus bait and food,an implicit aggregate index of labour quantity (X1) was obtaiiied.The price of fuel (F.2) was obtained on a regional basis from Chevron Canadaand adjusted by the fishing dates of the vessels in 1988. Dividing the fuel priceindex into the expenditures on fuel obtained from the CES, an implicit quantityindex (X2) was derived. The price of other species (P3) was also obtained from DFOlanding statistics. Specifically, an aggregate price index per vessel was obtained byconstructing a Laspeyeres and Paasche index for each vessel relative to the meanprice and total landings per species for all vessels in the sample. Taking a geometricChapter 5. Rent and the BC Sablefish Fishery 122average of the two indexes, a Fisher price index [Diewert (1989)] per vessel for allspecies other than sablefish was obtained. This index was then divided into the totalrevenue from other species other than sablefish to obtain an implicit quantity index.The price of sablefish (F4) was obtained directly from landing statistics routinely keptfor all registered commercial fishing vessels in BC. The price measured in $/kg wasindexed and divided into the revenue per vessel obtained from the CES to derive animplicit quantity of sablefish (X4).Appending an additive disturbance term to each of the equations in (5.5) and(5.6), an estimate of the unknown parameters may be obtained. In estimation it wasassumed that the disturbance vector is independently and identically distributed withmean vector zero and a constant, nonsingular covariarice matrix. The disturbances areassumed to arise from errors in optimisation by fishers. In estimating the unit profitfunction, one observation was dropped from the sample. The vessel dropped from thesample only harvested sablefish and consequently no price variable was available forspecies other than sablefish.Following estimation of the unknown parameters, the properties of the unit profitfunction may be examined. Because the eigenvalues of the A matrix were not allnonnegative, the function was not found to be globally convex. A rejection of theconvexity property implies that the input demands and output supplies may not bewell-defined. As a result, it may be possible to alter a combination of olltputs andinputs and increase the variable profit of a fisher. Convexity may be violated for anumber of reasons. Wales (1977) has shown that estimates of a flexible functionalform may violate convexity even if the data come from a well-behaved technology.Squires (1987) also notes that inconsistent aggregation in constrllcting the price andquantity variables may also contribute to the problem. Because of nonconvexity,equations (5.5) and (5.6) were re-estimated with curvature imposed using a methodChapter 5. Rent and the BC Sablefish Fishery 123described by Wiley, Schmidt, and Bramble (1973). This involved replacing the Amatrix by a lower triangular matrix E and its transpose such that A = EET. Aconsequence of the procedure is that the unit profit function becomes nonlinear insome of the unknown parameters. The ak parameters as specified in (5.4) can beretrieved from the coefficients of the E matrix as per Table 5.5.Because of nonlinearity in some of the unknown parameters with curvature imposed, the model was estimated using a nonlinear Quasi-Newton maximum likelihoodprocedure in a general computer program for econometric methods [White (1990)].This procedure uses the Davidson-Fletcher-Powell algorithm to converge to a maximum. When using such a method, convergence to a local rather than global maximumis possible. For this reason, the model was estimated with starting values of unityand then re-estimated with starting values equal to five. Although not a test for aglobal maximum, both sets of starting values converged to the same final values.The results of estimation of the unit profit function a.re presented in Table 5.5.The table presents estimates of the unknown parameters, their standard errors, thevalue of the log likelihood function, and the generalised R2 for the system of equationsestimated. The generalised R2 is due to Baxter and Cragg (1970) and is defined by(5.7).Generalised R2 = 1 exp[2(Lo— Lmax)/kl (5.7)where L(Lmax) is the value of the log-likelihood function when all parameters areconstrained to zero (unconstrained) and k is the total number of observations.Individual r2 between observed and predicted values for the estimated equationsare provided in Table 5.6. Consulting Table 5.6, apart from the other species outputequation the individual r2 are relatively high for cross-sectional data ranging from0.57 to 0.71. It should be noted, however, that maximum likelihood estimation doesChapter 5. Rent and the BC Sablefish Fishery 124not in general maximise the individual r2 values but minimises the determinant ofthe residual cross-products matrix. In addition, using the predicted outputs andinputs to construct predicted vessel profits per vessel, an r2 of 0.47 was calculatedbetween predicted and observed profits. Observation of the predicted output suppliesand input demands revealed that the monotonicity condition was satisfied for everyobservation. Monotonicity is satisfied when all the predicted values of the inputdemands are negative and the predicted output supplies are positive.To examine the robustness of the estimates to the choice of the functional form,a translog unit profit function was also estimated using the same set of data. Thisfunctional form represents a second order Taylor’s series approximation in logarithmsof an arbitrary unit profit function. Such a profit function was first defined by Diewert(1974) and has been used in a fisheries context by Squires (1984, 1987) and by Bjørndaland Gordon (1989).Imposing linear homogeneity, cross-price symmetry and an ad hoc dummy variablefor the trap vessels, the function is defined by equation (5.8).inH(P, Z1) = in(Pi) + o + in(P/Pi) + in(Zi) +[in(Zi)j2 + ii[inPi/Pi]2 +ciin(P/Pi)ln(Zi) +a23in(P/P)in(P3i)+i=24in(P/Pi)in(P4i)+cx34in(F/Pi)in(P4j)+N6in(P/P1)D (5.8)i=2where the variables are as defined previously, in is a logarithmic transformation, ando, ai, ozi, c and ö are unknown parameters to be estimated.Using Hotelling’s lemma the revenue and cost share equations may be obtainedChapter 5. Rent and the BC Sablefish Fishery 125by logarithmically differentiating (5.8) with respect to the input and output prices.By convention, the cost shares are affixed with a negative sign. For i = 2, 3, 4:NW =k=2+aln(Zi) + 45D (5.9)The system of equations to be estimated include (5.8) and N-i share equations. Appending an additive disturbance term to equations (5.8) and (5.9), and using a maximum likelihood procedure, the parameter estimates, standard errors, value of thelog likelihood fuiiction and a generalised R2 for the system of equations are providedin Table 5.7. Individual r2 between observed and predicted values for the estimatedequations are given in Table 5.8. As with the normalised quadratic function, thetranslog fails to satisfy the appropriate curvature properties. Appropriate curvatureproperties were not, however, imposed on the function since it reduces the flexibilityof the function and its ability to identify individual elasticities of substitution.To obtain an estimate of the profits of fishers using the estimated profit functionsit is necessary to subtract an appropriate share of the rental price for services providedby the restricted factor Z1, i.e.,= H(P, Z1)— o[mZ1] (5.10)where H is total sablefish profit, H is variable sablefish profit, o is the factor forallocating indirect costs to sablefish operations, and m is the unit rental price of thefixed input of vessel length.The factor used for allocating variable costs and overhead in 1988 was set equalto the ratio of direct costs attributable to sablefish as a proportion of total directfishing costs. For 1990 predicted sablefish profits, the ratio equalled the proportion ofpredicted gross earnings from sablefish to gross earnings from all species. An estimateChapter 5. Rent and the BC Sablefish Fishery 126of the rental price of the fixed factor was obtained from consultations with a fish boattrader and by reviewing commercial fishing magazines. Using quoted asking pricesfor comparable vessels from 1990 issues of the West Coast Fisherman, a median priceper metre of comparable second-hand vessels used in the fishery was obtained. Suchvessels would be the likely replacement for the current vessels used in the fishery. Themedian price of some $3,250/metre was then used to derive a flow rental price for thefixed input by assuming a straight line depreciation rate (e) and a interest rate facedby fishers of (r) per stock price (v), i.e.,m = v[E+rj (5.11)where it was assumed r was 1% above the prime business lending rate and E = 0.05on the assumption that on average vessels have a 20 year life after purchase. Fromthe vessel lengths of vessels and a measure of the unit rental price (rn), an estimateof total sablefish profits were obtained as per (5.10).A comparison of the 1988 estimates of sablefish profits using the two profit functions is presented in Table 5.9. Both the normalised quadratic and translog functionsgive similar values for sablefish profits by gear-type, but exceed those obtained directly from the costs and earnings survey given in Tables 5.1 and 5.2. In particular,the estimated mean profit for trap and longline vessels with the normalised quadraticwas some $327,00 and $107,000. The mean over all gear-types is some $189,000. Forthe translog function, the estimated mean profit was some $334,000 and $112,000,respectively, for the trap and longline vessels with the overall mean being $194,000.In comparison, using a direct approach to estimate the profits of fishers, the meanprofits of trap and longline vessels was found to be $211,000 and $79,000 with anoverall mean of $136,000. The difference between the measures of sablefish profitprovided in Table 5.2 and 5.9 is, however, mostly explained by