University of Wisconsin-Madison 

Department of Agricultural & Applied Economics

 February 2003 Staff Paper No. 458 

 Estimating Post-Harvest Benefits 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 

__________________________________ 

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 Impingement and Entrainment Losses at Power Plants1

by 

Richard C. Bishop and Matthew T. Holt2

Abstract 

A variety of regulations may affect commercial fish catches. We take here as a case in 

point steps to reduce losses of aquatic organisms 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 approach to estimating ex vessel demand by Holt 

and Bishop (2002) to address the portion of the benefits that occur post-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 explore the potential magnitude of post-harvest 

benefits for Great Lakes fisheries. We then turn to a possible approach to benefits 

transfer for cases where such a model is not available. A semi-realistic case example 

involving I&E losses to Great Lakes 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 methods of measuring the 

post-harvest welfare effects that may accrue to fish wholesalers, retailers, and final 

consumers. Using a model of ex vessel fishing demand by Holt and Bishop (2002), we 

explore potential methods of estimating these 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 plants, 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, Professor 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 outset, we will examine post-harvest benefits in a simple conceptual model that 

will help us account for a full set of commercial use benefits and provide a context for the 

rest of the paper. Then we will turn our attention to possible empirical methods for 

estimating post-harvest benefits using the Holt-Bishop model. This will demonstrate how 

the model could be used to estimate post-harvest benefits from increases in Great Lakes 

catches. Obviously the fish harvesters themselves and those who supply them with inputs 

may also benefit, but we will not delve into empirical procedures for evaluating benefits 

to fishermen and their suppliers here. The paper will conclude by laying out an approach 

to benefits transfer, with an application to the Great Lakes. 

The Conceptual Model 

Figure 1 is a simple supply and demand model that will illustrate how an increase in 

supply, say as a result of reduced I&E, would translate into benefits. It follows the 

F2

P(F) 

T

V

W

Y

Z

F F 1

$ 

U X

P1

P2

C 

Figure 1: Conceptual Model of Benefits from an Increase in Fish Catch 

convention of modeling fish demand as an inverse demand system, where the price, P, is 

a function, P(F), and F is the output of fish to this market. We take this to be the 

dockside or ex-vessel demand. An inverse demand function is used because fish are 

perishable and must be marketed soon after they are caught. Hence, price is driven by 

quantity rather than vice versa in the short run. For simplicity, we assume that this 

fishery is managed on a quota basis where the current quota is F1

 so that the ex-vessel 

price is P1

. Assuming a quota makes the story simple. Roughly the same principles 

apply under other management regimes, such as closed seasons and gear restrictions, 

since the goal is usually the same, that is to limit total catch. Average cost is equal to 

marginal cost at C, again by assumption. A more complicated model could have an 

upward sloping marginal cost function. 

Consider P(F) for a moment. This is not the demand for a finished product, but for an 

intermediate good, fish that have just been harvested. What does it tell us about social 

2
welfare? Let us assume that the markets down the marketing chain from fish harvesters 

to final consumers are competitive and adjust quickly to changes in dockside supply and 

that none of the demand functions at successive stages is perfectly elastic. This will 

allow us to expect that P(F) will reflects the dockside prices that would prevail after all 

the downstream markets have adjusted. Hence, P(F) is not a Marshallian demand 

function, since all other prices down the processing and marketing chain and across the 

compliments and substitutes for the fish species in question would not be held constant if 

the supply of that fish species would change. Rather P(F) is a “general equilibrium

demand function” (Just, Hueth, and Schmitz, 1982; Thurman and Easley, 1992) 

expressing the prices of F that would prevail after markets in the rest of the economy 

have adjusted to changes in F. As the derived demand for F, it represents the maximum 

marginal willingness to pay for F by processors, marketers, and final consumers. To the 

extent that firms down the marketing chain will earn rents at the margin and consumers 

will earn consumer surplus at the margin as F changes, their marginal values would be 

reflected in P(F). And the definition of the so-called welfare triangles under P(F) is a bit 

broader than is usual in textbook examples, which deal with final demand. Here, the 

welfare triangle includes not only consumer surplus but also post-harvest rents.3

So let’s consider the welfare implications of catching F1

 of fish. Total benefits from this 

fishery at F1

 are given by Area T+U+V+W. Fish harvesters earn total revenue equal to 

U+V+W. W is the total input costs, leaving rents to fish harvesters of Area U+V. Area T 

represents consumer surplus and post-harvest rents to firms down the marketing chain. 

