### University of Wisconsin-Madison Department of Agricultural & Applied Economics

February 2003 Staff Paper No. 458



### Estimating Post-Harvest Benefit s from Increases in Commercial Fish Catches with Implications for Remediation of Impingement and Entrainment Losses at Power Plants

By



### Richard C. Bishop University of Wisconsin-Madison



### Matthew T. Holt North Caroline State University

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## AGRICULTURAL &

APPLIED ECONOMICS

____________________________


## STAFF PAPER SERIES

Copyright © 2003 Richard C. Bishop and Matthew T. Holt. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.Estimating Post-Harvest Benefits From Increases in Commercial Fish Catches with Implications for Remediation of Impingeme nt and Entrainment Losses at Power Plants 1

by

Richard C. Bishop and Matthew T. Holt 2



### Abstract

A variety of regulations may affect commercial fish catches. We take here as a case in point steps to reduce losses of aquatic or ganisms due to impingement and entrainment (I&E) at power plants. Methods to evaluate the benefits of such measures are needed for benefit-cost analysis. We use a new appr oach to estimating ex vessel demand by Holt and Bishop (2002) to address the portion of the benefits that occur pos t-harvest, that is, down the marketing chain after fishermen sell their catches. The model deals with the dockside prices and quantities for six major commercial species harvested from the U.S. Great Lakes. We use the model to expl ore the potential magnit ude of post-harvest benefits for Great Lakes fisheries. We then turn to a possible a pproach to benefits transfer for cases where such a model is not available. A semi-realistic case example involving I&E losses to Great La kes fisheries illustrates how benefits transfer would work.



### Introduction

When fish catches increase as a result of regulations, benefits may accrue through the production and marketing chain that begins with those who supply inputs to fishermen and ends with final consumers. This paper is concerned with met hods of measuring the post-harvest welfare effects that may accrue to fi sh wholesalers, retailers, and final consumers. Using a model of ex vessel fishing demand by Holt a nd Bishop (2002), we explore potential methods of estimating thes e effects for Great Lakes fish and draw implications for benefits transfer.

The analysis is motivated in part by a real world policy issue. Changes in cooling water intake structures and other steps at power plants can reduce impingement and entrainment of aquatic organisms (hereafter referred to I& E losses) at power plan ts, but at a cost. Reducing I&E losses could have many benefits, including the benefits associated with increased commercial fish harvests.

1 Research supported by the Wisconsin Sea Grant Institute, the Wisconsin and North Carolina Experiment Stations, and the U.S. Environmental Protection Agency. Thanks are due to Tom Ottem, Robert Raucher, and Lynn Tudor for many helpful comments on earlier drafts. All errors remain the responsibility of the authors.

2 Authors are, respectively, Professo r and Chair, Department of Agricultural and Applied Economic, at the University of Wisconsin-Madison, and Professor, Agricultural and Resource Economics, North Carolina State University.At the outs e t, we will exa m ine post-harvest b e nef its in a sim p le concep tua l m odel that will help us account for a full se t of commercial use benefits and provide a contex t for the rest of the p a per. Then we will tu rn our attention to possib l e em pirical methods for estim ating p o st-harvest benefits us in g the Ho lt-Bishop m odel. This will d e m onstrate how the m odel could be used to estim a te post-harv est benefits fro m increases in Great Lak e s catches. Obviously the fish harvesters them se lves and those w ho supply them with inputs

m a y also benef it, but we will not d e lve into em pirica l proc ed ures f o r eva l uating ben e f its to f i sherm e n and their su pplie rs her e

. The paper will conc lud e by laying out an appro ach to benef its tr ansf er, with an application to the Great Lakes.



### The Conceptual M o del Figure 1 is a sim p le supply and dem a nd m odel that will illustrate how an increase in supply, say as a result of reduced I&E, would translate into benefits. It follows the

F 2 P(F) T

V

W Y

Z

F F 1 $

U X P 1

P 2

C

Figure 1: Conceptual Model of Benef its from an Increas e in Fish Catch

convention of m odeling fish dem a nd as an i nverse dem a nd system , where the price, P, is a function, P ( F), and F is the output of fish to this m a rket. W e take this to be the dockside or ex-vessel dem a nd. An inverse dem a nd function is used becau se fish are perishable and m u st be m a rketed soon after th ey are caught. Hence, price is driven by quantity rather than vice vers a in the short run. F o r sim p licity, we assum e that this fishery is m a naged on a quota basi s where the current quota is F 1 so that the ex-vess e l price is P 1 . Assum i ng a quota m a kes the story s imple. Roughly the sam e principles apply under other m a nagem e nt regimes, such as closed seasons and gear restrictions, since the goal is usually the sam e , that is to lim it tota l catch. Average cos t is equ a l to

m a rginal cost at C, again by assum p tion. A m o r e com p licated m odel could have an upward sloping m a rginal cost function.

