CONFERENCE 2015

New management issues within the reformed Common Fisheries Policy:implementation and socio-economic impacts28th – 30th April 2015, University of Salerno, Italy

An Application of Life-Cycle Theory to the West of Scotland Cod Fishery

P.E. Rodgers

College of Social Science

University of Lincoln

Brayford Pool

Lincoln LN6 7TS

United Kingdom

ABSTRACT

This paper applies a life-cycle approach to the West of Scotland fishery for atlantic cod. It acknowledges the fish stock as a harvestable resource regardless of growth levels and drops the assumption usually accepted in fishery models that a long-run non-zero bioeconomic equilibrium will develop where the catch and growth will be equal. Instead, successive short-run economic equilibria develop at the cost of long-run equilibrium. The impact of this is to treat the growth and output as corrections to the volume of the fish stock reserve. A second consequence is that the control variable representing the presence of the fish stock in the production function can be re-defined to accommodate it. The model simulates the rise and fall of the fishery from 1950 to 2011and calculates the coefficients of a production function.

Keywords:Life-Cycle, Gordon-Schaefer, Production Function

JEL Classification: Q22

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An Application of Life-Cycle Theory to the West of Scotland Cod Fishery

I have long thought that the paucity of economic data on fisheries was a serious impediment to the development of economic models of fisheries. This paper rather disproves this assertion while at the same time highlighting the gains that could be made in improved specification of the basic economic model of fisheries if data for the time series in the functions were available.

This view is illustrated by applyinga life-cycle approach to the West of Scotland fishery for atlantic cod which isachieved by dropping the assumption usually accepted in fishery models that a long-run non-zero bioeconomic equilibrium will develop where the catch and growth will be equal (Gordon 1954, Schaefer, 1954).

Instead, it is assumed only that successive short-run economic equilibria develop and this proves to be at the cost of long-run equilibrium. The Gordon-Schaefer model only reaches bionomic equilibrium because it assumes in the first place that it will be achieved.

By dropping this assumption we can observe that the fish stock resource would be harvestable just like a mineral reserve even if it were unable to grow or reproduce. This means that growth may be treated as a correction to the size of the fish stock reserve rather like new reserves of a mineral being found but the implication is that there is no reason for a fishery under open access to come to a biological equilibrium where there is economic activity.

A second consequence is that the control variable representing the presence of the fish stock in the production function can be re-defined to accommodate this. The model simulates the rise and fall of the fishery from 1950 to 2011 and calculates the coefficients of a production function.

Consider the standard Gordon model of fisheries. In open access economic equilibrium will be achieved at zero profit,, in each time period such that

whererepresents the price achieved in time period t and is exogenously given by the availability of fish elsewhere. represents the short-run equilibrium volume of output and represents the total cost of output.

Since

whererepresents capital, the lone variable input in the model, if we assume, thenthe constant , the unit cost of capital, may be calculated as

From (3), the capital used may be determined for each time period from a re-arrangement of (1) with (2) substituted

By assigning a value of unity to the volume of the fish stock used in the base year, a value for the constant term, α0,may be determined in a short-run Cobb-Douglas production function

where is an index of the amount of the fish stock reserve used in production (Cobb and Douglas 1928).

The question then arises as to how much of the output in each period is contributed by growth of the fish stock reserve (which does not therefore deplete it) and how much the reserve is depleted.

The short-run economic equilibriumpersists throughout the life cycle but the levels of revenue product and use of the non-fish stock factors of production vary with the declining volume of the fish stock.

may be determined by re-arranging (5)and multiplyingit by the production function constant, γ, to raise it from an index to absolute values

Since represents the part of output drawn from the reserve fish stock, , the reserve fish stockmay then be back-calculated by summing the.

However, in the absence of values for the production functioncoefficients and the model remains unidentified. This difficulty may be overcome by using ICES[1] fish stock assessments, but of course application of the model is then limited only to those fisheries which are subject to ICES attention.

European Union management of the fishery has followed the usual CFP[2] rules of a quota system (which may or may not have involved tradeable rights).There were also technical measures relating to gears, minimum landing sizes and so on but management failed and the fishery is now subject to a moratorium. Figure 1 shows the progress of the fishery from 1950 to 2011.

ICES fish stock assessments for West of Scotland codcommenced only in 1983 (ICES 2015) so the values of the coefficients, α1and α2, were estimated over the period 1983 to 2011 by minimizing the sum of squared differences between the model estimates of the fish stock reserve and the ICES estimates. The estimate for α1was 0.9138 with α2 acquiring a value of 0.6713 – both reflecting diminishing returns to scale. α0 adopted the value of the 1950 volume of landings, 5,144 and was the value of output in 1950, €5.062m.