As we noted at the outset, we will not deal empirically with costs or rents to fish 

harvesters. Nevertheless, we will want to keep track of them conceptually in accounting 

for benefits. It is well known that theory predicts zero rents to fishery resources under 

open access. However, there could still be rents in the fishery for two reasons. One is 

that if the quota of F1

 is allocated to fishing firms as individual quotas, then the fishery 

would no longer be operating under open access.4

 Second, even if rents to the resource

are zero, there could still be rents to other resources such as scarce fishing skills. Thus, 

we will allow positive rents to be a possibility in accounting for benefits. 

Now suppose that the quota is increased to F2

. For example, remedial steps that reduce 

fish losses due to I&E might increase the harvestable surplus of fish. Let us do the 

benefit-cost analysis in three steps that are set up to help avoid confusion later on. 

•

•

 

In step 1, we assess the net benefits for consumers and downstream firms. With 

an increase in quantity from F1

 to F2 and a decline in price from P1 to P2, 

consumers and downstream producers gain U + X. 

In step 2, let’s assess the net benefits to harvesters. Their total revenue is now 

Area V+W+Y+Z. Hence the change in total revenue is Area Y + Z – U, which 

3

 As is well known, the welfare triangles associated with P(F) are not “exact” welfare measures because of 

possible income effects. We do not bother to address that issue explicitly here, but the empirical results 

presented below do involve estimates of “exact” measures of welfare. 4

 Or the quota could be enforced by at tax of t per unit caught where t = P1 – C, with the rents going to the 

taxing entity. 

3
could be positive or negative. Costs increase by Area Z. Hence, the change in 

rents associated with fish harvesting is Y –U, which again could be positive or 

negative. Consumer surplus and downstream rents become Area T+U+X. 

In step 3, we calculate the increase in net social benefits when the quota increases 

from F1

 to F2 by adding the results of steps 1 and 2, which leaves Area X+Y. 

Area U does not result in an increase in total benefits because it is merely a 

transfer from harvesters to downstream firms and consumers and cancels out. 

•

This framework helps conceptualize what we want to do in the rest of this paper. In the 

next section, we will explore what Step 1 might look like for an actual benefit-cost

analysis using the Holt-Bishop model of Great Lakes demand. Our estimates will be the 

conceptual equivalent of Area U + X in this simple model. Steps 2 and 3 of the process 

suggested in the preceding paragraph would require data on fishing costs, which will not 

be addressed here. 

Next, we will consider an approach to benefits transfer that is suggested by the simple 

model. It may not be feasible to do an empirical demand 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 empirical 

study in one region of the country to get a rough estimate of what downstream rents plus 

consumer surplus would be for fisheries in another region where no empirical analysis 

exists, how might one proceed? One approach would be to start with total revenues of

fish harvesters. Since most significant commercial fisheries are regulated, there are often 

data available to estimate the ex-vessel value of catches. 

Suppose for the time being that Figure 1 represents the situation for the Great Lakes as 

reflected in an actual empirical study. We know total revenue at baseline, which is equal 

to Area U+V+W. We can use the empirical model to predict price and the associated 

increase in post-harvest benefits that will result from an increase in catch. For example, 

we already saw in Figure 1 how an increase in catch to F2

 would result in a price of P2

and an associated increase in post-harvest benefits of Area U+X. Let K2 equal the ratio 

of this increase in downstream rents plus consumer surplus to total revenues of the 

fishery, where 2 is a superscript, not an exponent. That is, K2

 = (Area U + X)/(Area U + 

V + W). (The superscript 2 signifies that this is the value of the ratio K associated with 

an increase in catch to F2

.) 