Consider P(F) for a m o m e nt. This is not th e dem a nd for a finished product, but for an interm ediate good, fish that have just been ha rvested. W h at does it tell us about social

2welfare? Let us assum e that the m a rkets dow n the m a rketing chain from fish harvesters to final cons um ers are co mpetitiv e an d adjust qu ickly to chang e s in docks ide supply an d that none of the dem a nd functions at success i ve s t ages is perf ectly elas tic. This will allow us to e xpect th at P( F) will r e f l e c ts th e dock s ide pr ices that would pr evail af ter a l l the downstream m a rkets have adjusted. He nce, P(F) is not a Marshallian dem a nd function, since all othe r prices down the processing and m a rketing chain and across the

com p li m e nts and substitutes for the f i sh specie s in question w ould not be held constant if the supply o f that fish sp ecies would change . Rather P(F) is a “general eq uilib rium dem a nd function” (Just, Hueth, and Sc hm itz, 1982; Thurm a n and Easley, 1992) expressing the prices of F that would prevai l after m a rkets in the rest of the econom y have adjusted to changes in F. As the de rived dem a nd for F, it represents the m a xi m u m

m a rginal willingness to pay for F by processors , m a rketers, and final consum ers. To the extent that firm s down the m a rketing chain wi ll earn rents at the m a rgin and consum ers will ea rn co nsum er surplus at the m a rgin as F ch anges, the i r m a rginal values would be reflected in P(F). And the definition of the so-ca lled welf ar e triangles under P(F) is a bit broader than is usual in textbook examples, which deal with f i nal dem a nd. Here, the welfare triangle includes not only consum er surplus but also p o st-harvest rents. 3

So let’s cons ider the welf ar e im plications of catching F 1 of fish. Total benefits from this fishery at F 1 are given by Area T+U+V+ W

. Fish ha rvesters earn total revenue equal to U+V+ W

. W is the total input costs, leaving re nts to fish harvesters of Area U+V. Area T represents consum er surplus a nd post-harvest rents to firm s down the m a r k eting chain.

As we noted at the ou tse t , we will not deal em pirically with c o sts or rents to f i sh harvesters. Neverthe les s , we will want to ke ep track of them conceptua l ly in accoun ting for benefits. It is well know n that theory predicts zero re nts to fishery resources under
open acces s. However, there cou l d still b e ren t s in the fisheryfor two reas ons. One is that if the quota of F 1 is allocated to fishing firm s as individual quotas, then the fishery would no longer be operating under open access. 4 Second, even if rents to the resour c e are zero, there could still be rents to other resou r ces such as s carce fish in g skills. Th us, we will allo w positive rents to b e a po ssibility in accountin g for benefits.

Now suppose that the quot a is increased to F 2 . F o r exam ple, rem e dial steps that reduce fish losses d u e to I&E might in crease the ha rvestable surplus of fish. Let us do the benefit-cost analysis in thr ee steps that are set up to help avoid confusion later on.

•

• In step 1, we assess the net benefits for consum ers and downstream fir m s. W ith an increase in quantity from F 1 to F 2 and a declin e in price from P 1 to P 2

, consum ers and downstream producers gain U + X. In step 2, let’s assess the net benefits to harvesters. Their tota l revenu e is now Area V+ W + Y+Z. Hence the change in total revenue is Area Y + Z – U, which

3 As is well k nown, th e wel f are triang les associatedw ith P(F) are not “e xact ” we lfa r e m easures beca use of
p o s sib l e in co me effects. We d o no t b o t h e r to ad dress th at i ssu e exp licitly h e re, b u t t

h e em p i rical resu lts
prese n t e d bel o w do i n vol ve e s t i m a t e s of “ex act ” m easures of wel f a r e. 4 Or th e quo ta co u l d b e en fo rced b y at tax of t p e r un it caugh t wh ere t = P 1 – C

, wi t h t h e r e nt s goi ng t o t h e tax i n g en tity.

