A Cost-Production Analysis of Trap and Hand Line Fishing in Puerto Rico

This study analyzes the cost-production relationship of trap and hand line fishing in Puerto Rico. A model of the fishing family firm is designed which is similar to the traditional neo-classical model of the fishing industry. The catch functions, of the Cobb-Douglas type, are estimated using the single least squares methods. Tests of technical efficiency and tests of price efficiency are then conducted to establish if some groups of fishermen are more efficient than others and to verify if the fishermen maximize their profit, given the technical coefficients of the catch function and the level of the prices. The results of those tests show that some fishermen are significantly more skillful than others. They also indicate that, as a rule the fishermen do not maximize their profit, that is, that they do not choose the optimum combination of inputs. Those conclusions suggest a certain number of policy measures. It is shown that improving the fishermen's skill would substantially increase their catch. The same results would be obtained if, with proper advice, they selected the optimum combination of inputs. Given the lack of sufficient data on the fish population it was not possible to measure the precise extent of the effects of those policy measures. However this study provides a useful guide for the policy makers.

Number of Interviews in Each Community of Cabo Rojo, 1973 . 30 Characteristics of Fishing Family Firms in the Areas Surveyed. This study provides the decision makers with information, not otherwise available, concerning the productivity of some fishing methods as well as the economic behavior of the fishermen. It shows what can be expected from a change in the input combinations presently adopted ~y the fishermen as well as some of the effects which could result from improving their fishing skills. These are tools which will help design the policies necessary to imorove the economic situation of the fishermen and to develop the artisanal fishery.
Several approaches were considered. For the purpose of policy makinq, a dynamic model would have probably been more appropriate. However, insufficient data were available on the fish population. In addition, it would have been very difficult to obtain information on the levels of input usea by fishermen for more than one or two years.
For several inputs the direct interviews were the only source of data, and, in many occasions, the fishermen had difficulties remembering their past investments.  Table I-1 compares the artisanal fishery industry with the total economy and the agricultural sector.
As shown in Table I-1 the artisanal fishery employs only a small amount of the total labor force, and it produces an even smaller part of the Island income.
The local fishery is one of the less developed sectors of the economy. Using the aggregate figures of Table I-1 it is possible to roughly compare the average productivities of labor. In the total economy it is around $6200 (column I divided by column 4).
In agriculture it is slightly over $3200 while in the fishery it is only about $2000.
The actual difference is even larger since for the fisheries gross income is used instead of net income. For the United  Rico, 1972, p. 6.
( 2) Ibid. , p. 7. U1 (3) Commonwealth of Puerto Rico, Department of Agriculture, Status of Fisheries in Puerto Rico, 1972, by Jose A. Suarez Caabro, Agricultural and Fisheries Contributions, Vol. V, No. 3, Cabo Rojo, Puerto Rico, p. 47. 8 The incomes of the fishermen reflect this to some extent. Ninety -one percent of the fishermen, and 55 percent of the non-fishermen have annual incomes in the $1000 -$3999 range, while 30 percent of the fishermen and 27.3 percent of the others have incomes between $4000 -$5999.
This suggeststhat a few fishermen are earning fairly good incomes. At the same time none of the fishermen, but 18.2 percent of the non-fishermen, have incomes less than $1000.
The traditional character of the fishery is also revealed by the fact that "in general, the part-time fishermen and the non-fishermen· showed a somewhat more prevalent tendency than did the full-time fishermen for continuing to work at a different job if their current occupation could no longer be followed (in that situation) 47.8 percent of the full-time fishermen and 41.7 percent of the non-10 fishermen indicated that they would not work". This is further emphasized by the fishermen's justifications for not working if they could not fish any longer. Forty-two point seven percent indicated that they knew nothing else, while only 22.2 percent of the non-fishermen justified their a .
h. 11 nswer in t is way. lO_Ibid., p. 16 11 Ibid . ' Table lSb . 9 From those observations it appears that the artisanal fishery in Puerto Rico is still largely traditional, and that most of the fishermen are not fully integrated into the market economy.
While some fishermen are modernizing their operations and introducing new techniques of fishing or of management, most of them are still attached to the traditional methods.

II
Trap and Hand Line Fishing As shown in Table I In Puerto Rico the most common fish trap is the arrow-head typP.. They are made of chicken wire around a frame of either mangrove wood or iron rods. "Normally, it is fishe d in shallower depth (less than twenty fathoms) because of the lack of mechanical hauling equipment'~. 13 In addition, the boats have no navigation equipment to aid the captain in finding his traps. Land marks are used which_is very inefficient as soon as it is misty or foggy.
On fishing grounds known for their high productivity there are often a very large number of traps and sometimes it is necessary to navigate carefully to avoid cutting the ropes tying the buoys to the traps. Generally, the fish pots are not deliberately baited but sometimes the fishermen will leave inside some fish which are too small to sell or for which there is no demand.
Hand line fishing "while requiring a small investment requires considerable more ability and knowledge of fish habits 11 • 14 In this type of fishing the fishermen use long lines (300 to 500 feet).