Now let’s carry the approach a step farther in the following way. Let us think of F1

, the 

current catch as a parameter, the baseline. Define the change in catch as a proportion, L2

= (F2

 – F1)/F1. We could do this for other values of F, say F3, F4, and so on. Likewise, 

we can calculate L3

 = (F3 – F1)/F1, L4 = (F4 – F1)/F1, and so on. And associated with each 

L would be a K, K2, K3, K4, and so on, expressing the change in post-harvest benefits 

associate with each F, expressed as a proportion of baseline total revenue. Using our 

empirical model in Figure 1, we could consider alternative values of F and each 

associated value of L and K until we had traced out a function, K = K(L). Each value of

L, the proportional increase in catch, would be associated with a proportional increase in 

4
benefits. This function would be empirically based on the Great Lakes fishery as 

depicted in Figure 1. 

Now consider a fishery in another area, perhaps a coastal fishery. Before the intervention 

in question, the other fishery has total revenues, which we will symbolize as R, the ex

vessel value of the catch there. Symbolize the catch in this new fishery as G, and 

suppose the intervention (e.g., I&E remediation) will lead to an increase in the quota 

there from G1

 to G2. Let Q = (G2 – G1)/G1. The benefits transfer approach we propose 

would calculate K = K(Q), where K(.) is still based empirically on the Great Lakes 

situation in Figure 1. Then one would estimate the resulting increase in post-harvest 

rents plus consumer surplus for the costal fish as K(Q)*R. 

The next step is to examine the Holt-Bishop model and consider possible magnitudes of 

downstream rents and consumer surplus from some hypothesized changes in Great Lakes 

catches. This will allow us to explore the magnitudes of K(L) for typical Great Lakes 

species and eventually to consider the efficacy of our proposed approach to benefits 

transfer. 

Valuing Increases is Catch Using the Holt-Bishop Model 

There have been numerous efforts over the years to estimate the demand for fish. Wellknown examples from the published literature include Barten and Bettendorf (1989), 

Thurman and Easley (1992), Eales, Durham, and Wessells (1997), and Beach and Holt 

(2001). Our paper (Holt and Bishop, 2002) was our attempt to improve the methods 

available by adapting the work of Diewert and Wales (1988a, 1988b) to inverse demand 

systems. 

The Holt-Bishop model is a “semiflexible normalized quadratic inverse demand system.” 

It is flexible in the sense that, within limits, it allows the estimated demand functions to

be shaped to better fit the data, but it is semiflexible in that it imposes enough structure to 

meet the curvature conditions of microeconomic theory, a desirable property in a model 

to be used in welfare analysis. Our demand system is quadratic to allow for non-linear 

demand functions if the data call for them. An inverse demand system is used to capture 

the fact that, for highly perishable fish products, prices are endogenously determined 

based on landings. It is a demand system in that six demand functions for different fish 

species were estimated simultaneously. The demand system is normalized to address 

technical issues that are beyond the scope of this paper. 

The model was estimated for six types of fish landed at Great Lakes ports in the U.S. 

These included lake whitefish, lake trout, yellow perch, lake herring, chubs, and smelt. 

Though many other fish are caught from the Great Lakes, these six account for a large 

share of the catch in terms of value. For example, in 1999, the last year for which data 

have been published, these six species accounted for more the 92 percent of the Great 

Lakes commercial catch in dollars. Other species typically have low prices and/or are 

caught in smaller quantities. 

5
We started with monthly data for the period 1971 through 1991. Monthly catches and 

prices were combined into bimonthly values to avoid the problem of very small catches 

in some months. A summary of the data can be found in Holt and Bishop (2002, Table 

1). The amount of variation in the data was sufficient to allow us to ferret out the 

demand relationships across the six types of fish. And it turned out that our model fit the 

data quite well and outperformed the popular Almost Ideal Demand System across 

several criteria when the latter was fitted to the same data set. 

For purposes of this paper, we applied the model as estimated in Holt and Bishop (2002) 

to estimate the post-harvest welfare implication of increases in two of the Great Lakes 

most important 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, compensating variation (post-harvest benefits) was 

estimated for 1 percent, 5 percent, and 10 percent increases in catch. These percentages, 

as expressed in the first column of the tables, are the analogue of the proportional 

increases in catches, L, in the conceptual model discussed in the preceding section. For 

example, in Table 1, we estimated that at L = 5 percent for whitefish, post-harvest 

compensating variation would increase by $292,000 after rounding. Likewise, in Table 

2, at L = 10 percent for yellow perch, post-harvest welfare would increase by about 

$265,000. 