3could be pos itiv e or nega tive. Costs increas e by Area Z. Hence, the ch a nge in rents associated with fish harvesting is Y –U, whi c h again could be positive or negative. Consum er surplus and downstream rents becom e Area T+U+X. In step 3, we calculate the increase in net social benef its when the quota increases fro m F 1 to F 2 by adding the results of steps 1 and 2, which leaves Area X+Y. Area U does not resu lt in an increase in total benefits becaus e it is m e rely a transfer from harvesters to downstream fir m s and consum ers and cancels out. •

This fram ework helps co nceptualize what we want to do in the rest of this paper. In the next section, we will exp l ore what S t ep 1 m i ght look like for an actual benefit-cos t analys is using the Holt-Bishop m o del of Great Lakes dem a nd. Our estim a tes will be the conceptual equivalent of Area U + X in this sim p le m odel. Steps 2 and 3 of the process suggested in the preceding paragrap h would re q u ire data on fishing costs

, which will not be addressed here.

Next, we will cons ider an approach to benefits transfer that is suggested b y the sim p le model. It may not be feasible to do anem pirical dem a nd model for each case where changes in I&E losses due to new regulations need to be evaluated or other steps are taken that increase supply. If one wanted to try to use the results of an actual em pirical study in one region of the count ry to get a rough estim ate of what downstream rents plus

consum er surplus would be for fisheries in another region where no em pirical analysis exists, how m i ght one proceed ? One approach w ould be to s t art with total revenues of fish harvesters. Since m o st significant comm er cial fisheries are regu lated, there are often data availab l e to es tim ate the ex-v ess e l valu e of catches.

Suppose for the tim e being that Figure 1 repr esents the situation fo r the Great Lakes as reflected in an actual empirical study. W e know tota l revenue at baseline, which is equal to Area U+ V+W

. We can use the empirical m o del to p r edict price and the associated incre a se in p o st-ha r vest benef its th at will r e sult f r om an increase in c a tch. For exam ple, we already saw in Figure 1 how an increase in catch to F 2 would result in a price of P 2 and an associated increas e in post-ha rvest benefits of Area U+X. Let K 2 equal the ratio of this increase in downstream rents plus consumer surplus to to tal revenues of the fishery, where 2 is a superscript, not an exponent. That is, K 2 = (Area U + X)/(Area U + V + W ) . (The superscript 2 signifies that this is the valu e of the ra tio K a ssocia t ed with an increase in catch to F 2 .)

Now let’s carry the approach a step farthe r in the following way. Let us think of F 1 , the current catch as a parameter, the baseline. Define the change in catch as a proportion, L 2 = (F 2

– F 1 )/F 1 . W e could do this for other values of F, say F 3 , F 4 , and so on. Likewise, we can calculate L 3 = (F 3 – F 1 )/F 1 , L 4 = (F 4 – F 1 )/ F 1 , and so on. And associated with each L would be a K, K 2 , K 3 , K4 , and so on, expressing the change in post-harvest benefits associate with each F, ex pressed as a pr oportion o f baseline to tal revenue. Using our

em pirical model in Figu re 1, we cou l d c onsid er alternative values of F and each associa t ed v a lue of L and K until we had tra ced out a f unctio n, K = K(L). Each value of L, the proportional increase in catch, would be associated with a proportional increase in

4benefits. This function w ould be empirically based on the Great Lakes fishery as depicted in Figure 1.

Now consider a fishery in another area, perhap s a coastal f i s h ery. Bef o re the in terv e n tion in question, the other fis h ery has to tal revenu es, which we will sym bolize as R, the ex vessel value of the catch ther e. Sym bolize the catch in this new fishery as G, and suppose the intervention (e.g., I&E rem e diation) will lead to an increase in the quota there from G 1 to G 2 . Let Q = (G 2 – G 1 )/G 1 . The benefits transfer approach we propose would calculate K = K(Q), where K(.) is still b a sed em pirica lly on the Great Lakes situation in Figure 1. T h en one would estim a te the resulting incre a se in p o st-ha r vest rents plus consum er surplus for the costal fish as K(Q)*R.

The next step is to examine the Holt-Bis hop m o del and consider possible m a gnitudes of downstream rents and consum er surplus from som e hypothesized changes in Great L a kes catche s . This will a llow us to explo r e the m a gnitudes of K(L) f o r typic a l Great Lakes species and eventually to consider the effi cacy of our proposed approach to benefits transfer.