11
At the end of the line 4, 6, 8 hooks are hung from a hard frame of galvanized wire, with a three 1 50 five pound lead attached to the center 11 • Those hooks are baited with small fish which the fishermen catch with their cast nets.
When fishing with hand lines, some of the fishermen will let the boat~ drift once they are on the fishing grounds. Others prefer to keep the boat still, and in some areas there will be one man in the boat whose sole task is to steer the boat while the others are fishing.
14 Study of the Fisheries Potential of the Virgin Islands, Special Report, Caribbean Research Institute Contribution, No . 1 Virgin Island Ecological Research Station, August, 1969, p. 41. 15 Estado Libre Asociado de Puerto Rico Departamento de Agricultura Contribuciones Agropecuarias y Pesqueras, Vol. II, No. 1, San Juan Puerto Rico,p. 28. In areas where conditions are suitable for trap and hand line fishing many fishermen practice both methods.
There is a significant difference between the species c aught by traps and the species caught by lines. The l a r ges t s o urce of revenue from traps is lobster (35.5 perc ent nf the total value of the catch from traps in 1971) . 16 Bu t, l obsters aside, the difference in the species composition of the fin-fish catch from traps and hand lines is i mpor t a nt .
While the weight of the fish caught with traps is 60 pe rce n t larger than the weight of the landing from lines, t his d i fference is reduced in value to 22 percent. (Table I-  In contrast porgies "do not seek shelter in reefs but rely on keeping a considerable distance between themselves 20 and a potential source of danger".
This explains why they are not found in the fish traps.
As for the silk snappers, the majority are caught with hand lines because they are "a deeper-water species than most, (it is often found between) 21 300 and 800 feet". The number of personal interviews conducted in each of the municipalities is shown in Table II-2.  TABLE II-1   SOME CHARACTERISTICS OF THE PORTS SURVEYED  AND COMPARISON WITH THE REST OF THE ISLAND The average ex-vessel price per pound was $.56. This was the lowest fish production of the island and conversely, it was the area whe2e the highest price ,,;as paid for fish".
Much of the information concerning the geographical characteristics of the various areas and derived from Ra~ael ~ico, Nueval Geografia du Puerto Rico (Editorial Universitaria.
Universidad de Puerto Rico , 1969

III Guanica
Guanica was the last community surveyed. Here too the fishermen use traps but in fewer numbers than in the other ports. Most of the fishermen own only 20 or 30 traps. The boats and motors too are usually smaller than in the rest of the island. This is probably related to the fact that most fishermen go fishing alone in their boats.
In none of the other communities visited is this a common practice.
In one of the barrios where the fishermen live, some condominiums and summer houses are now being built. This presently provides jobs to some fishermen and is a welcomed second source of income. However, many of the fishermen interviewed resent the development of tourism in that area.
They view it as an infringement of their freedom. In Tab le II-5 and Table II-6 the sample is divided into homo ge neo us subsets according to the power of the boats . This comp aratively large investment is not only due to the boat and its motor but also to the fact that they fish more traps and u s e mechanical winches.
Another important finding is that most fishermen fish mainly with either traps or with lines. As a general rule they do n o t divide their time equally between both methods.   This may be due to the preference of the fishermen, but it also reflects the natural conditions around the ports where the fishermen live.

40
This tends to be confirmed by the fact that all the large boats were found in areas of trap fishing (see Table II-4) where they are used for that type of fishing.
In addition, larger boats are able to go to or beyond the edge of the continental shelf where most line fishing takes place. An econometric analysis of the data based on a theoretical mode l o f the fishing family firm will show the relative impor t a n c e o f the various inputs.
A prior i , Table II After the presentation of the catch function and the cost function it will be possible to turn to more practical problems. To estimate a catch function it is necessary to specify its form as well as the variables which will be chosen to enter in the regressions.
In the fishery economic (2) a catch function  dollars. This a p proach is questionable since it does not take into account the life of the boat. Usually, some measure of depreciation is preferred to a mesure of total assets. In estimating agricultural production functions.
The historical tendency has been ... to measure the input of durable assets by the actual maintenance and depreciation costs associated with their ~se rather th~n ~~ their capital value on an inventory basis.
If this measure of capital is selected some difficulties remain, however, since there are various alternatives to compute depreciation costs. "A practicable measure of the true cost of using a machine for a particular purpose is the return from the next most profitable use of replacement-cost depreciation, whichever is highern. 14 Opting for replacement-cost hardly solves the problem, for "Reproduction cost is an imaginary cost 1115 and one has to decide upon a definition of replacement cost.
For instance, should it be "the current cost of a new Given the difficulties discussed above, present market value of the asset appears to be especially useful given its practical advantage of being relatively easily determined. In Holmsen's study of the small trawler fleet.
The owner of the vessel was asked what he considered the market value. This figure was checked with the last appraisal of the vessel by an independent surveyor either for a bank or for an insurance firm. More numerous examples of attempts at measuring management can be found in farm management studies. In most of t his work the methodology used is directly linked to the mean chosen to estimate the production functions.
For that reason it will be treated in the next section which deals with estimation of the catch function.