the different measuresChapter 5. Rent and the BC Sablefish Fishery 127of the value of assets employed in the fishery. For example, using the mean price permetre/vessel from the survey one may calculate another measure of the rental costfor the fixed factor. Using this rental price, the normalised quadratic and translogfunctions, respectively, estimate a mean sablefish profit for all fishers of some $143,000and $149,000.Using the predicted profits of vessels, an estimate of the total sablefish profits inthe fishery may be obtained from the two profit functions. Such an estimate is notwithout problems since it presupposes that the sablefish profits of the vessels not inthe costs and earnings survey are exactly the same per quantity of sablefish landedas those in the survey. Nevertheless, an estimate of total sablefish profits in 1988is presented for comparison purposes. Table 5.10 presents the estimated rent thataccrues to the vessel owners and is calculated by multiplying the total harvest in kg.for each vessel type by the mean sablefish profit/kg. for the two gear-types. Thenormalised quadratic and translog functions suggest that total sahiefish profits were,respectively, some $8.6 million and $9.3 million in 1988. These estimates of the rentin the fishery reflect both resource and intra-marginal rents.In assessing the sablefish profits in the fishery, it should be emphasised that the estimates reflect only the returns to the vessel owners. In the sablefish fishery, crew aregenerally paid on a share system equal to 50Y of the total revenue less all operatingexpenses. As a result, it is likely that a share of the rents also accrue to labour. Forexample, in 1988 the average remuneration per crew-member from sablefish fishingalone was some $23.000 for less than 21 days work. This represents an amount approximately equal to the average annual earnings of manufacturing workers in BritishColumbia for that year. To obtain a measure of the rents that accrue to labour andvessel owners, a labour cost for sablefish crew based solely on an opportunity costwage may be estimated. The total opportunity cost was calculated as an expectedChapter 5. Rent and the BC Sablefish Fishery 128average weekly earning per vessel based on their homeport multiplied by the numberof weeks engaged in sablefish fishing by the crew.2 Using this approach, the calculatedlabour expenditures per vessel become equal to the actual labour costs in all otherfisheries plus the opportunity cost wage for crew fishing for sablefish. Re-estimatingthe profit functions as described earlier with convexity imposed for the normalisedquadratic function, an estimate of the rents to the vessel owners and labour may beobtained. For the translog function, the mean value for both gear-types was some$269,000 or some 40% more than that obtained using the actual labour expendituresof vessels. Using the normalised quadratic function, the mean value of the sablefishprofits was some $260,000 or 37% more than that obtained using actual labour expenditures. It suggests that a substantial portion of the total resource rent in thesablefish fishery is received by the crew of vessels.A justification for high earnings by crew members in a fishery is that it reflects apayment for the hazards of the job and for the risk involved in accepting a share ofthe gross returns rather than a fixed wage. Under a limited fishing season, where theskill and efforts of each crew member are important in determining the returns to thevessel and crew, a share system also helps to elicit effort that might otherwise not beforthcoming. Under individual quota management with a binding quota constraint,however, crew earnings can be known with a reasonable degree of certainty becausevessels are reasonably assured of harvesting their annual quota. Further, without alimited fishing season vessel owners may be able to substitute crew skill for extra timeat sea. Not unsurprisingly, therefore, there has been a move by some vessel ownersto pay crew a daily wage rate rather than a share of gross revenue with the adventof individual vessel quotas [Dave Ellis, pers. com.J. A question that arises is why allvessels have not moved to a fixed wage payment of crew. A possible explanation for2see Appendix B for details.Chapter 5. Rent and the BC Sablefish Fishery 129its continued existence is that the individual quota management scheme is in a trialperiod until the end of 1992. By changing or reducing the earnings of crew, quota-holders may attract attention from such organisations as the United Fishermen andAllied Workers’ Union who have consistently opposed rights based management inBC. Such attention may provide further stimulus for lobbying against the currentquota management scheme with DFO.3Estimates of the 1990 sablefish profits of fishers from the two profit functions andfor the two gear-types are provided in Table 5.11. The estimates are obtained fromthe predicted profits of 15 trap and 15 longline vessels that harvested sablefish in 1990and represent the returns to the vessel owners only. These estimates were obtainedby using the estimated coefficients of the respective profit functions and updatingthe input and output prices for 1990 and by specifying the vessel lengths and gear-type of the 30 vessels that participated in the fishery in 1990. Total sablefish profitsin 1990 were calculated in a similar manner to 1988 by subtracting from predictedvariable profit a rental cost per vessel. The share for allocating the wage and fuelexpenditures to sablefish and rental cost of the fixed factor was set equal to the ratioof the predicted revenue from sablefish to total revenue from all species includingsablefish. For both the normalised quadratic and the translog profit functions, allvessels fishing for sablefish in 1990 had positive profits. In the case of the normalisedquadratic, the mean profit of vessels in 1990 was some $231,000 while for the translogfunction the mean vessel profits was some $223,000. The predicted total sablefishprofits in 1990 for the fishery are presented in Table 5.12. For the normalised quadraticand translog functions, respectively, the total sablefish profits are some $7 million and$6.7 million.3The Union sponsored an inquiry into the BC fishing industry in 1991. The inquiry stated thatthe continued existence of the IVQ sablefish programme, “... should be contingent on an equitableshare agreement between the quota-holder and crew members ... “ [Cruickshank (1991), 68]Chapter 5. Rent and the BC Sablefish Fishery 130A comparison of the total sablefish profits in 1988 and 1990 in Tables 5.10 and 5.12suggests that the rent fell from 1988 to 1990 despite the fact that the average profitper vessel of each gear-type increased over the period. This puzzling result stemsfrom the fact that in 1990 there were 16 fewer vessels harvesting sablefish than therewere in 1988 as a direct consequence of the introduction of transferable quotas. Mostof the sablefish licence-holders who were not active in the fishery in 1990 leased theirquota to other fishers. The estimated coefficients of the profit functions, however,are derived from 1988 data which does not account for the structural change thattook place in the fishery in 1990 and the subsequent increase in sablefish harvests pervessel. Consequently, the predicted 1990 sablefish harvests of most vessels for boththe normalised quadratic and translog functions underestimate the actual harvestsin the fishery. For example, the actual harvest of all fishers in 1990 was some 4,260MT while the normalised quadratic and translog functions, respectively, predict totalharvests of 3,366 MT and 3,364 MT.To obtain a measure of the total sablefish profits in the fishery accounting forthe structural change in 1990, the predicted individual vessel sablefish profit/kg wasmultiplied by the actual harvest of each vessel in 1990. The estimates of the totalsablefish profits, accounting for the structural change in the fishery, for both profitfunctions and by gear-type are presented in Table 5.13. The total sablefish profits forthe normalised quadratic and translog profit functions calculated using this approachare, respectively, some $8.7 and $8.5 million and includes both the resource rent andintra-marginal rents. For the normalised quadratic, the total sablefish profits in 1990exceed their value in 1988 while for the translog function the 1990 sablefish profitsare less than in 1988.Using the estimates given in Table 5.13, the proportion of total sablefish profitto total sablefisli revenue in the fishery is some 49% and 47%, respectively, for theChapter 5. Rent and the BC Sablefish Fishery 131normalised quadratic and translog profit functions. This compares favourably tostudies ill Australia which indicate potential rents in fisheries ranging from 25 to 60%of the gross landed value [Campbell and Haynes (1990)]. The estimates may alsobe compared to the rent that accrues to vessel owners under the traditional sharesystem for paying crew. Under this system, 50% of the gross revenue accrues to thevessel’s owner out of which must be met all indirect expenses. The upper bound forthe sablefish profits in 1990 is, therefore, 50% of the gross landed value of sablefishthat year or some $9 million.Another approach to estimating the rent in the fishery in 1990 is to use themarket price of quota. Depending upon the uncertainty in the fishery and the riskaversion of fishers, the resource rent should be equal to or greater than the annualvalue of quota holdings. Employing this approach, an estimate of the annual valueof quota-holdings was obtained from a market price of quota for sablefish coupledwith a sablefish fishing licence. This price, which varied from $8.94-9.30/kg over fivetransactions in 1990, was obtained from a Vancouver fish boat trader in early 1991[K. Gaynor, pers. comm.]