### Valuing Increases is Catch Using the Holt-Bishop Model

There have been num erous efforts over the y ears to estim a te the dem a nd for fish. W e llknown examples from t h e published literatur e include Barten a nd Bettendorf (1989), Thurm a n and Easley (19 92), Eales, Durh am , and W e ssells (1997), and Beach and Holt (2001). Our paper (Holt and Bishop, 2002) wa s our attem p t to im prove the m e thods available by adapting the work of Diewer t and W a les (1988a, 1988b) to inverse dem a nd system s.

The Holt-Bishop m odel is a “sem iflexible norm alized quadratic inverse dem a nd system.” It is flexib l e in the s e nse that, within lim its, it allo ws the estimated dem a nd f unctions to be shaped to bette r f it th e data, bu t it is semi flexible in that it im poses enough structure to

m eet the curvature conditions of m i croeconom ic theory, a desirable property in a m odel to be used in welfare analysis. Our dem a nd system is quadratic to allow for non-linear dem a nd functions if the da ta ca ll f o r them . An inverse dem a nd system is used to capture the fact that, for highly perishable fish products, prices are endogenously determ ined based on landings. It is a dem a nd system in that six dem a nd functions for different fish species were estim ated simultaneously. The demand system is normalized to address technical issues that are be yond the scope of this paper.

The m odel was estim ated for six types of fish landed at Great Lakes ports in the U.S. These included lake whitefish, lake trout, ye llow perch, lake herring, chubs, and sm elt. Though m a ny other fish are caught from the Grea t Lakes, these six account for a large share of the catch in term s of value. For exam ple, in 1999, the last year for which data have been published, these six species account ed for m o re the 92 percent of the Great Lakes comm ercial catch in dollars. Other spec ie s typic a lly h a ve lo w prices and/or are caught in smaller quantities.

5We started with m onthly data for the pe riod 1971 through 1991. Monthly catches and prices were com b ined into bim onthly values to avoid the problem of very sm all catches in som e m o nths. A summ ary of the data can be found in Holt and Bishop (2002, Table 1). The am ount of variation in the data was suf f i cient to allow us to f e rre t out the dem a nd relationships across the six types of fis h. And it turned out that our m odel fi t the data quite w e ll and outperform ed the popul ar Almost Ideal De m a nd Sys t em across

severa l cr ite ria when th e latter was f i tted to the s a m e data set.

For purposes of this paper, we applied the m odel as estim ated in Holt and Bishop (2002) to estim a te the post-ha rv est welf are implicati on of increases in two of the Great Lakes most im portant species, lake whitefish and yellow perch, with the results displayed in Tables 1 and 2 respectively. Figures in the table are for average conditions between 1971 and the end of 1991. In both tables, com p ensa ting variation (post-harvest benefits) w a s estim ated for 1 percent, 5 percent, and 10 perc ent increases in catch. These percentages, as expressed in the first colum n of the tables, are the analogue of the proportional increases in catches, L, in the concep tual m odel discussed in the preced in g section. For

exam ple, in Table 1, we estim ated th at at L = 5 p e rcen t for whitefish, pos t-harv est

com p ensating variation would increase by $292,000 after rounding. Likewise, in Table 2, at L = 10 percent for yellow perch, pos t-harvest welfare wo uld increase by about $265,000.

Table 1: Post-Harvest Com p ensating Variati on from Increases in Great L a kes W h itefish Catches.

Catc h Inc r ease ( L ) V a l u e Comp en satin g Variation

(CV) CV/Value (K) 1% $ 5,657,20 6 $ 58,342 1.0% 5% $ 5,657,20 6 $ 291,539 5.2% 10% $ 5,657,20 6 $ 582,654 10.3%

Table 2: Post-Harvest Com p ensating Variat ion from Increases in Great L a kes Yellow Perch Catches.

Catc h Inc r ease (L) Value Comp en satin g Variation

(CV) CV/Value (K) 1% $ 3,025,07 0 $ 26,524 0.9% 5% $ 3,025,07 0 $ 132,493 4.4% 10% $ 3,025,07 0 $ 264,667 8.7%

The right-hand percent colum n s in the two tables show com p ensating variation as a percentage of the dockside value of the catch before the hypothetical increases occurred. These figures are the analogue of K for the sim p le m odel. That is, for example, if L = 10 percent for yellow perch, K = 8.7 percent.

6For both whitefish and perch, the relationship K( L) is very close to being linear and is slightly steeper for whitefish. The slope fo r whitef i sh is app r oxim a tely u n ity, while the slope for perch is approxim ately 0.9.