19
Noetzel and Norton , Costs and Earnings in the Boston !!_awler Fleet. 20 Bell, "The Relation of the Production to the Yield on Capital for the Fishing Industry," p. 114.

III E s timating the Catch Function
Cobb-Douglas functions are those most frequently used to describe catch functions. This section will consider t h e problems associated with estimating a function o f that f o rm .
Then some remarks will follow dealing with the a ctual measurement of diverse types of managerial abilities.

I Estimating a Cobb-Douglas Production Function.
Marsc h a k and Andrews are among the first economists to have given much attention to the difficulties of pro-1 .

per y estima ting pro uction unctions.
They show that "the economist is confronted not only with a single equation, but ·with a system of ( . .. ) equations none of which h .
,, 22 e can ign o re .
This system of equations contains a "production equation ." In a two-input case it will have the form:  , and x 2 . Those equations are further specified by introducing the concepts of "technical efficiency" and "economic efficiency".
The production function will change, even within the same industry, from firm to firm and from year to year, depending on the technical knowledge, the will, the effort and luck of a given entrepreneur; these facto23 can be summarized as "technical efficiency".
Assuming that the production function is the same for all firms except for the "technical efficiency" represented by Ef (3-1) will become: Then "economic efficiency" is defined by Marschak and on the other hand, in the latest literature, the concept of "economic efficiency'' is used to refer to the combination of technical and price efficiency. This terminology will be used throughout the remainder of this study.
Economic efficiency accounts "for firms that produce different quantities of output from a given set of measure inputs of production. This is the component of differences in technical efficiency ...
It also takes into account that different firms succeed to varying degrees in maximizing profits, i.e., in equating the value of the marginal product of each variable factor of production to its price.
This is the component of price efficiency 11 Introducing price efficiency µf and Bf into the "marginal-productivity equation, "equations (3-2) becomes: The next step is to find a proper method to estimate these equations and to express the model accordingly. If we desire to estimate the value of x if x and x 2 should be determined not by that 0 set of random causes which existed in the past but by deliberate action then we have to estimate the coefficients in the equation (3-3) .27 In fact, since "each of the three variables x o' changes as the result of variations in the random xl' features £ ' µ ' e ' from firm to firm. ,,28 One has to estimate simultaneously the system of equations (3-3) (3-4) since least squares estimates of equation (3-3) alone will be biased and inconsistent.
In the case of a production function of the Cobb-Douglas type: (3-5) x 0 u 0 u 0 = random variable with mean unity.
Under perfect competition (this assumption will be maintained throughout this chapter) the system of equations to be estimated can be written: But there is more to it than that.
The variation in output of a particular firm from year to year may be due to exogenous random causes (such as the weather) but the differences between one firm and another due to the 'ability' of the entrepreneur w~~l be constant over time for a particular firm. one may add that even for cross-section data the variation in output between different firms may be partly due to "exogenous random causes" such as different quality inputs.
If this is so one can write is a stochastic disturbance representing the "exogenous 33 random causes".
But now output is a function of V . *.

01.
Consequently, ... the production function and profit function for the individual entrepreneur are stochastic ... Thus, the rationale for assuming deterministic profit maximixation, as is done in the traditional approach, is at variance with the above interpretation of V . ; an interpretation which appears to be consistent ... Where u . is a random disturbance representing factors su8fi as weather, unpredictable variations in machine or labor performance and so on. Whenever the production process is not instantaneous, the effect of the disturbance on output cannot be known until after the preselected quantities of inputs have been employed in production.35 33 A. Zellner, J. Kmenta, and J. Dreze, "Specification and Estimation of Cobb-Douglas Production Function Models", Econometrica, 34 (October, 1966), p. 786. 34 1 ~., p. 786.
It is assumed that the entrepreneur attempts to maximize his expected profit and that the prices are known with certainty.
Expected profit can be expressed as:     (3-26) provides another method to compute the coefficients of the production function. This i s re-£erred to as the factor shares method. Despite its obvious simpli city it has not been used frequently.
The reason for this neglect was probably the desire of early authors to test their estimates of the production function against the known facts about ~he 43 distribution of income among factors of production.
As mentioned earlier, the classical model, with its assumption of maximized profit, was not adequate to represent the true economic behavior a traditional economic ac-   In the present study, if it is assumed: 1) that the population is homogeneous and therefore that interspecies relationships can be ignored , 2) that the catch affects the population in the same fashion, whatever the fishing method used, then FN can be divided in three elements EXT .
. l l = total annual catch from traps total annual catch from hand lines = total annual catch from all other methods.
Combining equations (4-1) , (4-2) and (4-6) the growth rate  In reality, it is likely that the first order conditions for maximizing profit will not be exactly satisfied.
Two sets of reasons may concur to lead to a less than optimum combination of inputs:

a)
The firms may be subject to a common set of co nditions which influence the ir choice of the q uantity o f inputs . Those conditions may b e d ue to tradition or to the institutions.
In that case, a term Rq, common to al l firms, may be introduced in the first orde r conditio n equations to account for that <listurbance.

R2
This shows that, assuming that the u 1 i and u 2 i are statistically independent of u . , lnx 1 . and lnx 2 . are also staoi i i tistically independent of u . , and consequently, the least oi square estimate of (4-26) is consistent and unbiased. A special case arises in the fishery when any kind of lay system is used to pay the crew members.
In what situation the total wage actually paid is a function of the actual output. Yet it can be assumed that the amount of labor hired is a function of the expected output, since the decision of hiring is taken before the fishing trips.
In the simplest lay s y stem: In the present study X will be considered given, 2i or, which is the same, determined by factors outside the where the values of s 1 , s 2 , and s 3 are 0 or 1 according to the subset to which firm i belongs. Each subgroup but one will be characterized by the presence of one or more of the o 1 in its production function as shown by     However, in order to use ordinary least squares for this estimation it is necessary to assume that the fishermen maximize the expected profit rather than the actual profit. Given this assumption, tests of technical efficiency and of price efficiency can be conducted which will provide further information concerning the behavior of the fishermen.

V ESTIMATION OF THE CATCH FUNCTION
A Cobb-Douglas type function was chosen as the theoretical form of the catch function. The production function of equation (4-14) suggested that such a form should be used.
x .  Table V-1. Table V-1 should be read vertically.

The regressions in
For instance, the first regression in Table V-1-a is:  The f i r s t number in each group is the coefficient of the variab le . The first number in parenthesis is the standard error and the second number is the t-statistic.  The first number in each group is the coefficient of the variable. The first number in parenthesis is the standard error and the second number is the t-statistic.
) The first number in each group is the coefficient of the var i able . The first number in parenthesis is the standard error and the second number is the t-statistic. F tests confirm that all the regressionsin Table V  Aside from the special case just presented, Table V-1 shows that the coefficient measuring the influence of the length of the boat is significantly positive. This is not surprising.
Bigger and more powerful boats allow the fishermen to go on more distant grounds and, for instance, to fish at the edge of the continental shelf which is more productive. The larger boats can also fish under rougher weather conditions. They can go at sea more often (and this will be accounted for in another variable) and they can also stay at sea longer. On a given day when the weather becomes menacing, the smaller boats have to return sooner. This means that they cannot fish a long time with their lines.
Given the high significance of the regressions, a case can be made to use any of them as representative of the fishing operation. Later in this chapter when additional independent variables are introduced, the comparison of the results is made using the regression with the length of the boat since it has the highest R 2 and F statistics. On the other hand, in subsequent chapters, it will be more convenient to use others, particularly when testing for price efficiency. However it should be noted that because of the high significance of all the regressions and of their similarity, comparable results could be obtained no matter which regression is used.

II Traps
The natural logarithm of the number of traps owned appears to be an important variable in the explanation of the size of the catch. In all the regressions of Table   V   on the other hand, if a fisherman owns many traps he will put them in quite different areas in order to spread the various risks, risk of catching fish of course, but also risk of having his traps stolen or lost. Then, this behavior is better accounted for by introducing in the regression a variable which represents the number of traps owned as in the regressions of Table V-1-a.

III Lines
The number of lines used during a fishing trip is introduced as an independent variable to attempt to explain the catch from lines. Interestingly, it is insignificant. Understandably, it is a small sample and it is difficult to argue that if the 6 boats using fewer lines than men or the 3 boats using more lines than men operated exactly as many lines as men they would be more or less efficient.
Probahly the combination lines-men chosen by each crew corresponds to the characteristics of this particular crew, and one suspects that the fishermen of each boat chose the optimum combination in most cases.