. Assilming an infinite pay-back period and multiplyingthe quota price by the total quota owned by fishers for 1990 and by an interest rateconsistent with the opportunity cost of capital faced by fishers, an annual value ofquota-holdings is calculated to be some $4.8 million. Assuming a pay-back period offive and ten years, the estimated annual resource rent that accrues to vessel owners is,respectively, some $11 and $7.2 million. This represents an estimate of the resourcerent to vessel owners in the fishery less any discounting due to risk by fishers. Unlikean estimate of the total sablefish profits, however, the annual value of quota-holdingswill not include any intra-marginal rents due to differential fishing skill or technologydifferences.Chapter 5. Rent and the BC Sablefish Fishery 1325.6 OverviewThree approaches are used to estimate the total rent in BC sablefish fishery in 1988.In a direct approach using data directly from a cost and earnings survey, the totalfishery profits for 1988 are estimated to be $6.2 million with a lower range of $5.2million. Using a licence value approach, the mean value of sablefish licences obtainedfrom the CES was used to determine a capitalised value of the resource rent less anallowance for risk. Using a discount rate equal to the opportunity cost of capitalfaced by fishers, an estimate of the annual resource rent less discounting for risk wasobtained of some $1.6 million. Assuming a different time horizon for fishers of only fiveand ten years, the annual resource rent that accrues to vessel owners is, respectively,some $3.7 and $2.4 million. In a third approach to estimating sablefish profits in 1988,a normalised quadratic and translog unit profit function were estimated. The meanprofit per vessel for each gear-type from both functions gave a similar estimate to thatusing the direct approach after corrections were made for the use of different assetvalues. In total, the estimated sablefish profits in 1988 for the normalised quadraticand translog functions were some $8.6 and $9.3 million. All three approaches suggestthere were substantial returns to be made in the BC sablefish fishery in 1988.Updating output and input prices for 1990, the two profit functions were used topredict the individual profits of vessels in 1990. Under the translog specification totalpredicted sablefish profits are some $6.7 million while with the normalised quadraticfunction total sablefish profits are estimated to be some $7.0 million. Accountingfor the structural change in the fishery between 1988 and 1990, an estimate of thetotal 1990 sablefish profits of $8.7 and $8.5 million is obtained, respectively, from thenormalised quadratic and translog functions. This compares to an estimate of thesablefish profits using the traditional remuneration system in the fishery. Specifically,Chapter 5. Rent and the BC Sablefish Fishery 133vessel owners receive as a maximum return 50% of the gross landed value of sablefishout of which must be covered indirect expenses. This vessel share represents an upperbound for the estimated rents that accrue to vessel owners in the fishery and in totalwas some $9 million in 1990.In an alternative measure of the rent in the fishery, the market price of quota in1990 was used to estimate the total value of quota-holdings. Multiplying this totalvalue by an interest rate equal to the opportunity cost of capital faced by fishersgives an estimate of the annual expected resource rent that accrues to vessel owners.Assuming an infinite time horizon or planning period by fishers the resource rent thataccrues to vessel owners is estimated to be some $4.8 million. Assuming a differentpay-back period, the annual resource rent that accrues to vessel owners is estimatedto be $11 and $7.2 million, respectively, for a pay-back period of five and ten years.In reviewing the various estimates of the rent in 1990, it would seem that thetotal sablefish profits that accrues to vessel owners is no more than $9 million and, ifone accepts the predicted profits from the profit functions, it is some $8.5-8.7 million.Such a prediction compares favourably to an estimate of the annual resource rent thataccrues to vessel owners using the traded quota price and assuming a ten year payback period. Using the normalised quadratic and translog profit functions predictedprofits in 1990, with the adjustment for structural change in the fishery, the differentmethods of rent capture are examined in chapter 6.Chapter 5. Rent and the BC Sablefish Fishery 134Table 5.1: 1988 Summary Statistics of FishersVariable Mean Minimum Maximum C.VVessel Profits 231,144 51,885 839,390 0.675Sablefish Profits 136,030 30,398 703,640 0.955Price of Sablefish 3.71/kg 3.29 4.47 0.067Price of Fuel 0.34792/litre 0.3179 0.3790 0.063Kilos of Sablefish 104,070 33,408 319,260 0.720Kilos of Other Fish 354,640 0 2,963,800 2.284Crew size (excluding skipper) 3.85 0 12 1.28Vessel Length 19.32 m 10.01 37.19 0.331Vessel Registered Tonnage 34.64 7 194.71 1.091Vessel Age 17 years 7 48 0.78614Value Sablefish Licences 277,310 100,000 600,000 0.427Sablefish Revenue 385,870 121,910 1,293,000 0.743Direct Fishing Expenses 314,620 84,400 830,400 0.567Indirect Expenses 97,176 15,700 263,520 0.784Sources:1. DFO 1988 costs and earnings survey of 28 sablefish licence-holders.2. DFO 1988 catch statistics.3. Chevron Canada.4. Vancouver Ship Registry.Chapter 5. Rent and the BC Sablefish Fishery 135Table 5.2: Estimates of 1988 Mean Net Returns and Profitability Ratios using theSurvey Data DirectlyMeasure Trap Longline All VesselsSablefish Profit:Mean 211,490 79,430 136,030Median 184,448 69,724 99,960Sablefish Profit/Sablefish Revenue:Mean 33% 37% 35%Median 30% 36% 33%Vessel Profit/Equity:Mean 26% 38% 33%Median 22% 32% 25%Sablefish Profit/Sablefish Landed:Mean $1.2Okg $1.38kg $1.3OkgMedian $1.O4kg $1.35kg $1.2lkgChapter 5. Rent and the BC Sablefish Fishery 136Table 5.3: Predicted Mean Sablefish Profit for Non CES Vessels in 1988 ($) usingSablefish Landings and Age of Vessel DataGear-Type No. Vessels Mean Profit Lower 95% C.I Upper 95% C.ITrap 10 189,647 105,508 273,786Longline 8 63,865 44,080 83,649Table 5.4: Direct Estimates of Total Sablefish Profits in 1988 ($) using Survey Dataand Sablefish Landings and Age of Vessel DataData Source No. Vessels Sablefish ProfitCES 28 3,809,000Non CES 18 2,407,000All Vessels 46 6,216,000Chapter 5. Rent and the BC Sablefish Fishery 137Table 5.5: Nonlinear Parameter Estimates of the Normalised Quadratic Unit ProfitFunctionVariable Value Std. Error Variable Value Std. Erroreff -264.19 95.03 c4z 0.23517E+06 0.27871E+06eof 90.58 70.46 ci 94,163 96,277eoo 192.92 103.81 c2 18,322 13,447esf 176.43 172.05 c3 3,243 93,243eso 577.58 186.89 c4 -0.26092E+06 0.11617E+06ess -0.10989E-04 762.77 d1 -65,967 52,425clz-0.1.5166E+06 0.21385E+06 d2 -26,890 8,048c2z -36,539 72,492 d3 -275.89 44,234c3z 0.20809E+06 0.14826E+06 d4 0.21417E+06 77,767Note:1. Log-likelihood function =- 1351.2452. Generalised R2 = 0.643. The ak coefficients of the profit function are obtained as follows: a22 = eff2,a23 = eff x eof, a24 = eff x esf, a33 = eof2+eoo,a34 = eof x esf+eoox eso,a44 = esf2 + eso2 + ess2.Chapter 5. Rent and the BC Sablefish Fishery 138Table 5.6: R-Square Values for Normalised Quadratic Profit FunctionEquation R-Square between Observed & PredictedLabour Demand 0.5942Fuel Demand 0.5719Other Species Output 0.1012Sablefish Output 0.7127Profit 0.4667Chapter 5. Rent and the BC Sablefish Fishery 139Table 5.7: Parameter Estimates of the Translog Unit Profit FunctionVariable Value Std. Error Variable Value Std. Errorao 6.8968 6.538 a23 -0.9231E-02 0.5936E-01a2 -0.1982 0.3028 a24 0.2894 0.1395a3 1.0977 1.0403 a34 0.6289E-01 0.2834a4 0.7493 1.198 a2z 0.8292E01 0.694E01az 1.497 4.36 a3 0.4431E01 0.3911a22 0.1059E-01 0.1517 a4 0.29953 0.34458a33 -0.1664 0.3583 -0.1169E-02 0.3465E-01a44 -0.1818 0.5921 -0.4272 0.1899a -0.1979 1.4656 0.1736 0.99731E-01Note:1. Log-likelihood function = 28.652. Generalised R2 = 0.89Chapter 5. Rent and the BC Sablefish Fishery 140Table 5.8: R-Square Values for Translog Unit Profit FunctionEquation R-Square between Observed & PredictedProfit 0.3411Fuel Demand 0.1416Other Species Output 0.3016Sablefish Output 0.1311Chapter 5. Rent and the BC Sablefish Fishery 141Table 5.9: Estimated Mean 1988 Sablefish Profits ($) for Profit FunctionsEstimate Trap Vessels Longline Vessels All VesselsNormalised Quadratic 327,000 107,000 189,000Translog 334,000 112,000 194,000Table 5.10: Estimated Total 1988 Sablefish Profits ($) for Profit FunctionsEstimate Trap Vessels Longline Vessels All VesselsNormalised Quadratic 6,177,000 2,489,000 8,666,000Translog 6,672,000 J 2,661,000 9,333,000Chapter 5. Rent and the BC Sablefish Fishery 142Table 5.11: Predicted Mean 1990 Sablefish Profits ($) for Profit FunctionsEstimate Trap Vessels Longline Vessels All VesseiNormalised Qiladratic 330,000 132,000 231,000Translog 300,000 145,000 223,000Table 5.12: Predicted Total Sablefish Profits in 1990 ($) for Profit FunctionsEstimate Trap Vessels Longline Vessels All VesselsNormalised Quadratic 4,946,000 1,976,000 6,960,000Translog 4,505,000 2,180,000 6,685,000Table 5.13: Predicted Total Sablefish Profits in 1990 ($) from the Unit Profit Functions and Accounting for Structural ChangeEstimate Trap Vessels Longline Vessels All VesselsNormalised Qiladratic 6,589,000 2,111,000 8,670,000Translog 6,536,000 1,952,000 8,489,000Chapter 6Rent Capture Methods and the BC Sablefish FisheryA tax upon the reit of land which varies with every variation of therent, ... , is recommended by the sect of men of letters in France, whocall themselves the ceconomists, as the most equitable of all taxes.Adam Smith (1723-1790) An Inquiry into the Nat’ure and Causes of the Wealth ofNations, Vol II, Book V, Chapter II, Part II, Article I, p 355.6.1 IntroductionThis chapter uses the estimates of the sablefish profits of fishers in chapter 5 to assessthe effects of different methods of rent capture on the BC sablefish fishery in 1990.The purpose of the analysis is to explore the implications of rent capture for the fishery and in