Figure 1: The Life-cycle in Open-Access of the Westof Scotland Cod Fishery

The present value of the contribution to social welfare from West of Scotland cod over the period 1963 to 2011 discounted at an annual rate of 5% is estimated to have been some €7,711m at 2011 prices. This was determined as the sum of the short-run producer surpluses, the area between the perfectly elastic demand curve (which offered no contribution from consumer surplus) and the supply curve.

The graph in Figure 1illustrates results from the model that imply that the fish stock was already in sharp decline in 1950. We appear to be observing the tail-end of the life cycle.

The ICES fish stock assessment is also shown in Figure 1. The correlation coefficient between the model’s fish stock reserve estimate and the ICES assessment is 0.9742 over the period 1983-2011, with a mean percentage difference of 6.01% and a percentage standard deviation of 27.62%.

References

Cobb C.W. and P.H. Douglas (1928) A Theory of Production, American Economic Review, Papers and Proceedings, Vol 18 Supplement, 139-165.

Gordon H.S. (1954) The economic theory of a common property resource: the fishery, Journal of Political Economy, 62, 124-42.

ICES (2015) viewed 3rd March.

Schaefer M.B. (1954) Some aspects of the dynamics of population important to the management of commercial marine fisheries, Inter-American Tropical Tuna Commission Bulletin, 2, 247-85.

