Renewable resource topics

Renewable resource topics Growth curves Rate of exploitation Costs and revenues Optimal harvest Renewable resource: The case of fishery Definition: Renewable resources are those could reproduce or replenish after being exploited or harvested. These resources also are capable of being fully exhausted if too many harvesting and extraction activities are carried over some period of time. Stock and flow of the resource Stock: the population or the biomass of the resource measured at a point in time (number of fish or the average weight of the fish population) Grow in number or weight or both Diminishing as fish die, being removed, killed by environmental contaminants Changing over time Flow: the change in the stock over an interval of time resulting from biological factors (birth, death), and economic factors (harvesting) The logistic growth curve Stock (S) Time St : The stock at time t Gt: The growth in the stock : Gt = G (St) The logistic growth curve Stock (S) Time ( t) Stock (S) Rate of Stock Growth SMax : maximum population SMin : minimum population S MSY:a particular stock size at which the stock growth is maximum Growth rate = 0 at SMax,& Smin Catching effort and resource stock Stock (S) G (St) (ton) Harvest/time (ton) Renewable resource Rate of exploitation E = catching effort S = stock H = harvest Maximum sustained yield occurs when the rate of growth of the resource reaches a maximum. MSY can be harvested from the stock and if allowed to regenerate itself, MSY can be harvested next time around and so on. Relationships between harvest, population size and effort Harvest per unit of time (H) Stock (S) MSY E1 E* S1 H1 E2 H2 S2 From growth-effort to effort-harvest functions E5 Stock (S) H Effort (E) H E4 E3 E2 E1 h1 h2 h3 h4 h5 E1 E2 E4 E5 E3 S4 S5 S3 S2 S1 Economics of fishery management Effort (E) R∏ TC = PE X E Profit maximisation R - C = Max C∏ E∏ Revenue, cost (€) TR = PH X HE Renewable resources: open access Effort (E) HPROF TC = PEE Profit maximisation R - C = Max EPROF Revenue, cost (€) EOA EMAX TR = PH HE HOA Open access = EOA and HOA Private property = EPROF and HPROF [Source: Pearce and Turner, 1990] Remarks Profit maximizing equilibrium does not coincide with MSY (highest sustainable harvest) Optimal harvest in our example implies that the stock is larger than that corresponding with MSY Effect of a tax on fishing effort $ Effort TC0 TC1 E0 A unit tax t on Effort TC1 = PEE + tE = (PE +t ) E Effect of a tax on unit of fish catch $ Effort TR0 TR1 E0 A unit tax t on fish catch TR1 = (PH - t ) H TC