IV Measuring Labor
Labor is measured as the number of man days at sea.
The number of men in the boat is multiplied by the number of days the boat went to sea.
In trap fishing as well as in line fishing, the coefficient of man days at sea during the year is highly signifi-cant. This is not surprising since the dependent variable is the annual catch. However, where the daily catch is used as the dependent variable and the number of men in the boat is the measure of labor input the coefficient of the latter variable is significant for traps but not f o r hand lines as shown by equations (5-14) and (5-15).
( One would expect the number of men in the boat to be a significant explanatory variable as far as catch from traps are concerned. Having two men instead of one will allow the placing of more traps in deeper water since it will be easier for two men rather than just for one to pull the traps. When the effects of using a pot hauler are investigated in the next chapter, it will be shown that being able to pull the traps from deeper water is an important factor. As far as line fishing is concerned, the coefficient of the labor variable would tend to be negative although it is significant only at the 15% level. This suggests that given a fixed number of lines, having an extra man to keep the boat still is not productive. This already appeared in equation (5-13) where it was shown that given a fixed number of men in the boat it was just as productive to have everyone attend a line. However, the same caution is necessary here concerning the size and the structure of the sample.

V Role of the Fishing Grounds
No direct attempt was made to determine the effect on the catch from fishing in the various fishing grounds. During the field interviews it appeared that the fishermen often changed fishing grounds. In. addition, they were rarely able (or willing) to state with precision where they fished. For these reasons another approach was substituted: The fishermen were asked how many gallons of gasoline they used on each trip, on the average. This was expected to give an indication as to how far from their home port they went fishing.
Since the dependent variable is the yearly catch, the number of gallons of gasoline used on each trip has been multiplied by the number of trips. As shown in Table V-1 the coefficient of that variable is not significant for trap fishing only at low degrees of confidence.
One of the reasons f or this comes from the difficulty for the fishermen to give an accurate measure of the number of gallons of gasoline used during one trip . During many interviews it seemed that the fishermen did not have a good idea of this figure. Futhermore, discussions with a boat dealer showed that, given a 16-foot boat of the type used in Puerto Rico, a 6 HP. motor would consume 1 to 1/2 gallons of gasoline in one hour at 4 .5 mph. while an 18 HP. motor would consume 2 to 2-1/2 gallons in one hour at 10 mph .
In other words, to go the same distance, the two motors would use the same amount of gasoline providing that the boat with a small motor goes at half the speed of the other boat. And even if they go the same distance at the same speed the difference in consumption of gasoline is likely .
to be small. This suggests that it is not such a good variable to estimate how far the fishermen g o fishing.
In addition, the small amount of gasoline involved explains why the fishermen could not give a value which was precise enoug h to be significant in the re g ression .  The first number in each group is the coefficient of the variabl e .
The first number in parenthesis is the standard error and the second is the t-statistic.

Given a Cobb-Douglas type production function:
If some of the variables (the catch and those which are a multiple of the number of trips) are multiplied (or divided) by a constant c. In fact, the constant term is only slightly changed; this is because the sum of the coefficients of LH and LV is close to one. LH and LV are the independent variables which were divided by .75 to adjust for the missing sale tickets.
This chapter shows that the boat and its motor are the most important factors to explain the level of the catch from hand lines and from traps.
The second significant independent variable is the number of man days at sea. In fact, those two elements are the only ones which were found to be significant to explain the catch from lines. To explain the catch from traps, the number of traps owned is also an important explanatory variable.
Among the variables which might have been important The first number in each group is the coefficient of the variable .
The first number in parenthesis is the standar d error and the second number is the t-statistic.

128
it must be noted that the number of gallons of gasoline used in a year is not a good explanatory variable.
It is also interesting to recall the conclusion concerning the rumber of men in the boat.
For trap fishing, it was found that, everything else being equal, there was a positive correlation between the number of men in the boat and the size of the catch, however, for line fishing, the number of men in the boat does not affect the catch.
Despite the various problems encountered in defining and measuring several of the inputs, the results of the regression are, in general, very significant, and they provide a useful basis forfurther analysis of the fishermen's behavior. it is profitable to invest in a winch.

I Technical Efficiency
The technical efficiency tests are based on the assurnption that for the same fishing methods all the boats have the same catch function e x cept for one parameter which embodies the difference in technical efficiency.
The catch function has the general form n For this test the catch functions used were the same as those described in Chapter V.
Various criteria were used to divide the sample of boats in two groups, then, technical efficiency was compared between groups.

Division I:
(1) motor less than or equal to 30 hp ( 2) motor over 30 hp.
Division II: ( 1) motor less than or equal to 40 hp ( 2) motor over 40 hp.
Division III: (1) fishermen using a winch ( 2) fishermen not using a winch Division IV: ( 1) fishermen fishing with traps only ( 2) fishermen fishing with lines and traps Division V: ( 1) fishermen fishing with lines only ( 2) fishermen fishing with lines and traps For each division a regression was computed where the dependent variable was the annual catch, while the independent variables . were,  The first number in each group is the coefficient of the dummy variable. The first number in parenthesis is the standard error and the second number is the t-statistic.