Appendix: Results of the Model of the West of Scotland Cod Fishery, 1950 to 2011

Year / q / TR / k / Brelative / dB / B / Real Price (2011=1) / ICES Stock Assessment / SW
1950 / 5,144 / 5 / 1.000 / 1.000 / 5,144 / 221,249 / 984 / 106.882
1951 / 5,826 / 5 / 0.959 / 1.440 / 7,406 / 216,105 / 833 / 97.511
1952 / 8,628 / 9 / 1.700 / 1.224 / 6,298 / 208,699 / 997 / 164.423
1953 / 12,417 / 12 / 2.332 / 1.572 / 8,085 / 202,400 / 951 / 214.543
1954 / 15,024 / 15 / 3.056 / 1.473 / 7,578 / 194,316 / 1,030 / 267.428
1955 / 15,516 / 15 / 3.002 / 1.640 / 8,436 / 186,737 / 979 / 249.913
1956 / 15,680 / 15 / 3.019 / 1.663 / 8,555 / 178,301 / 975 / 239.036
1957 / 18,059 / 20 / 4.005 / 1.360 / 6,995 / 169,746 / 1,123 / 301.670
1958 / 17,001 / 20 / 3.863 / 1.266 / 6,512 / 162,751 / 1,150 / 276.765
1959 / 13,959 / 16 / 3.207 / 1.137 / 5,849 / 156,239 / 1,163 / 218.560
1960 / 11,668 / 15 / 2.878 / 0.920 / 4,734 / 150,391 / 1,249 / 186.598
1961 / 10,378 / 13 / 2.521 / 0.899 / 4,626 / 145,657 / 1,230 / 155.477
1962 / 9,764 / 10 / 2.020 / 1.180 / 6,072 / 141,031 / 1,047 / 118.513
1963 / 13,746 / 16 / 3.153 / 1.132 / 5,826 / 134,959 / 1,161 / 175.946
1964 / 23,164 / 30 / 5.878 / 1.181 / 6,074 / 129,134 / 1,284 / 311.975
1965 / 23,033 / 29 / 5.765 / 1.208 / 6,216 / 123,059 / 1,267 / 291.069
1966 / 17,133 / 20 / 4.022 / 1.195 / 6,148 / 116,843 / 1,188 / 193.178
1967 / 23,025 / 25 / 4.945 / 1.607 / 8,265 / 110,696 / 1,087 / 225.908
1968 / 24,357 / 24 / 4.725 / 1.991 / 10,242 / 102,431 / 982 / 205.309
1969 / 21,739 / 22 / 4.315 / 1.814 / 9,332 / 92,189 / 1,005 / 178.371
1970 / 12,682 / 15 / 3.034 / 1.011 / 5,201 / 82,856 / 1,211 / 119.281
1971 / 10,666 / 16 / 3.226 / 0.605 / 3,114 / 77,656 / 1,531 / 120.649
1972 / 14,699 / 28 / 5.558 / 0.460 / 2,365 / 74,542 / 1,914 / 197.749
1973 / 12,263 / 29 / 5.798 / 0.280 / 1,440 / 72,177 / 2,393 / 196.233
1974 / 13,652 / 27 / 5.327 / 0.420 / 2,159 / 70,736 / 1,975 / 171.504
1975 / 13,163 / 23 / 4.510 / 0.526 / 2,707 / 68,577 / 1,734 / 138.117
1976 / 17,405 / 37 / 7.392 / 0.399 / 2,053 / 65,870 / 2,150 / 215.310
1977 / 12,619 / 34 / 6.634 / 0.233 / 1,197 / 63,818 / 2,661 / 183.812
1978 / 13,521 / 34 / 6.727 / 0.266 / 1,368 / 62,620 / 2,518 / 177.301
1979 / 16,242 / 39 / 7.779 / 0.309 / 1,592 / 61,253 / 2,424 / 195.028
1980 / 17,870 / 35 / 6.981 / 0.472 / 2,426 / 59,661 / 1,977 / 166.478
1981 / 23,950 / 40 / 7.887 / 0.738 / 3,794 / 57,235 / 1,667 / 59,001 / 178.917
1982 / 21,965 / 40 / 7.929 / 0.598 / 3,078 / 53,441 / 1,827 / 58,258 / 171.098
1983 / 21,491 / 38 / 7.606 / 0.615 / 3,163 / 50,363 / 1,791 / 49,549 / 156.116
1984 / 20,552 / 39 / 7.720 / 0.540 / 2,775 / 47,200 / 1,901 / 53,107 / 150.744
1985 / 18,614 / 33 / 6.591 / 0.577 / 2,966 / 44,425 / 1,792 / 36,318 / 122.424
1986 / 11,526 / 25 / 4.954 / 0.325 / 1,674 / 41,459 / 2,176 / 34,433 / 87.533
1987 / 19,199 / 41 / 8.071 / 0.425 / 2,184 / 39,785 / 2,128 / 43,552 / 135.640
1988 / 19,182 / 41 / 8.037 / 0.427 / 2,197 / 37,601 / 2,121 / 42,508 / 128.486
1989 / 15,425 / 32 / 6.345 / 0.402 / 2,065 / 35,404 / 2,082 / 36,667 / 96.486
1990 / 11,777 / 24 / 4.664 / 0.383 / 1,968 / 33,339 / 2,005 / 26,936 / 67.470
1991 / 10,628 / 25 / 5.037 / 0.262 / 1,346 / 31,371 / 2,399 / 23,652 / 69.312
1992 / 9,022 / 21 / 4.074 / 0.267 / 1,371 / 30,024 / 2,286 / 23,542 / 53.317
1993 / 10,475 / 21 / 4.054 / 0.379 / 1,952 / 28,653 / 1,959 / 28,067 / 50.469
1994 / 9,131 / 17 / 3.412 / 0.381 / 1,961 / 26,701 / 1,892 / 26,570 / 40.408
1995 / 9,660 / 13 / 2.661 / 0.690 / 3,547 / 24,741 / 1,394 / 27,118 / 29.977
1996 / 9,580 / 14 / 2.685 / 0.665 / 3,423 / 21,194 / 1,418 / 24,049 / 28.768
1997 / 6,992 / 10 / 1.964 / 0.577 / 2,968 / 17,771 / 1,422 / 24,507 / 20.017
1998 / 5,671 / 9 / 1.766 / 0.434 / 2,232 / 14,803 / 1,577 / 17,234 / 17.127
1999 / 3,447 / 7 / 1.297 / 0.245 / 1,262 / 12,571 / 1,904 / 14,082 / 11.958
2000 / 3,064 / 6 / 1.144 / 0.236 / 1,213 / 11,310 / 1,891 / 14,853 / 10.041
2001 / 2,440 / 4 / 0.870 / 0.233 / 1,197 / 10,096 / 1,805 / 12,366 / 7.261
2002 / 2,231 / 4 / 0.801 / 0.221 / 1,137 / 8,899 / 1,817 / 11,461 / 6.356
2003 / 1,298 / 2 / 0.479 / 0.165 / 850 / 7,763 / 1,868 / 7,625 / 3.617
2004 / 596 / 1 / 0.222 / 0.115 / 594 / 6,912 / 1,885 / 4,641 / 1.594
2005 / 421 / 1 / 0.162 / 0.094 / 482 / 6,319 / 1,942 / 3,434 / 1.104
2006 / 491 / 1 / 0.186 / 0.102 / 527 / 5,837 / 1,920 / 3,662 / 1.210
2007 / 487 / 1 / 0.182 / 0.105 / 542 / 5,310 / 1,888 / 4,141 / 1.123
2008 / 445 / 1 / 0.167 / 0.101 / 517 / 4,768 / 1,895 / 3,621 / 0.980
2009 / 234 / 0 / 0.072 / 0.109 / 562 / 4,251 / 1,556 / 3,518 / 0.402
2010 / 249 / 0 / 0.091 / 0.082 / 420 / 3,689 / 1,847 / 4,228 / 0.484
2011 / 205 / 0 / 0.081 / 0.065 / 334 / 3,269 / 1,996 / 3,801 / 0.409

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[1]International Council for the Exploration of the Sea

[2]Common Fisheries Policy