particular the distribution of profits by fishers and gear-type. Whereverpossible, the empirical results and findings will be compared to those obtained usingthe theoretical model. In this approach, the assumption of short-run profit maxrnisation for a given capital stock with no uncertainty is preserved as is the notion of twotypes of fishers using different harvesting technologies. The two types are representedby fishers who use either pots or traps, or bottom longline gear. The empirical analysis, however, does not address llncertainty or rent collection costs and its implicationsfor rent capture.The methods of rent capture examined in this chapter include a quota rental143Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 144charge, profit charge, net cash flow charge, ad valorem royalty, and a lump sum fee.A quota transfer charge is not compared to the other rent capture schemes as it hasbeen shown in the theoretical model to affect both the number of trades and thequota price. Consequently, analysing its effects with the equilibrium existing in 1990would be misleading. The effects of an auction on the fishery is not examined as itwould also require imposing additional assumptions with respect to the post auctionquota distribution and auction price.In comparing the various methods of rent capture, individual predicted profits offishers for 1990 from the normalised quadratic and translog profit functions are used.The predicted profits for the two profit functions include an adjustment to reflect thestructural change in the fishery brought about by individual quota management. Theestimated mean profits by gear-type for the normalised quadratic and translog arepresented in Table 5.13. Using the two estimates of the 1990 sablefish profits, eachrent capture scheme is compared at equivalent rates of rent capture of 10, 20, 30, 40,50, and 90%. These rates of rent capture are referenced to the predicted sablefishprofits of fishers and may include both a resource rent and intra-marginal rents. Inthe case of the normalised quadratic, a 10% rate of rent capture is equivalent tocollecting some $867,000, while a 90% rate of rent capture collects some $7.8 million.For the translog function, the rent collected represents some $849,000 at a 10% rateof rent capture and $7.64 million at a 90% rate of rent capture.Tables 6.1-6.5 present the mean, standard deviation, the range, and the numberof fishers facing losses under each scheme for each rate of rent capture. The profitsrepresent the sablefish profits after imposition of the method of rent capture at thegiven charge rate. The quota rental charge is calculated by multiplying the individualharvests of vessels by an identical amount per kg such that the total rent collectedis the same for the other rent capture schemes. It differs, therefore, from the chargeChapter 6. Rent Capture Methods and the BC Sablefish Fish eiy 145specified in chapter 4 because it may capture both resource and intra-marginal rents.The rent collected with a profit charge is determined by multiplying the predictedsablefish profits by the specific rates of rent capture of 10% to 90%. The net cash flowcharge is set at a fixed proportion for all vessels and at a level that collects the samerent from the fishery as the other rent capture schemes. The net cash flow of vesselsis assumed to equal the predicted variable sablefish profits. An ad valorem royaltycharge is calculated as a proportion of the harvest of fishers multiplied by the price ofsablefish faced by fishers. This is not the same as an ad valorem royalty where fishersface the same output price or are charged on the basis of an average output price forthe fleet. Finally, a lump sum charge is set by dividing the total amount of rent tobe collected by the number of vessels fishing for sablefish in 1990. This amount, thesame for all fishers, is subtracted from predicted sablefish profits to obtain the profitsof vessels after imposition of the lump sum fee.Using the predicted fisher profits in Tables 6.1-6.5, the burden of the differenttypes of rent capture and distribution of profits are examined. In a separate section,the effects of rent capture on the quota equilibrium in the fishery are also addressed.6.2 Fisher ProfitsExamining Tables 6.1-6.5 it can be seen that the estimates of the post-rent captureprofits of fishers are similar for both the translog and normalised quadratic profitfunctions. Using the normalised quadratic estimates, one may rank the rent capturemethods according to the total amount of rent paid by each type of vessel. On thisbasis, trap vessels collectively prefer in descending order of preference a lump sumfee, ad valorem royalty, net cash flow charge, profit charge, and a quota rental charge.In contrast, the longline vessels collectively prefer in descending order of preferenceChapter 6. Rent Capture Methods and the BC Sablefish Fishery 146a quota rental charge, profit charge, net cash flow charge, ad valorem royalty, and alump sum fee. The translog provides a similar ordering with the exception that theordering of the profit charge and quota rental charge are reversed for the trap andlongline vessels.A closer examination of the predicted profits reveals the reasons for the differencesin the rental paid by the two types of vessels. A comparison of Tables 6.1 and 6.2,shows that with the normalised quadratic, trap vessels collectively pay less rent witha profit charge than a quota rental charge while the opposite is true for the longlinevessels. Following proposition 4.4, one would expect that the trap vessels collectivelywould have a lower predicted profit per quantity of sablefish landed than the longlinevessels. This is indeed the case with the sablefish profits being $1.94/kg and $2.00/kg,respectively, for the trap and longline vessels. In this scenario, those fishers who havehigher net earnings per quantity of sablefish are relatively better off with a quotarental charge compared to an equivalent profit charge. Using the translog profitfunction, trap vessels collectively are predicted to have sablefish profits of $1.95/kg.while longline vessels collectively have profits of $1.88/kg. Using these values, the trapvessels collectively have the higher profits per quantity of sablefish and consequentlywill prefer a quota rental charge over an equivalent profit charge.A comparison can also be made between the quota rental charge and a lump sumfee. In 1990, there were 15 trap and 15 longline vessels operating in the fishery.Imposing a lump sum fee of an equal amount on all vessels that harvested sablefishgenerates the figures presented in Table 6.5. Using the nornialised quadratic estimates, fishers pay a rental of $29,000 at a 10% rate of rent capture and $261,000 ata 90% rate of rent capture. In the case of the longline vessels, a rate of rent captureat only 50% of the predicted sablefish profits results in a loss for 9 of the 15 longlinevessels operating in the fishery. The burden imposed on longline vessels with a lumpchapter 6. Rent Capture Methods and the BC Sablefish Fishery 147sum fee is a direct result of their low quota-holdings relative to that of trap vessels.Collectively, longline vessels harvested some 24% of the TAC while trap vessels harvested the remainder. Following proposition 4.5, therefore, a quota rental charge willbe preferred over a lump sum fee by longlirie vessels while the reverse is the case fortrap vessels. It can also he shown that the proportion of the total sablefish profit andnet cash flow in the fishery accounted for by longline vessels in 1990 is predicted tobe some 24%. As this proportion is less than the proportion of vessels liable for alump sum charge, a profit and net cash flow charge will also he preferred by longlinevessels. This is also true of the ad valorem royalty where longline vessels collectivelyaccount for 27% of the gross landed value of sablefish in the fishery.A comparison between the ad valorem royalty and quota rental charge also revealssome important differences between charging a royalty on the average landed priceand the price actually received by fishers. In the case where fishers are charged on anaverage output price for the fishery, an ad valorem royalty and quota rental charge areidentical by proposition 4.1. If, however, the ad valorem royalty charge is based uponthe actual price received for sablefish which differs across vessels, the two rent captureschemes will differ. For example, using the predicted sablefish profits of vessels, onefisher is found to pay $259,000 with an ad valorem royalty at 90% rent capture whilewith a quota rental charge at the same rate of rent capture the same fisher payssome $406,000. In contrast, aiiother fisher is found to pay some $511,000 with anad valorem royalty at 90% rent capture but pays only $295,000 with a quota rentalcharge. The difference between the two methods of rent capture is entirely basedupon the price received for sablefish by the fishers relative to the average price for thesablefish fishing fleet. Those fishers who receive a lower than average price for theiroutput will be relatively favoured with an ad valorem royalty compared to a quotarental charge. For example, the fisher who pays less with the ad valorem royaltyChapter 6. Rent Capture Methods and the BC Sablefish Fishery 148received a mean price for sablefish of $2.61/kg while the average price over all thirtyvessels in the sablefish fleet was some $3.97/kg. A comparison can also be made withrespect to the two types of vessels in the sablefish fleet. Collectively, longline vesselsreceive a higher price for their sablefish ($4.13/kg.) than trap vessels ($3.90/kg.). Asa result, longline vessels as a group are relatively better off with a quota rental chargethan an ad valorem royalty. The reverse is true for trap vessels who collectively preferan ad valorem royalty over a quota rental charge.A comparison may also be made between a quota rental charge and a net cash