I Big Boats and Small Boats
The first important finding is the non-significance of the coefficient of the dummy variable for powerful boats. This is the case for fishermen using either traps or hand lines.
It is also true whether the boats are divided on the basis of motors more or less powerful than 30HP or more or less powerful than 40HP. This means that there is no significant difference between the technical ability of the captains of big boats and the technical ability of the captains of small boats. As shown in Chapter V the size of the boat is an important factor to explain the size of the catch but what Table VI-1 indicates is that, given the same equipment, the captains of big boats will have the same catch as the captains of small boats.

II Traps and Lines as a Combined Enterprise
On the other hand, this is not the case if the trap fishermen are divided between those fishing with traps only and those fishing with both traps and lines. The fishermen practicing both methods are on the average more technically efficient than the fishermen using traps only.
In the preceding chapter it was suggested that skill could be an important element in explaining the catch from lines.
This is now reinforced by the estimates given in Table   VI-1. This shows that, all other inputs being equal, the 135 fishermen who fish with lines and traps catch more fish in their traps. This is not a surprising finding. It is usually recognized that line fishing requires better knowledge of fish behavior. In this study it appears that the fishermen who have this knowledge use it to improve the catch from traps. It is not possible to tell if this knowledge is acquired through the practice of line fishing or if the fishermen decide to fish with lines because they already know the fish's behavior. Whatever the answer, this result emphasizes the importance of the skill as an input factor. Everything else being equal, the fishermen using both traps and lines, on the average, catch 77 percent more than the fishermen using traps only.
When the line fishermen are divided into two groups, those using lines only and those using lines and traps, it appears that there is no significant difference of skill between those groups. This means that trap fishing does not require any special knowledge nor does it teach anything that is not already necessary for line fishing.

III Efficiency of a Winch
If the trap fishermen are divided between those using a winch and those using a winch, Table VI-1 shows that the coefficient of the dummy variable representing the winch is significantly positive. However, the coefficient of the dummy variable is more difficult to interpret. To a large extent it measure s t h e e ffects of the winch itsel f . Yet it is conceivable that some fishermen decided to buy a winch because they had chosen to fish in more productive and deeper grounds. If this is so the coefficient of the dummy variable reflects both the effects of the winch and the technical efficiency of the captains. For these reasons it is not surprising to find that using a winch makes a significant difference in the catch (61 percent) . In Chapter V it was shown that the number of men in the boat was significant, that is, the more power there was to pull the traps, the larger the catch. The positive coefficient of the dummy variable associated with the winch confirms this finding. The fishermen using pot haulers can lay the traps at greater depths. This gives them a larger choice of fishing grounds and therefore they can fish the more profitable deeper waters.
Despite the fact that the use of a winch makes a significant difference, this does not mean that it is profitable to own one. The added cost may not be compensated by the increase in the catch. This will be tested in the last section.
In addition, the last criteria can be used in combination to account at the same time for the fishermen who fish with traps and lines as well as for the fishermen who use a winch. In this case the following regression was obtained.  This tends to confirm that, in fact, when the efficiency of us ing a winch is tested independently, two elements are me asured, the effect of the winch itself and the captain's efficiency. Here the captain's efficiency is already partly embodied in Q. B) Test of technical efficiency when the input boatmotor i s measured in monetary terms. The ave rage power of the boat, the average price of a horsepower and the value of the dummy variable when the present value of the boat and of the motor is used to measure the combined input boat-motor are shown in Table   VI-2.
The technical efficiencies which were proven to be signific antly different earlier are confirmed to be so in Table VI- Table V-1) .
In this case, the dummy variable does not measure fishing a bility, it is only an effect of the cost structure.      The symbols are the same as in equation ( 6-3) The value of equation ( The difference between those two numbers is sufficiently large to conclude that, given the present level of the other inputs, the fishermen are investing too much in traps.

II Line Fishing
In this case the test of price efficiency was conduc-  The result of those computations are summarized in Table VI-3.
In Division IV the sample is divided between those using both traps and lines and those using traps only.
In Division V, fishermen using both traps and lines are compared to those fishing with lines only. The analysis  In Table VI -4 it is also shown that there is a significant difference between the price efficiency of the owners of s mall boats when they invest in traps. Earlier it was foun d that, as a whole, the fishermen had a tendency to have too many traps but, as it appears now, this varies considerabl y among the groups within divisions. In Table VI

I
The Present Economic Performance The total value of the annual catch, the return to the captain and the crew, and the return on the present value of the boat plus motor by various motor sizes and equipment types for trap fishermen are given in Table   VII-1. Similar information for line fishermen is presented in Table VII-2. (7-1) 1) The total annual catch is measured in dollars TR 2) The total annual return to the captain, TRC, includes his profit plus his return on capital and on labor and management. It is what he has left after he has paid all his fixed and variable costs. TRC = TR -Depreciation -maintenance -crew's sharecost of gasoline -cost of the traps (or cost of the lines) The depreciation in this case is the straight line depreciation on the boat, the motor, and the winch.

