ENGS 41. SUSTAINABILITY and NATURAL RESOURCE MANAGEMENT. Biomass. (Lynch book, Chapter 2) Benoit Cushman-Roisin 16 January Exhaustible resource

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1 ENGS 41 SUSTAINABILITY and NATURAL RESOURCE MANAGEMENT Biomass (Lynch book, Chapter 2) Benoit Cushman-Roisin 16 January 2018 From Lynch s book preface (page xiv), augmented Exhaustible resource S Renewable resource Q Sterile Coal Oil Minerals Water Living Forest Pasture Fish Forest Pasture Fish descent into exhaustion resource mining Unlike exhaustible resources, living systems present the possibility of sustained resource usage. But achieving sustainability requires caution, less one overexploits the resource. 1

2 Sustainability of exploitation of a living resource requires meeting two aspects: 1. Balance between growth and extraction, 2. Balance between nature and economy. The natural balance: We define the following variables: The mass balance is: B(t ) = amount of biomass at time t G(t ) = biological growth rate H(t ) = harvesting rate db G H dt A realistic growth rate function is the so-called logistic function: GB ( ) gb1 B K Logistic Growth: GB ( ) gb1 B K For small amount B of biomass, G gb This is the frontier situation with exponential growth: Example: Invasive species in its early stage. db gb B B 0 e gt dt Peak growth occurs for K 1 B Gmax gk 2 4 When B reaches K, growth stops. Thus, K is the carrying capacity of the system. If there is no harvest, B grows until it reaches K : db 0 when G 0 for B K dt 2

3 Growth with harvest: Harvest rate Harvest with effort: Any harvest, such as cutting trees in a forest or pulling fish from the sea, necessitates people and equipment. This need acts as a factor in the rate of harvest: H heb in which E is the effort expanded. The stronger the effort E, the greater the harvest H. The coefficient h represents the harvesting technology (higher for more efficient technology). The last factor B is included because the more biomass is present, the more can be extracted at a fixed level of effort. 3

4 At steady (sustainable) state, HG H heb g B B E 1 G gb1 h K K g h g 2h E Collapse (lots of effort on the little there is) MSY Clearly, excessive effort (E > g/2h) will lead to collapse. K 2 100% bio K B From this perspective, we deduce that the Maximum Sustainable Yield is somewhat precarious. A little more load on the system, such as slight harvest increase by a few cheaters or slightly reduced growth due to inclement weather, and the system risks collapsing. Compensatory vs. depensatory growth: 4

5 Revenue from harvesting: Harvesters may not be interested in the Maximum Sustainable Yield of the system. They are more likely to be interested in maximize their profit. If p = market price of 1 unit of harvest and c = cost of 1 unit of effort, then the revenue (rent) is: ph ce H G B cg B At steady state: ( B) ph c pg c pgb 1 1 hb hb K h K Depending on slope of cost, the MSY may correspond to negative revenue! Revenue as a function of harvest: H ph ce with E hb c ( H) p H hb Clearly, revenue will be a profit (>0) only if c c p 0 B hb ph The above revenue considerations were based on consensus among the various actors, acting together as a monopoly. This situation is called controlled-access equilibrium. What happens when the actors behave independently? One way to tackle this is to ask: With actors currently acting with consensus, how would a new, independent actor behave? 5

6 New harvesters will enter the business as long as the market value of the harvest exceeds the cost of harvesting, that is, as long as money is to be made ( > 0). This depresses the biomass (B) and causes a drift away from MSEY to point R 0, when the net revenue vanishes. At R 0 : 0 B B 0 c ph Point R 0 is a stable equilibrium: Move left, people lose money and exit the business, B, move back right. Move right, money is to be made, new entrants, B, move back left. This laissez-faire situation is called free-access equilibrium. Effort dynamics: If money is to be made, existing harvesters if allowed will have a tendency to increase their effort to increase their revenue. This can be modeled as follows: db G H dt B G gb1 K H heb ph ce de v new dt These dynamics leads to the ultimate state of vanishing revenue, possibly after some oscillations during which actors may temporarily lose money. Excel simulation:fish1.4.xlsx 6

7 What happens when the effort depends strongly on the revenue. Initial costless harvesting: Consider a new fishery. One or several fishers go in for a first time, they make a first huge harvest, earning them a substantial lump sum that they invest in the bank, earning interest r. Afterwards, they all continue harvesting at the sustainable rate (H = G) for the remaining biomass B. Initial harvest: Thereafter: K Money being made: Maximum to this? B H G gb 1 B K ph rp( K B) d dg dg 0 p rp r db db db Note: r must be less than g= dg/db B=0, otherwise the system will be run to extinction. 7

8 In this scenario, r must be less than g= dg/db B=0, otherwise the system will be run to extinction. Thus, for a slowly growing resource (g < r), a one-time big harvest leads to extinction. Explanation: Money grows faster in the bank than the resource, and the strategy of deplete + invest is the most lucrative one. It is economically sustainable. Of course, this is terrible from the perspective of the biological system, which is ruined. Thus, governmental regulations are essential whenever g < r. Special attention is required when interest rates go up. 8