flowcharge. From proposition 4.3, those fishers with a higher than average ratio of thevalue of their quota-holdings to net cash flow will pay more with a quota rental chargethan an equivalent net cash flow charge. Using the normalised quadratic estimates,trap vessels collectively have a ratio of the value of quota-holdings to net cash flow ofsome 4.57 while longline vessels collectively have a ratio of 4.42. Consulting Tables6.1 and 6.3, it can be shown that as predicted, trap vessels collectively prefer a netcash flow charge while longline vessels collectively prefer a quota rental charge.A related issue to the distribution of the burden of the different rent captureschemes is the degree of concentration around the mean profit for the fleet. ConsultingTables 6.1-6.5, the standard deviation of the post-rent capture profits of fishers forthe different rent capture schemes is presented. In the case of a lump sum charge,the standard deviation of the profits of fishers of both gear-types is unaltered by therate of rent capture. This is a direct result of the fact that subtracting a constantfrom every observation in a sample will leave the variance unchanged. In contrast,subtracting an equal proportion from every observation will reduce the variance ofa sample. As a result, the greater the level of rent capture with a profit charge thegreater will be the degree of concentration around the mean and the lower will bethe variance of fisher profits. Examining the standard deviation of profits of fishersChapter 6. Rent Capture Methods and the BC Sablefish Fishery 149with a quota rental charge and net cash flow charge also reveals that, in the fishery,increasing the rate of rent capture will increase the degree of concentration aroundthe mean profit. Unlike with the profit charge, however, this is not a general resultsuch that increasing the rate of rent capture may actually increase the variance offisher profits. This is also true for an ad valorem royalty and is illustrated in Table6.4 where for longline vessels the variance of profits actually increases as the rate ofrent capture rises from 50% to 90%.6.3 Distortions to the FisheryAn issue as important as the relative burdens of the different methods of rent captureis the effect of rent capture on the short-run quota equilibrium. In the empiricalanalysis, distortions from rent capture are addressed by the losses imposed uponfishers. In this approach, if a method of rent capture imposes losses on certain fishersat the short-run quota equilibrium then the supposition is that such individuals willbe driven from the fishery. The exit of such fishers, at least in the short-run, willreduce the total sablefish profits because quota-trading should already have allowedfishers to trade such that the marginal value of additional quota was the same for allfishers.The method of rent capture that appears to distort the quota equilibrium the mostis a lump sum charge. Observation of Table 6.5 reveals that at relatively low levelsof rent capture a lump sum fee leaves a number of fishers with losses. For example,using the normalised quadratic and translog profit functions, respectively, some 17%and 20% of the total number of vessels face losses at a rate of rent capture of only30% of total sablefish profits. The fishers facing losses at this rate of rent capture,however, are not necessarily the least profitable fishers but rather those fishers withChapter 6. Rent Capture Methods and the BC Sablefish Fishery 150relatively smaller quota-holdings and consequently smaller total profits. For instance,at a 30% rate of rent capture one of the vessels facing a loss has one of the highestratios in the fleet of profit per kg. of sablefish harvested.Comparing the effects of lump sum fee on gear-types, it should be noted that itis longline vessels that generally have smaller quota-holdings relative to trap vessels.As a result, imposition of a lump sum fee would have the effect of driving longlinevessels from the fishery. Using the predictions from the normalised quadratic at a 90%rate of rent capture, it is found that only 2 out of the 15 longline vessels previouslyfishing for sablefish would remain in the fishery after imposing a lump sum charge.At this same rate of rent capture, six trap vessels would also face losses such thatjust over one third of the fleet would have positive profits. A consequence of forcingprofitable fishers with small quota-holdings from the fishery is to favour those fisherswith large quota-holdings and with higher absolute profits. Using the normalisedquadratic estimates, for example, the fisher with the largest quota-holdings has aprofit of some $814,000 at a 90% rate of rent capture and pays a rental charge equalto only 24% of the total profit before rent capture.In contrast to the lump sum charge, a profit charge and net cash flow charge areshown to leave fishers with positive profits irrespective of the rate of rent capture. Theexception being one of the trap vessels with a net cash flow charge at a rate of rentcapture of 90% using the estimates from the normalised quadratic profit function. Itillustrates an interesting result that a net cash flow charge imposed uniformly on allvessels at a rate that collects less than the total profits can still leave certain fisherswith a loss. The individuals that would incur losses with a net cash flow charge wouldbe owners of vessels with the highest ratio of net cash flow to profits. Such vesselswould be characterised by relatively high fixed or indirect costs but not necessarilylow profits per quantity of sablefish harvested. In the case of a profit charge, providedChapter 6. Rent Capture Methods and the BC Sablefish Fishery 151that profits are estimated correctly, such a method of rent capture would never leavethose fishers that have positive pre-rent capture profits with a loss.The other methods of rent capture to he considered include an ad valorem royalty and a quota rental charge. Consulting Table 6.4 for the normalised quadraticestimates, an ad valorem royalty leaves no fishers with a loss at a 50% rate of rentcapture but imposes losses on five vessels at a 90% rate of rent capture. Using thetranslog estimates, one longline vessel experiences a loss at a 50% rate of rent captureand three vessels experience a loss at a 90% rate of rent capture. Those vessels experiencing the losses are the quota-holders with the lowest ratio of sablefish profits togross revenue from sablefish. For example, the average proportion of profit to grossrevenue for the vessels incurring losses is some 33% while the average for the fleet issome 49%. Most of these vessels also have some of the lowest profits per sablefishlanded in the fleet. The correlation between vessels with low profits per quantity ofsablefish and low profits as a proportion of gross revenue is not, however, perfect. Forinstance, there are fishers with lower profits per sablefish landed than some of thevessels experiencing losses with an ad valorem royalty at a 90% rate of rent capturebut who have positive profits at the same rate of rent capture.Using the normalised quadratic estimates, a quota rental charge imposes losseson one trap vessel at a 40% rate of rent capture, on two trap vessels at 50% rentcapture, and on four trap and two longline vessels at a 90% rate of rent capture.Using the translog estimates, only at a rate of rent capture of 90% are there vesselsexperiencing losses of which four are trap vessels and five longline vessels. In the quotarental charge it is those vessels with the lowest sablefish profit per kg. of sablefishharvested that incur losses at the high rates of rent of capture. For example, usingthe normalised quadratic estimates the six vessels experiencing losses at a rate of rentcapture of 90% receive a mean sablefish profit per kg. harvested of $1.34 comparedChapter 6. Rent Capture Methods and the BC Sablefish Fishery 152to the average for the fleet of $1.94/kg.The existence of fishers with losses with a quota rental charge at less than a 100%rate of rent capture is an interesting result because such a method of rent captureshould only collect the resource rent that accrues to quota-holders. It should not,therefore, leave fishers with losses after imposition of the charge. The result arisesfrom the fact that the quota rental charge is set at a level where at a 90% rate of rentcapture much more than the expected resource rent will be collected. For example,using an interest rate of 11.83%, a quota price of $9.3/kg, and a long term planninghorizon by fishers, an estimate of the annual resource rent in the fishery is some$4.8 million. This represents some 55% and 56%, respectively, of the total predictedsablefish profits using the normalised quadratic and translog functions.Given that the assumptions used to estimate the annual resource rent in the fisheryare appropriate, it would suggest that quasi-rents in the fishery represent somewhatless than half the total sablefish profits. Imposition of a quota rental charge thatcollects more than $4.8 millIon such that the quota rental charge rate is greater thanunity will, therefore, collect some intra-marginal rent and may leave certain fisherswith losses. Using the normalised quadratic, a quota rental charge, and a rate ofrent capture such that no more than the estimated resource rent of $4.8 millionis collected from the fishery, there are just two trap vessels with predicted losses.Using the translog estimates, there is only one vessel with a predicted loss. Thisresult is interesting as it suggests that there may be fishers who face a loss with aquota rental charge that collects no more than 100% of the estimated annual valueof quota-holdings. The result may be an error in prediction in the profit functions ormay reflect the fact that there may indeed be fishers prepared to accept short-termlosses in terms of economic profits. Such fishers would, ex-post have been better off’selling or leasing their quota to another