The estim ates of K for lake whitefish and ye llow perch are more or less typical of the Great Lakes commercial species included in the model. For exam ple, under average conditions, for a 10 percent reduction in catch as considered in Table 8 of Holt and Bishop (2002), K ranged from about 8 percen t for sm elt to 12.12 percent for chubs for a weighted average of 10.03 per cent. Hence, for the Great Lakes, we propose that K = K(L) can be approxim a ted by K = L for relatively sm all changes in catches. That is, at leas t for the Great Lakes species included in the Holt-Bishop m odel, the change in postharvest ren t s and consumer welfare as a percen tage of ex vessel value is estim ated to be, on average, approxim a tely equal to the percen tag e change in catch.

Now, if K = L holds to a reasonable appr oxim a tion for the m a jor Great Lakes species, would such a relationship be suitable for bene f its transf er to othe r species and regions? Adm ittedly, this is a purely pragm a tic appro ach. Beyond saying that as sim ilar products, fish products m i ght have sim ilar demand stru ctures, there is no theoretical reason to suppose that post-harvest changes in welfare, as a percentage of dockside value, should be sim ilar across fisheries. The consistency acros s Great Lakes species is encourag ing in this regard, but it is hardly conclusive. But there is encouraging evidence about the robustness of this relationship. Beach and Holt (2001) estimated a m odel very sim ilar to Holt and Bishop (2002) for nine types of fish in the South Atlantic region. The weighted
average v a lu e of K for a 10 percen t reduction in catch was very close to 1 0 percen t, which would further support the case for K = L. At this point, the only other study that we have found that would provide a point of co mparison involved red drum in the Gulf of Mexico, where Thurm a n and Easley (1992, p. 236) estim a ted that post-harvest welfare would by 6 percent for a 10 percent reduction in catch. This would indic a te th at K = L

m i ght not be as robust across fisheries as we would like, but more research is needed before m u ch m o re can be said.



### Implications for Benefits from I&E Remediation For any of the species covered in the Ho lt-Bish op m odel, es tim a tion of post-harvest benefits would be relatively straightforw ard. Beyond running the m odel and reviewing the results for changes in circum stances sinc e 1991 (when the data set ended), only m i nor steps like allowing for inflation and discounting would be needed.

On the other hand, if the analysis needed to address a species or an area not covered by the m odel and origin al r e sear ch is n o t f easible , benefits transfer w ould be necessary. W e can illustrate how this would wo rk using a Great Lakes example.

U.S. EPA’s estim ates of I&E loss es at th e Monroe and J.R. Whiting power plants on Lake Erie are presented in Table 3. Th ese estimates were developed for the 2002 Proposed Section 316(b) Phase II Existing Facilities Rule. EP A developed these estim ates us ing I&E data collected b y the M onroe and J.R. Whiting power plants in the

71970s and extrapolated the estim a tes of I&E at all in-scope facil ities based on average daily f l ow at all Gre a t La kes f acilities af f ect ed by the ru le. EPA will be re vising th e se t of f acilities d e f i ned to be in the Grea t Lakes reg i on and the es tim a ted I&E impacts in th e analys is f o r the f i nal Pha s e II rule. T hus, these re sults a r e use d f

o r illus t ra tive pu rpose s only. Full details on the m e thods used to estim a te I&E im pacts are provided in the Case Study Docum e nt for the proposed rule (U.S. EPA, 2002).

Table 3: Es tim a ted Comm ercial Harvest Lost from I m pingem e nt and Entrainm ent in the Great Lakes Under Conditions Assum e d inthe EPA Analysis (pounds per year)

Species Estimated I & E Losses a t J.R. Whiting and Monro e Estimated I & E Losses a t all Grea t Lake s In-Scope Facilities B u l l h e a d 5 2 2 0 6 Cha nnel catfish 767 1,518 Comm on carp 239,47 8 949,18 0 Gizzard sh ad 2,555,85 4 10,130,2 18 Sucker spp. 1,233 4,887 White ba ss 115,82 7 229,54 4 B u r b o t 2 0 6 4 0 8 Fre s h w ater d r um 19,148 75,894 S m e l t 8 1 0 1

, 6 0 5 W h i t e f i s h 7 3 1 4 3

Two species that were in cluded in th e Holt-Bi shop analysis appear on th is list, white f ish and sm elt. However, the quantities of both species are too s m all to affect the p r ices much, if at all, so the Holt-Bishop m odel is no t directly applicable to this problem . The other species in the list are not included in the Holt-Bishop m odel and, hence, would need to be valued using benefits tr ansfer. If the figures in Ta ble 3 were final estim ates, how

m i ght benefits transfer work?