3)
Annual net income to the captain This was computed by subtracting from the total annual return the interest the captain pays on his boat and motor.
An interest of 5 percent was used because it is the cost Of capital to the fishermen taking loans from the Puerto Rican Department of Agriculture.
This represents the return to the captain's labor, management and profit.

4)
The annual crew's share CS, is equal to: (7-2) CS = 1/3 (TR -cost of gasoline) This is the most common way of remunerating the crew, although there are other systems.

5)
The average annual return on the present value of the boat and the motor 2 is computed as follows:  one can make recommendations in order to attempt to maxirnize profit, which apply to line fishing as well.
In Chapter VI it was shown that the fishermen fishing also with lines caught on the average 77 percent more fish in their traps than the fishermen fishing with traps alone.
In addition, the fishermen who owned a winch caught 61 percent more fish. When both factors were combined their individual effect was reduced but it was still significant. In Section II of Chapter VI it was shown that, in general, fishermen had a tendency to underestimate the price of the traps although it was pointed out this varied considerable between groups.
If the number of traps owned by the fishermen were adapted to their actual needs, returns could also be increased.
In order to demonstrate some of the effects which could be expected from such a measure, the optimum number of traps was computed for each fisherman given his present level of the other inputs: boat, moto~ presence of a winch, and number of men days at sea. Equation All the other coefficients are also from equation (7-7 For comparative purposes the percentage change in return to the captain resulting from optimal investment 172 in traps was also computed. To that effect, equation (7-9) could be used as a guide.
Many factors specific to each fisherman will affect the optimum number of traps he can handle. In most cases, however, substantial deviation from the estimate obtained from equation (7-9) should be corrected.

II Maximizing Profit
In order to maximize profit fishermen must not only choose the optimum level of variable inputs but they must also operate an optimum size boat. Practically this corresponds to two different types of decisions. In one case the fisherman will consider his boat as a constraint and he will want to invest in the number of traps which maximizes his profit given his present boat. In the second case, at other time, he will want to change boat and choose one which will maximize his profit, given some of his firm's characteristics like the number of days he goes at sea. It is this kind of situation which is discussed here. The decision process for this choice is ihe same for trap fishing and hand line fish- The number in parenthesis is the standard error of the variables in their respective samples. ing, and therefore the following discussion applies equally to both methods. If the boat was to be used in more than one activity lnD should be replaced by lnD+lnZ, where Z would be the share of the activity studied in the total revenue.

When investing in a boat
Here too, it is necessary to recall the previous notes of caution, that because of the effect of externalities these equations should only be considered as a guide.
In addition, in this study none of the boats were equipped with echo sounders, radar, nor radio, all of which might increase the productivity of a given boat. To decide if it is judicious to invest in a boat equipped with such aids, simply by using equation (7-12) there could be erroneous results.
It was shown earlier that the fishermen underinvested in their boats, and that large boats with inboard motors were more profitable. Despite these findings, before undertaking any government program to increase boat size, it must be kept in mind that large boats require more harbor facilities, and these represent an added cost to the pro-graM. In the present study they are not.
Using the coefficients of equation ( Before closing this part of the section one important note must be added. It appeared in Chapter VI that the catch increased with the size and the power of the boats presumably because the larger, more powerful boats allow the captains to fish at the edge of the continental shelf.
The sub samples of powerful boats, however, were small; there were only six boats over 30 HP., and four over 40 HP., all of the latter from Puerto Real. Suggesting that more powerful boats will catch more fish implies that the difference of productivity between the edge of the continental shelf and the closer fishing grounds is everywhere as significant as in Puerto Real. There is presently insufficient data to prove such an assumption. However, the exploratory fishing and gear tests which have been conducted off Puerto Rico suggest that the edge of the continental shelf is always more productive than the on-shore 1 grounds.