fisher and investing the proceeds elsewhere inChapter 6. Rent Capture Methods and the BC Sablefish Fishery 153the economy. For such fishers, there may be non pecuniary benefits associated withfishing, or they may simply have had lower than expected earnings from using theirsablefish quota themselves.An important issue addressed in the examination of the quota rental charge is theseparation of resource and intra-marginal rents. In earlier chapters, it was stressedthat collecting intra-marginal rents may impose certain costs in terms of efficiencythat capturing the resource rent may not. In practice, however, separating the tworents in an estimate of the profits of fishers is a difficult if not impossible task. If thereexists a competitive quota niarket where quota is freely tradeable then an estimateof the present value of the expected resource rent less any discounting because ofrisk should be reflected in the quota price. Multiplying the total quota-holdings bythe traded quota price, in turn, provides an estimate of the present value of theexpected resource rent less any discounting because of risk. To obtain an estimateof the annual expected resource rent one must impose assumptions with respect tothe discount rate used by fishers and the expected pay-back period. Using a rate ofdiscount equal to the assumed opportunity cost of capital faced by fishers, variousestimates of the expected resource rent can be obtained depending upon the pay-backperiod. Assuming a five year pay-back period, the annual expected resource rent lessany discounting because of risk is some $11 million, assuming a ten year pay-back itis some $7.2 million, and with an infinite pay-back period it is some $4.8 million.If the resource owner wishes to minimise the likelihood of capturing intra-marginalrents, therefore, it may be preferable to use lower estimates of the expected resourcerent and capture a share of such an amount and leave the remaining rents in thefishery. In such a situation, a preferred method for collecting the rent is one whichdoes not capture the intra-marginal rents. Provided there exists a competitive quotamarket, an obvious way to collect only the expected resource rent less any discounting‘hapter 6. Rent Capture Methods and the BC Sablefish Fishery 154because of risk is to use a quota rental charge. From proposition 4.1, an equivalentad valorem royalty based on the average output price for the fleet would also collectthe same amount from each fisher. In comparison, other methods of rent capture,such as a profit charge or net cash flow charge, force fishers to pay a rental in equalproportion although the share of the resource rent accruing to fishers will differ acrossthe fleet. For example, for a particular fisher if half the profits are attributable to hisor her own fishing skills then at a high rate of rent capture with a profit charge thefisher will pay all the resource rent and most of the intra-marginal rent. In contrast, afisher earning only resource rents and no intra-marginal rent will with a profit chargestill retain a share of the resource rent even at a high rate of rent capture.In a related issue, imposing rent capture requires estimates of the profits and rentsin the fishery. In the case of the sablefish fishery, two estimates of individual vesselprofits are used for examining the consequences of rent capture. In any approach toestimating the profits of fishers, however, there must exist some measurement error.If the discrepancy between the estimated profits and actual profits is sufficientlylarge, there exists the possibility of capturing more than just rent from the fishery.If avoiding the possibility of capturing more than rent from fishers is a priority, thegreater the expected error in estimating the profits of fishers then, ceteris paribus,the lower should be the intended rate of rent capture.Another concern in capturing more than rent from the fishery is the issue ofquota-trading prior to the introduction of a rent capture scheme. If a method of rentcapture is introduced subsequent to quota-trading and where there was no expectationof rent collection, the new owner will have paid the previous quota-holder an amountexceeding the expected resource rent net of rental payments. Imposing any methodof rent capture on the fishery will, therefore, result in the capture of some of theintra-marginal rents of fishers or even losses for some of the new quota-holders. InChapter 6. Rent Capture Methods and the BC Sablefish Fishery 155the short run this may reduce the total rent in the fishery as otherwise profitable andskilled fishers are forced to exit the fishery. To avoid such distortions, therefore, itis advisable to announce the type and rate of rent capture prior to quota trading.In the case of the BC sablefish fishery, much of the trading since the introduction ofITQ’s has involved the leasing of quota from one fisher to another. This is in partexplained by a restriction by the regulator not to allow any permanent transfers ofquota during a defined trial period for the management scheme [Canada Departmentof Fisheries and Oceans (1990b)]. Despite the regulation there have, however, beenfive permanent transfers of quotas which have circumvented the injunction by theoutright purchase of a sablefish licence with the attached quota. For such vesselowners, imposition of a method of rent capture in the future may prove problematic.In summary, it would seem that a lump sum charge is potentially one of the moredistorting methods of rent capture for the sablefish fishery. Iii comparison, a profitcharge does not leave fishers with losses at any rate of rent capture but is capable ofcollecting intra-marginal rents from some fishers while leaving others with a share ofthe resource rent. A quota rental charge is found to leave certain fishers with lossesat rates of rent capture more than 40% while an ad valorem royalty has this featureat rates of rent capture more than 50%. A quota rental charge also has the potentialto collect only the expected resource rent.6.4 OverviewThe examination of the different methods of rent capture in the BC sablefish fisheryillustrates some of the important results of the thesis. It is also the first empiricalexamination of different methods of rent capture in a rights based fishery. As such itprovides resource owners with a framework for comparing and evaluating methods ofChapter 6. Rent Capture Methods and the BC Sablefish Fishery 156rent capture in other fisheries.In the BC sablefish fishery, it is shown that the gear-type used by fishers has aneffect on the rental paid under the various rent capture schemes. Using the normalisedquadratic function, trap fishers collectively prefer in descending order of preferencea lump sum charge, ad valorem royalty, net cash flow charge, profit charge and aquota rental charge. In contrast, longline vessels have a reverse ordering for the rentcapture schemes. The relative preference for one rent capture scheme over another isdependent on the various characteristics of the vessels. For instance, longline vesselsare collectively shown to prefer a quota rental charge as they earn a higher profit perkg. of sablefish harvested than trap vessels. Similarly, trap vesels collectively prefera lump sum charge over a quota rental charge as the proportion of the total quotathat they own exceeds their proportion of the total number of fishers.The chapter also addresses the effects of distortions that might arise from collecting rent from the fishery. Using the number of fishers who face post-rent capturelosses as an indicator of the distortion to the short-run quota equilibrium, a lumpsum charge is shown to imposes inefficiencies on the fishery at relatively low ratesof rent capture. In particular, it imposes rental charges that are relatively moreburdensome on fishers with smaller quota-holdings, most of whom use longline gear.Another important issue that is examined is the distinction between resource rentand intra-marginal rents. Using an estimate of the expected annual resource rent lessany discounting because of risk, the relative break-down of profits into intra-marginalrent and resource rent is attempted. Provided that there exists a competitive quotamarket and price for quota, a quota rental charge may be a suitable means for tryingto capture the expected resource rent less any discounting because of risk.Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 157Table 6.1: Predicted 1990 Profits of Fishers at Different Levels of Rent Capture witha Quota Rental Charge using a Normalised Quadratic and Translog Profit Functions($)Scenario 10% 20% 30% 40% 50% 90%Norm. QuadraticTrap:Mean 39.5,090 350,920 306,740 262,570 218,390 41,695Mm 47,190 33,245 13,496 -31,638- 76,772 -257,310Max 975,170 876,060 776,950 677,840 578,730 290,190St.Dev 281,280 258,030 235,290 213,230 192,060 125,640No. with Losses 0 0 0 1 2 4Longline:Mean 126,900 113,070 99,250 85,425 71,601 16,303Mm 53,618 46,997 40,376 33,756 27,135 -7,150Max 277,480 252,100 226,730 201,350 175,980 74,478St.Dev 68,309 61,854 55,447 49,107 42,865 20,688No. with Losses 0 0 0 0 0 2TranslogTrap:Mean 392,660 349,560 306,460 263,360 220,260 47,851Mm 74,241 60,644 47,048 33,451 19,854 -151,080Max 893,010 796,310 699,610 602,900 524,270 277,250St.Dev 255,340 232,070 209,200 186,910 165,410 98,179No. with Losses 0 0 0 0 0 4Longline:Mean 116,650 103,160 89,670 76,181 62,692 8,737Mm 59,039 52,594 46,148 38,552 28,657 -10,920Max 247,940 220,150 192,360 164,580 136,790 33,523St.Dev 59,285 52,938 46,632 40,387 34,237 13,446No. with Losses 0 0 0 0 0 5Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 158Table 6.2: Predicted 1990 Profits of Fishers at Different Levels of Rent Capture witha Profit Charge using a Normalised Quadratic and Translog Profit Functions ($)Scenario 10% 20% 30% 40% 50% 90%Norm. QuadraticTrap:Mean 395,340 351,410 307,490 263,560 219,630 43,927Mm 55,004 48,892 42,781 36,669 30,558 6,112Max 966,850 859,430 752,000 