Conference 2015 New management issues within the reformed Common Fisheries Policy

New management issues within the reformed Common Fisheries Policy: implementation and socio-economic impacts 28th – 30th April 2015, University of Salerno, Italy

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New management issues within the reformed Common Fisheries Policy:
implementation and socio-economic impacts
28th – 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

phil@erinecon.com

prodgers@lincoln.ac.uk

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 2011 and calculates the coefficients of a production function.

Keywords: Life-Cycle, Gordon-Schaefer, Production Function
JEL Classification: Q22

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 applying a life-cycle approach to the West of Scotland fishery for atlantic cod which is achieved 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

where

represents 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

where

represents capital, the lone variable input in the model, if we assume

, then the 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, α_0, 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 equilibrium persists 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 multiplying it 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 stock may then be back-calculated by summing the

However, in the absence of values for the production function coefficients

and

the model remains unidentified. This difficulty may be overcome by using ICES¹ 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 CFP² 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 cod commenced only in 1983 (ICES 2015) so the values of the coefficients, α₁ and α_2, 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 West of 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 1 illustrates 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) http://www.ices.dk/marine-data/dataset-collections/Pages/Fish-catch-and-stock-assessment.aspx, viewed 3^rd 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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