Table 1: Post-Harvest Compensating Variation from Increases in Great Lakes Whitefish 

Catches. 

Catch 

Increase 

(L) Value

Compensating

Variation 

(CV) 

CV/Value

(K) 

1% $ 5,657,206 $ 58,342 1.0%

5% $ 5,657,206 $ 291,539 5.2%

10% $ 5,657,206 $ 582,654 10.3%

Table 2: Post-Harvest Compensating Variation from Increases in Great Lakes Yellow

Perch Catches. 

Catch 

Increase 

(L) Value 

Compensating

Variation 

(CV) 

CV/Value

(K) 

1% $ 3,025,070 $ 26,524 0.9%

5% $ 3,025,070 $ 132,493 4.4%

10% $ 3,025,070 $ 264,667 8.7%

The right-hand percent columns in the two tables show compensating 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 simple model. That is, for example, if L = 10 

percent for yellow perch, K = 8.7 percent. 

6
For both whitefish and perch, the relationship K(L) is very close to being linear and is 

slightly steeper for whitefish. The slope for whitefish is approximately unity, while the 

slope for perch is approximately 0.9. 

The estimates of K for lake whitefish and yellow perch are more or less typical of the 

Great Lakes commercial species included in the model. For example, 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 percent for smelt to 12.12 percent for chubs for a 

weighted average of 10.03 percent. Hence, for the Great Lakes, we propose that K = 

K(L) can be approximated by K = L for relatively small changes in catches. That is, at 

least for the Great Lakes species included in the Holt-Bishop model, the change in postharvest rents and consumer welfare as a percentage of ex vessel value is estimated to be, 

on average, approximately equal to the percentage change in catch. 

Now, if K = L holds to a reasonable approximation for the major Great Lakes species, 

would such a relationship be suitable for benefits transfer to other species and regions? 

Admittedly, this is a purely pragmatic approach. Beyond saying that as similar products, 

fish products might have similar demand structures, there is no theoretical reason to 

suppose that post-harvest changes in welfare, as a percentage of dockside value, should 

be similar across fisheries. The consistency across Great Lakes species is encouraging 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 model very similar to 

Holt and Bishop (2002) for nine types of fish in the South Atlantic region. The weighted 

average value of K for a 10 percent reduction in catch was very close to 10 percent, 

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 comparison involved red drum in the Gulf of 

Mexico, where Thurman and Easley (1992, p. 236) estimated that post-harvest welfare 

would by 6 percent for a 10 percent reduction in catch. This would indicate that K = L 

might not be as robust across fisheries as we would like, but more research is needed 

before much more can be said. 

Implications for Benefits from I&E Remediation 

For any of the species covered in the Holt-Bishop model, estimation of post-harvest 

benefits would be relatively straightforward. Beyond running the model and reviewing 

the results for changes in circumstances since 1991 (when the data set ended), only minor 

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 model and original research is not feasible, benefits transfer would be necessary. We

can illustrate how this would work using a Great Lakes example. 

U.S. EPA’s estimates of I&E losses at the Monroe and J.R. Whiting power plants on 

Lake Erie are presented in Table 3. These estimates were developed for the 2002 

Proposed Section 316(b) Phase II Existing Facilities Rule. EPA developed these 

estimates using I&E data collected by the Monroe and J.R. Whiting power plants in the 

7
1970s and extrapolated the estimates of I&E at all in-scope facilities based on average 

daily flow at all Great Lakes facilities affected by the rule. EPA will be revising the set of

facilities defined to be in the Great Lakes region and the estimated I&E impacts in the 

analysis for the final Phase II rule. Thus, these results are used for illustrative purposes

only. Full details on the methods used to estimate I&E impacts are provided in the Case 

Study Document for the proposed rule (U.S. EPA, 2002). 