644,570 537,140 107,430St.Dev 274,430 243,940 213,450 182,950 152,460 30,492No. with Losses 0 0 0 0 0 0Longline:Mean 126,650 112,580 98,507 84,434 70,632 14,072Mm 54,215 48,191 42,167 36,143 30,120 6,024Max 272,570 242,280 212,000 181,710 151,430 30,285St.Dev 67,320 59,840 52,360 44,480 37,400 7,480No. with Losses 0 0 0 0 0 0TranslogTrap:Mean 392,190 348,610 305,040 261,460 217,880 43,576Mm 79,054 70,271 61,487 52,703 43,919 8,784Max 890,740 791,770 692,800 593,830 494,860 98,972St.Dev 251,040 223,140 195,250 167,360 139,470 27,893No. with Losses 0 0 0 0 0 0Longline:Mean 117,120 104,110 91,095 78,082 65,068 13,014Mm 58,936 52,388 45,839 39,291 32,742 6,549IViax 248,150 220,580 193,010 165,440 137,860 27,573St.Dev 59,095 52,529 45,963 39,397 32,831 6,566No. with Losses 0 0 0 0 0 0Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 159Table 6.3: Predicted 1990 Profits of Fishers at Different Levels of Rent Capture witha Net Cash Flow Charge using a Normalised Quadratic and Translog Profit Functions($)Scenario 10% 20% 30% 40% 50% 90%Norm. QuadraticTrap:Mean 395,440 351,610 307,780 263,950 220,130 44,814Mm 54,525 47,934 41,343 34,752 28,161 -271Max 967,670 861,060 754,440 647,830 541,220 114,770St.Dev 274,890 244,850 214,820 184,790 154,760 34,890No. with Losses 0 0 0 0 0 1Longline:Mean 126,550 112,380 98,211 84,040 69,869 13,185Mm 54,038 47,837 41,636 35,434 29,233 4,429Max 272,780 242,710 212,630 182,560 152,490 32,195St.Dev 67,346 59,894 52,442 44,991 37,542 7,866No. with Losses 0 0 0 0 0 0TranslogTrap:Mean 392,230 348,700 305,170 261,640 218,110 43,982Mm 78,036 68,234 58,432 48,630 38,829 -1,247Max 892,100 794,490 696,687 599,260 501,650 111,119St.Dev 251,690 224,450 197,210 169,990 142,770 34,660No. with Losses 0 0 0 0 0 0Longline:Mean 117,080 104,020 90,960 77,901 68,843 12,608Mm 58,956 52,427 45,899 39,370 32,842 5,751Max 247,950 220,170 192,390 164,620 136,840 28,039St.Dev 59,128 52,594 46,062 39,531 33,001 7,006No. with Losses 0 0 0 0 0 0Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 160Table 6.4: Predicted 1990 Profits of Fishers at Different Levels of Rent Capture withan Ad Valorem royalty using a Normalised Quadratic and Translog Profit Functions($)Scenario 10% 20% 30% 40% 50% 90%Norm. QuadraticTrap:Mean 396,880 354,480 312,090 269,700 227,310 57,748Mm 51,027 40,938 30,850 20,761 5,510 -109,200Max 975,590 876,900 778,210 679,520 580,830 186,070St.Dev 278,820 252,810 226,900 201,140 175,590 79,802No. with Losses 0 0 0 0 0 3Longline:Mean 125,120 109,510 93,900 78,291 62,683 251Mm 52,907 45,575 38,243 30,910 18,907 -208,250Max 254,500 225,490 196,490 167,480 138,470 27,632St.Dev 63,462 52,835 43,441 36,254 32,759 58,516No. with Losses 0 0 0 0 0 2TranslogTrap:Mean 394,440 353,040 311,680 270,320 228,960 63,515Mm 77,995 68,151 58,308 48,464 38,621 -6,566Max 893,420 797,130 700,840 604,550 508,250 148,030St.Dev 253,240 227,570 201,960 176,410 150,960 53,068No. with Losses 0 0 0 0 0 2Longline:Mean 114,910 99,678 84,449 69,220 53,991 -6,924Mm 59,148 52,812 46,476 30,531 -24,879 -246,520Max 247,420 219,120 190,820 162,510 134,210 20,998St.Dev 55,315 46,085 38,776 34,626 34,785 66,414No. with Losses 0 0 0 0 1 1Chapter 6. Rent Capture Methods and the BC Sablefish Fishery 161Table 6.5: Predicted 1990 Profits of Fishers at Different Levels of Rent Capture witha Lump Sum Charge using a Normalised Quadratic and Translog Profit Functions($)Scenario 10% 20% 30% 40% 50% 90%Norm. QuadraticTrap:Mean 410,270 381,270 352,270 323,700 294,270 178,270Mm 32,116 3,117 -25,883 -54,882- 83,882 -199,880Max 1,045,300 1,016,300 987,280 958,280 929,280 813,290St.Dev 304,920 304,920 304,920 304,920 304,920 304,920No. with Losses 0 0 1 1 1 6Longline:Mean 111,720 82,725 53,725 24,726 - 4,274 -120,270Mm 31,239 2,240 -26,760 -55,759 -84,759 -200,760Max 273,850 244,850 215,850 186,850 157,850 41,857St.Dev 74,800 74,800 74,800 74,800 74,800 74,800No. with Losses 0 0 4 8 9 13TranslogTrap:Mean 407,470 379,170 350,880 322,580 294,290 181,111Mm 59,543 31,248 2,953 -25,342 -53,637 -166,820Max 961,420 933,130 904,830 876,540 848,240 735,060St.Dev 278,930 278,930 278,930 278,930 278,930 278,930No. with Losses 0 0 0 1 1 6Longline:Mean 101,840 73,546 45,251 16,956 - 11,339 -124,520Mm 37,190 8,895 -19,400 -47,695- 75,990 -189,170Max 247,430 219,140 190,840 162,550 134,250 21,071St.Dev 65,661 65,661 65,661 65,661 65,661 65,661No. with Losses 0 0 6 7 11 14Chapter 7Summary and ConclusionsBut the more I studied economic science, the smaller appeared theknowledge which I had of it, in proportion to the knowledge I needed; andnow, at the end of nearly half a century of almost exclusive study of it, Iam conscious of more ignorance of it than I was at the beginning of thestudy.Alfred Marshall (1842-1924), Quoted in J.M. Keynes, Essays in Biography, p 167.7.1 Summary of ContributionsThe thesis addresses an important problem in natural resource economics, the captureof rent in rights based fisheries. In addressing the problem, the thesis provides a reviewof the classical and modern views of rent and uses the general literature to providea context for definitions of various types of short run rent in a rights based fishery.In particular, the thesis separates the concept of management rent from a resourceor scarcity rent and introduces the notion of a marginal quasi-rent in a fishery. Thedesirability of capturing the various types of rent is discussed in the context of thepayment they represent to which factor of production.To examine the issues of rent capture, an original theoretical model is developed.Such a framework has general applications for examining a variety of questions inrights based fisheries. In the model, it is assumed there are two types of fishers162Chapter 7. Summary and Conclusions 163who differ only with respect to their harvesting functions and who maximise theexpected utility of economic profits. Using the model, the short-run quota equilibriumis compared to a first-best result where a resource owner is able to determine thenumber of fishers of each type, their catch, and the total harvest. Hitherto ignoreddifferences between the first-best, short run, and long run outcomes are emphasised.Using the conceptual framework the effect of uncertainty on the fishery is addressed under assumptions that fishers are risk averse. Given plausible assumptionswith respect to the cost curves of fishers, it is shown that the short-run equilibriumfor a given number of fishers without uncertainty and/or with risk neutral behaviourmaximises the expected short-run rent in the fishery. In general, uncertainty andrisk averse behaviour will reduce the expected short-run rent although a special caseis found where the equilibrium with and without uncertainty are identical. Such aresult is contrary to the accepted belief that a fixed producer price system is the onlymethod of regulation that generates a first best optimum under price uncertainty.Reducing the uncertainty faced by all fishers is shown not to decrease and in generalwill increase the expected rent although changing the risk faced by some but not allfishers may increase or decrease the rent.Applying the model to various methods of rent capture, general results are presented on the different effects of various rent capture schemes. Comparing the methods of rent capture, it is shown that if fishers face the same output price an ad valoremroyalty charged on the quota-holdings of fishers is identical to a quota rental charge.Fishers with a higher average profit per unit of quota are also shown to pay proportionately more with a profit charge than a quota rental charge in comparison tofishers with a lower average profit per unit of quota.Examining the methods of rent capture according to their effect upon the quotaequilibrium, it is shown that both a quota transfer charge and lump sum charge areChapter 7. Summary and Conclusions 164capable of changing the Pareto efficient outcome. In the case of risk averse behaviourand uncertainty with respect to the output price, it is shown that the profit charge,net cash flow charge, and ad valorem royalty are capable of changing the short-runquota equilibrium. Such methods of rent capture, by reducing the uncertainty facedby fishers, are shown to actually increase the expected rent in the fishery but at theexpense of reducing the expected utility of fishers. In comparison, a quota rentalcharge does not change the short-run quota equilibrium with or without uncertainty.The thesis also presents for the first time an empirical analysis of the effects ofrent capture in a rights based fishery. Prior to simulating the effects of rent capture,three different approaches for estimating the rent in the fishery in 1988 and 1990are provided. Using predicted profits in 1990, the year ITQ management was firstintroduced into the fishery, the different methods of rent capture are analysed. Someof the theoretical results are confirmed in that vessels of one gear-type collectivelyhave higher profits per quantity of fish harvested and correspondingly pay less with aquota rental charge than an equivalent profit charge. The simulations also show thatfishers with the highest ratio of net cash flow to profits are one of the least favouredwith respect to a net cash flow charge. An ad valorem royalty imposed on the actualoutput price received by fishers multiplied their landings is also shown to be quitedifferent in its effect than a quota rental charge. Under such a royalty, fishers witha lower than average price for their product are shown to pay less rent than with anequivalent quota rental charge.The effects of rent capture with respect to the quota equilibrium and efficiencyof fishers are also examined empirically. In the given fishery, a lump sum chargeis shown to be distortionary by favouring fishers with larger quota-holdings at theexpense of smaller but not necessarily less profitable operations. A method is alsoproposed using the traded quota price and a defined rate of interest, to