III Chasing between trap fishing and line fishing
Comparing the information in Table VII-1 and Table   VII-2 it appears that, presently, line fishing gives the higher return on the boat and the motor. It should be remembered however, that various measures could be taken to improve the returns from both activities and particularly from trap fishing.
Consequently, it is difficult to compare the potential returns from each activity and to make recommendations as to the optimum combination between trap fishing and line fishing.
Despite those limitations, some remarks can be made concerning a profitable combination. In some areas the choice must be limited because of the geographical conditions, but from many ports it is possible to fish with traps and lines.
If the fishermen had the proper training more could fish with lines. For the fishermen who fish only a few days a month it is certainly a more profitable method than trap fishing because of the lower level of investment required.
For the fishermen who fish more regularly, the present combination displayed by the more powerful boats seem to be quite profitable as the returns in Table VII-1, Table   VII-2 and Table VII-3 show.
Whatever the potential returns this model could exhibit for both activities, it would be unwise to give up completely one method for the other. In the present model the fish population has been treated as homogeneous, but in Chapter II it was shown that the catch from lines did not have the same species composition as the catch from traps.
Abandoning one method for the other, or even changing drastically the balance, would affect the fish population in a way that would make the assumption of the model unaccep- In addition, it should also be recalled that the number of days the fishermen go to sea is an important element in the selection of the other inputs. If the fishermen went to sea more often, larger, more powerful boats would be jus- Many more studies could be undertaken to improve the present one in order to provide information on economic aspects which have been ignored here.

183
For instance, it was not possible to evaluate with precision the effects of the policy measures suggested by the present analysis. This was due to the lack of knowledge concerning the level and actual growth function of the fish population and the crowding externalities, since it is difficult to design a management program without some knowledge of the fish population.
In addition, it is essential to know what the factors are which motivate entrance into the fishing industry. Profit is probably an important one, but the policy maker must know the effect his decisions will have on the number of persons who will enter into fishing. This will require analyzing the role of other factors outside fishery such as the general level of employment or the demand for labor from the agricultural sector. In this study, the number of days at sea was assumed constant. In fact, it is likely that an increase in the profit will encourage the fishermen to fish more often and this will lead to an increase in the catch. The policy maker should be aware of that effect.
Finally, no global management scheme for fishery was proposed. This should, in the future, be an important area of research. The analysis of fish marketing in Puerto Rico could also suggest important decisions to develop fishery. that some of the fishermen selected in that fashion did not report their catch to the Department of Agriculture.
Although, in the questionnaire, all the fishermen were asked to estimate the value of their catch, those estimates turned out to be quite different from the catch reported to the government. This suggested that the answer to that part of the questionnaire might not be highly reliable.
The answers given in the questionnaires were constantly understated, they averaged $3693 against $6321 on the sale tickets for the same fishermen. At the same time the smaller standard error (1432) instead of (6270) suggests that in the survey, the fishermen with the highest revenues tended to lower them to what they perceived as closer to the community's average.
Consequently, if systematic random sampling was used and if one was to discard the information given by the fishermen who did not report their catch .:to the government, this could have reduced considerably the size of the actual sample. For that reason, it was decided to interview, in the selected communities, all the fishermen for whom the government had catch figures and to limit the study to those fishermen.
A priori this method could have introduced a bias, but, as it will be shown later, it is likely to be negligible since often the fact that his catch is recorded 187 or not is independent of the fishermen. This means the recorded catches are not systematically the highest or the lowest ones. For all pratical purposes, it is possible that whether a catch is reported or not may be a random process. For that reason it was thought that the risk of introducing a slight bias was more than compensated for by the fact that the information obtained in that fashion was more reliable. Of all the informations given on the sale tickets the breakdown by species is the least reliable. The reason is that, in reality, many sale tickets are not filled out completely and, more often than not, only report the total catch. In addition, sometimes the fish are classified in three groups according to their price per pound rather than by species. From that information the staff of the Laboratory divide the catch among the various species, according to past experience.
In 1968  The interviews were all conducted with the help of an interpreter. The fishermen were usually cooperative.
Out of 70 fishermen contacted only two refused to answer.
The survey dealt with the fishing in 1972, but since the interviews were conducted at first during the summer of 1973, and then during the winter of 1974, 19 of the fishermen who were listed in 1972 were not fishing anymore.
Some had taken other jobs; others had moved to the continental United States. In general, there is no reason to doubt the reliability of the answers given by the fishermen except, as mentioned earlier, when they were asked to evaluate the value of their annual catch.
All the answers concerning the equipment owned or used are highly reliable. Most of the time the interviews were conducted on the beach and often it was possible to observe directly that the information provided by the fishermen was correct.
During the first stay in Puerto Rico, the study was intended to address itself more specifically to the way the fishermen allocated their resources between various economic activities. For this reason the year had been divided into three periods and to some of the questions the fishermen were expected to give an answer for each period of the year. This was the case for the number of days at sea for example. After analyzing the results of the first part of the survey, when it appeared that few fishermen had other economic activities, it was decided to ignore this aspect of the problem. Consequently, during the second set of interviews the fis hermen were asked to give only one aggregate answer for the whole year 1972.