Table 3: Estimated Commercial Harvest Lost from Impingement and Entrainment in the 

Great Lakes Under Conditions Assumed in the EPA Analysis (pounds per year) 

Species 

Estimated I&E Losses at

J.R. Whiting and Monroe

Estimated I&E Losses at all 

Great Lakes In-Scope 

Facilities 

Bullhead 52 206

Channel catfish 767 1,518 

Common carp 239,478 949,180 

Gizzard shad 2,555,854 10,130,218 

Sucker spp. 1,233 4,887 

White bass 115,827 229,544 

Burbot 206 408

Freshwater drum 19,148 75,894 

Smelt 810 1,605

Whitefish 73 143

Two species that were included in the Holt-Bishop analysis appear on this list, whitefish 

and smelt. However, the quantities of both species are too small to affect the prices 

much, if at all, so the Holt-Bishop model is not directly applicable to this problem. The 

other species in the list are not included in the Holt-Bishop model and, hence, would need 

to be valued using benefits transfer. If the figures in Table 3 were final estimates, how 

might benefits transfer work?

Carp, gizzard shad, suckers, and freshwater drum are relatively abundant species that are 

variously referred to as rough fish or underutilized species. Their production is much 

more limited by markets than by biological abundance. This is reflected in their dockside 

values, which averaged $0.09, $0.04, $0.07, $0.11 per pound, respectively, over 1995-99 

(compared to $2.43 for yellow perch and $0.75 for whitefish). The upshot is that 

increased abundance due to lower I&E losses would not be likely to increase catches 

much if at all. Hence, there would be few if any direct benefits to commercial fishing 

from lowering I&E losses of these species.5

 Furthermore, a few hundred dollars worth of 

channel catfish (dockside value of $745 based on average 1995-99 prices) and burbot 

($127) can safely be ignored.6

 

5

 It is conceivable that commercial fishing could be positively or negatively affected through ecosystem 

effects. If such impacts were identified, the methods proposed here could be applied. 6

 Prices here come from the National Marine Fisheries Service web site, 

http://www.st.nmfs.gov/st1/commercial/landings/gl_query.html

8
That leaves white bass as the focal point for the analysis. Let us assume that conditions 

in Great Lakes are currently similar to those in the 1970s (when the studies used by EPA 

to estimate losses were done) and will continue to be so for the foreseeable future. Thus 

we assume that average annual catches are about 1.7 million pounds with an ex vessel 

value of about $500,000. These are the actual averages over the period beginning in 

1971 and ending in 1979. If we assume that remediation is totally effective, this would 

mean an increase in annual catches of 230,000 pounds (Table 3) or about 14 percent. 

Applying the result from the Holt-Bishop model, 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 covered by empirical research like that found in Holt and Bishop 

(2002), post harvest changes in rents and consumer welfare from changes in catch can be 

addressed directly and should not be problematical. Where such research results are not 

available and cannot be produced in a timely manner, the only recourse will be to benefits 

transfer. Assuming that K = L in such cases seems to us to be a reasonable approach for 

now. The robustness of this formula across Great Lakes and South Atlantic fisheries 

provides an adequate basis for proceeding in this way. As more research becomes 

available, the formula may need to be modified or a new approach may present itself, but 

that is always the case with benefits transfer methods. 

Literature Cited 

Beach, R.H., and M.T. Holt. 2001. “Incorporating Quadratic Scale Curves in Inverse 

Demand Systems.” American Journal of Agricultural Economics 83(February): 230-45. 

Barten, A.P., and L.J. Bettendorf. 1989. “Price Formation of Fish: An Application of an 

Inverse Demand System.” Europiean Economic Review. 33(October): 1509-25. 

Diewert, W.E., and T. J. Wales. 1988a. “A Normalized Semiflexible Functional Form.” 

Journal of Econometrics 37(March): 327-42. 

__________. 1988b. “Normalized Quadratic Systems of Consumer Demand Functions.” 

Journal of Business and Economic Statistics 6(July): 303-12. 

Eales, J.S., C. Durham, and C.R. Wessels. 1997. “Generalized Models of Japanese 

Demand for Fish.” American Journal of Agricultural Economics 79(November): 1006-

17. 

Holt, M.T., and R.C. Bishop. 2002. “A Semiflexible Normalized Quadratic Inverse 

Demand System: An Application to the Price Formation of Fish.” Empirical Economics

27:23-47 

Just, R.E., D.L. Hueth, and A. Schmitz. 1982. Applied Welfare Economics and Public 

Policy. Englewood Cliffs, NJ: Prentice Hall, Inc. 

9
10

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 Proposed 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/.