separate theChapter 7. Summary and Conclusions 165intra-marginal rents and expected resource rent.7.2 Suggestions for Further ResearchThe conceptual framework of the thesis is used to present a number of importantresults. There exist, however, some useful additions to the work. In the thesis, theissue of uncertainty is examined only with respect to fluctuations in the output price.The analysis may be expanded by addressing fluctuations in the TAC, biomass, andinput prices. The theoretical model may also be extended by explicitly examining therent capture problem in a multi-species framework while retaining the assumption ofheterogeneous fishers. This would provide an opportunity to examine interactionsacross fisheries and the effects of different charge rates on different species and theoptimal output mix of fishers.Another extension to the work that may also prove useful would be to modelthe expectations of fishers explicitly. In this manner, the effects of exogenous shockson the fishery and the adjustment process may be analysed more effectively. Theadjustment process and effects of rent capture may also be assessed by examiningthe fishers’ problem with the use of stochastic dynamic programming. Such methodsmay also prove useful in explicitly modelling the investment of fishers under differentrent capture schemes and the risk attitude of fishers.In the empirical work, the predicted profits of fishers are derived without explicitreference to the uncertainty in the fishery. Incorporating estimates of fisher profitswith uncertainty, possibly in a multi-period framework, may add richness to theresults. It may also be useful to examine multi-species fisheries that are collectivelymanaged with ITQ’s. 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Bramble. 1973. “Studies of a Class ofCovariance Structures,” Journal of the American Statistical Association 68:3 17-323.Appendix APartial Derivatives of the Quota PriceTaking expression (3.17) and dividing the numerator and denominator by (ala2),where al = 2C + 2?b/31O3 and a2 = 2C + 2b34, the partial derivatives of thequota price with uncertainty and risk aversion are as follows:ap — — TAC(2)<0 (A 1)— (Xb2r+Yb2r)—— TAC( 2Yb4r7)0 A 2— (Xb2r + Yb2r)2 < (‘2 v,2 2ii2mAflI c I c2——a12 a22 0 A 3c9C — (Xb2r Yb2r“ al a2 Iap TAG9r — X?b2r Yb2r —= <OifF:>0 (A.4)aTAC = (Xb2rYb2r)<0 (A.5)174Appendix A. Partial Derivatives of the Quota Price 175apt — TAC(211b4r+ 2Y/3b4ra22 ) <0 (A.6)— 1Xb2r±Yb2r)“ al a2— >0 (A.7)aPrôP — TAc(41 4CYbr2 + a22 (A.8)91 — fXb2r±Yb2r)9al a2— TAC()al > 0 (A.9)3X — 1Xb2r± Y.b2r)al a2apt — TAC(’)a2 > 0 (A.10)—iXb2r±Ybr)al a24CeiXb2r— TAC( a12> 0 (A.11)— 1Xb2r±Ybr)al a24G2Ybr— TAC( a22> 0 (A.12)— (Xb2V+‘ al a2Appendix BDescription of the DataThe data used to estimate the two variable profit functions comes from a numberof sources. A costs and earnings survey (CES) undertaken by the Department ofFisheries and Oceans (DFO) for the year 1988 supplied information on total expenditures on fuel and labour, and total revenue from sablefish and other species. Thedata collected was obtained from 28 of the possible 46 fishers that actively fishedfor sablefish in 1988. In total, 17 out of 25 longline vessel owners and 11 out of apossible 21 trap vessel owners were interviewed. In addition, catch statistics dataincluding information on the quantity of fish landed by species and the price receivedby fishers was available for all fishers and for all years up to and including 1990.This information is collected separately by the DFO for all licensed fishing vessels inBritish Columbia. Diesel marine fuel prices were obtained from Chevron Canada bydifferent homeports of fishers for the years 1988 and 1990. Information on the registered tonnage of vessels and length of vessels was obtained from the Vancouver ShipRegistry. Information on the bank rate on prime business loans was obtained fromvarious issues of the Bank of Canada Review while data on weekly unemploymentbenefits, average weekly earnings, and unemployment rates by regions were obtainedfrom various publications available from Statistics Canada.Detailed information of the data sources and data generation used to estimate theprofit functions is listed below.176Appendix B. Description of the Data 177Sablefish Output and PriceUsing DFO catch statistics for 1988 and 1990, the total value and round weight ofsablefish landings by vessel were obtained. Using the 1988 data and for only thosevessels included in the CES, a sablefish price and output supply series was derived.For the normalised quadratic function, a price index was obtained such that the firstobservation was set equal to one. This procedure was followed for all other pricevariables. Dividing the total revenue from sablefish by this price index, an implicitquantity index was derived. To predict sablefish profits in 1990, the price of sablefishper vessel was obtained from 1990 catch statistics. In the case of the normalisedquadratic function, this price was indexed in the same fashion as for 1988 using thesame base price.Other Species Output and PriceCatch statistics from the DFO were also used to generate an aggregate price seriesand quantity variable for species caught other than sablefish. This aggregation acrossall species other than sablefish was performed for all 28 vessels in the CES. Theaggregation involved calculating a base quantity and base price over all the relevantvessels for each species. The base price being the mean price over all the sampleof vessels and the base quantity being the total catch in kg over all vessels. Usingthese base values, a Paasche and a Laspeyres price index was calculated for eachvessel. Taking a geometric average of the two indexes, a Fisher price index per vesselfor species other than sablefish was derived [Diewert (1989)]. Using the Fisher priceindex per vessel, an implicit quantity index was obtained by dividing the total revenueper vessel from species other than sablefish by the price index. A similar procedurewas followed for 1990 using the same base price and quantity values for 1988 but withAppendix B. Description of the Data 178price and quantity data for each vessel that fished in 1990.Fuel Price and Input DemandTo determine the fuel prices paid by fishers it is first necessary to know their home-ports. Using vessel and homeport information supplied directly by the DFO, eachvessel was assigned a particular location where it was assumed that purchases forprovisions and fuel took place. The homeports of the vessels included in the CES areas follows.1. Ucleulet2. Vancouver3. Steveston4. Victoria5. Sooke6. Sidney7. Gibsons/Sechelt8. Port HardyMarine diesel fuel prices for each of the homeports of fishers were obtained fromChevron Canada for each month of 1988. Vessels were then assigned the fuel priceexisting at the time they were fishing for sablefish that year. Fuel prices for 1990with the homeports of vessels that fished for sablefish in that year were also suppliedby Chevron Canada. A monthly average of the fuel price existing over that periodwas used to assign a. fuel price to each vessel. In the case of the normalised quadraticAppendix B. Description of the Data 179function, a fuel price index was derived from the price series such that the first observation was set equal to unity. A quantity of fuel per vessel was obtained by dividingthe fuel price or fuel price index assigned per vessel into the total fuel expendituresper vessel.Opportunity Wage and Labour ServicesIt is standard practice in fishing to pay the crew on a share basis. As a result wageexpenditures may be dependent on the returns and profits in the fishery. To avoid asimultaneity problem in estimation it is common practice to estimate an opportunitycost wage for a vessel.Following Dupont (1988: 218-221) the vessels used in the estimation were assigneda region according to the location of their homeports. These regions correspond toareas used by Statistics Canada and for coastal areas include:1. Metropolitan Vancouver2. Metropolitan Victoria3. Vancouver Island other than Victoria4. Lower Mainland5. Prince RupertUsing the unemployment rate for the relevant region, an industrial aggregate ofan average weekly wage in B.C, and an average weekly unemployment benefit onemay calculate an expected average weekly earnings per person per vessel (Dupont,1988: 218):EAWE = (1- U) * AWE + U * AWUIB (B.1)Appendix B. Description of the Data 180where AWE is average weekly earnings in the industrial aggregate for B.C. fromCanada Employment, Earnings and Hours, U is the regional unemployment ratefrom B.C. Labour Characteristics by Economic Region and MetropolitanArea, and AWUIB is the average weekly unemployment benefit from StatisticalReport on the Operation of the Unemployment Insurance Act, Table 6.This measure of expected average weekly earnings is the opportunity cost wagefaced by each vessel. It reflects both the alternative wage available to crew membersand the difficulty in finding alternative employment and was calculated for each vesselfor 1988 and 1990. Indexing the opportunity cost wage such that the first observationwas unity, a measure of the quantity of labour was derived by dividing the index intothe total labour expenditures per vessel including food and bait.To obtain an estimate of the total opportunity cost wage from fishing from sable-fish in 1988, data was obtained on the number of crew used in fishing for sablefishfrom the CES and the number of fishing days per vessel. Calculating the numberof weeks worked by the crew in total and multiplying by the EAWE one obtains anopportunity cost wage for the crew. Assuming one skipper per vessel and includingthe time spent on repairs and maintenance as given in the CES, an opportunity costwage for the skipper may also be determined using the same EAWE. Aggregating thetwo costs, one obtains a measure of the total opportunity cost wage per vessel fromsablefish.

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