Carp, gizzard shad, suckers, and freshwater drum are relatively abunda nt species that are variously ref e rred to as rough fish or underu tilized species. T h eir production is m u ch more lim ited by m a rkets than by bi ological abundance. This is reflected in their dockside values, which averaged $0.09, $0.04, $0.07, $0.11 per pound, respectively, over 1995-99 (com pared to $2.43 for yellow perch and $0.75 for whitefish). The upshot is that increased abundance due to lower I&E losses wo uld not be likely to increase catches much if at all. Hence, th ere would b e few if any direct benefits to comm e r cial fishing from lowering I&E loss es of these s p ecies. 5 Furtherm ore, a few hundred dollars worth of channel catfish (dockside va lue of $745 based on averag e 1995-99 prices) and burbot ($127) can safely be ignored. 6

5 It is co n cei v a ble th at co mm er cial fish ing cou l d b e po sitiv ely o r n e g a tiv ely affected throu g h eco s ystem effects. If s u c h im pacts were identifie d, t h e m e thods proposed here could be a pplied.

6 Prices h e re come fro m th e Natio n a l Mari n e Fish eries Serv i ce web site, h ttp ://www.st.n m fs.g ov /st1 /co mme rcial/lan d ing s /g l

_ qu ery

. h t m l

8That leav es white bass as the focal p o int for th e analysis. Let us a ssum e that conditions in Great Lakes are currently sim ilar to those in the 1970s (when the studies used by EPA to estim a te losses were d one) and will continue to be so for th e foreseeab le future. Th us

we assum e t h at average annual catch e s ar e about 1.7 m illion pounds withan ex vessel value of about $500,000. These are the actual averages over the period beginning in 1971 and ending in 1979. If we assum e that re mediation is totally e ffective, this would

m ean an increase in annual catches of 230,000 pounds (Table 3) or about 14 percent. Applying the result from the Holt-Bishop m odel, that is, K = L, the estimated postharvest benefits would be 14 percent of ex vessel revenue or about $70,000 per year before adjusting for inflation.



### Conclusions For species and regions covere d by empirical research like that found in Holt and Bishop (2002), post harvest changes in rents and cons umer welfare from changes in catch can be addressed directly and should not be problem atical. W h ere such research results are n o t available an d cannot be produced in a tim ely m a nne r, the on ly recours e will b e to ben e fits transfer. As sum i ng that K = L in such cases seem s to us to be a reasonable approach for now. The robustness of this form ula across Great Lakes and South Atlantic fisheries provides an adequate basis for proceeding in this way. As more res earch becom e s available, th e for m ula may need to b e m odifi ed or a new approach m a y present itself, but that is always the case with benefits transfer m e thods.



### Literature Cited Beach, R.H., and M.T. Holt. 2001. “Incorpo rating Quadratic Scale Curves in Inverse Dem a nd System s.” Ame r ican Journal of Agricultural Economics 83(February): 230-45.

Barten, A.P., and L.J. Bettendorf. 1989. “Price F o rm ation of Fish: An Application of an Inverse Dem a nd System.” Europiean Economic Review. 33(October): 1509-25.

Diewert, W

. E., and T. J. Wales. 1988a. “A No r m alized Sem i flexible Functional Form .” Journal of Ec onometrics 37(March): 327-42.

__________. 1988b. “Norm a lized Quadratic System s of Consum er De m a nd Functions.” Journal of B u siness and Economic Statistics 6(July): 303-12.

Eales, J.S., C. Durha m , and C.R. Wessels. 1997. “Generalized Models of Japanese De m a nd for Fish.” American Journal of Agricultural Economics 79(November): 1006- 17.

Holt, M.T., and R.C. Bishop. 2002. “A Se m i flexible Norm alized Quadratic Inverse De m a nd Sys t em : An Application to the Price Form ation of Fi sh.” Empirical Economics 27:23-47

Just, R.E., D.L. Hueth, and A. Schm i t z. 1982. Applied Welfare Economics and Public Policy. Englewood Cliffs, NJ: Prentice Hall, Inc.

910 Thurman, W.N., and J.E. Easley, Jr. 1992. “Valuing Changes in Commercial Fishery Harvests: A general Equilibrium Derived Demand Analysis.” Journal of Environmental Economics and Management 22(May):226-40

U.S. EPA. 2002. Case Study Analysis for the Propos ed Section 316(b) Phase II Existing Facilities Rule. Office of Water. February 2002. EPA-821-R-02-002. http://www.epa.gov/waterscience/316b/casestudy/

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