Characteristics of renewable resources and implications for allocation
 renewable resource "regrow" naturally, e.g. fisheries, forests, etc.

growth needs to be incorporated when deciding how to allocate resource over time, which requires consideration of net growth
What is net growth/a net growth function? (example: fisheries)

Net growth accounts for new offsprings and deaths (new offsprings  deaths)
 The net growth function show the net growth for a given population size, taking into account that:
 initially birth effects dominate leading to higher growth and an increase in the population size, but
 evenutally growth leads to overcrowding, which increases death rates and decreases the net growth
 The carrying capacity of the ecosystem (how many fish an eco system can sustain is represented by K, which results in a growth rate of zero.
 The maximum sustainable yield is reached at the top of the net growth curve (g(S_{MSY}) and S_{MSY}). This represents a biological optimum, not an economic optimum.
 initially birth effects dominate leading to higher growth and an increase in the population size, but
 evenutally growth leads to overcrowding, which increases death rates and decreases the net growth
Describe the dynamics of the growth function.
(equilibrium in absence of intervention, dynamics at different stock levels)
 If the population (S) stocks will increase due to positive net growth.
 If the population (S) > carrying capacity (K), stocks will decrease due to negative net growth.
 If the population (S) (the minimum stock needed for a species to survive), growth will be negative and the fish stock will collapse.

Without intervention, the stock will converge at S=K and will form an equilibrium. The stock will not change at this point. If there is a small deviation from this equilibrium, the system will automatically return to the equilibrium in the absence of human intervention.
What is the forumla for the evolution of a fish stock over time
 New stock = old stock + natrual net growth g(S)  harvest h (S_{t+1 }= S_{t} + g(S_{t})  h_{t)}
 When g(S_{t}) = h_{t} the stock remains the same.
Tragedy of the Commons (static model): What is the outcome in a competitive market in a static equilibrium? Will it result in MSY (maximum sustainable yield)?
Static equilibrium: point where stock does not change over time (harvest = growth)
 In open access fishery, where everybody can fish:
 revenues (R) = price (p) x harvest (h).
 total costs (TC) = constant marginal cost (c) x effort (E).

profit = revenues  total costs
 In a competitive market, an equilibrium is reached where profit = 0 (at E_{c}), as entry and exist of competitors ensures that profits are driven down to zero to avoid new entry.
 However, the profit maximizing outcome is reached when the slope R = slope TC (at E* where the difference between R & TC is maximised).
 Comparing E_{c} to E*: E_{c} = higher effort, results in lower proditcs and lower stock size.
 Thus, a competitive market will not result in MSY.
Tradegedy of the Commons (static model): Why is the competitive market outcome not efficient?
 Property rights are incomplete
 If crews were to reduce effort in order to increase stock/profits in the next period, another boat would come in and catch those fish, leaving the first crew without a reward.
 Externalities
 Selfinterested parties do not consider that fishing increases the cost for others, thus leading to externalities and an inefficient outcome.
 If crews were to reduce effort in order to increase stock/profits in the next period, another boat would come in and catch those fish, leaving the first crew without a reward.
 Selfinterested parties do not consider that fishing increases the cost for others, thus leading to externalities and an inefficient outcome.
What are key issues associated with the tragedy of the commons (static model)?
 too much effort
 below optimal profits (driven to zero)
 overfishing (lowering fish stock
Tragedy of the commons (dynamic model): How are growth and stocks size related in the dynamic model? What is the optimum if harvest costs are stock independent?

In the dynamic model two time periods are considered. Therefore, tradeoffs between the two periods have to be taken into account.

If harvest costs do not depend on the stock size (stockindependent harvest costs), harvest h0 will result in stock size S0. The growth rate or payoff in the next period is defined as g(S0) and harvested units can be "put in a back account" and earn interest (r).

If the current harvest is reduced by one unit, the resulting stock will be S0+1, thus increasing the stock and the growth rate or payoff in the next period (g(S0+1) = g(S0) + g'(S0).

The optimal stock is reached when g'(S*) = r, or when the the payoff in the next period is equal to the interest rate. The optimum is larger than the max. sustainable yield stock.
In the dynamic model two time periods are considered. Therefore, tradeoffs between the two periods have to be taken into account.
If harvest costs do not depend on the stock size (stockindependent harvest costs), harvest h0 will result in stock size S0. The growth rate or payoff in the next period is defined as g(S0) and harvested units can be "put in a back account" and earn interest (r).
If the current harvest is reduced by one unit, the resulting stock will be S0+1, thus increasing the stock and the growth rate or payoff in the next period (g(S0+1) = g(S0) + g'(S0).
The optimal stock is reached when g'(S*) = r, or when the the payoff in the next period is equal to the interest rate. The optimum is larger than the max. sustainable yield stock.
Tragedy of the commons (dynamic model): what is the optimum stock if harvest costs are stockdependent?
 Assumign stockdependent harvest costs, the optimum stock size will be smaller than the max. sustainable yield stock size.
 Hence by harvesting less now future harvest costs are reduced, as stock is higher and resulting harvest costs are lower.
What are two possible solutions to the openaccess/tragedy of the commons problem?
 informal local enforcemet / collectives e.g. maine lobster fisheries, which incentivises better stewardship by ensuring rewards can be reaped in the next period.
 Formal government regulation e.g. restriciting fishing (area, effort, or technology) or economic incentives
National vs international regulation of fisheries
 Internaitonal regulation: UN Covention on the Law of the Sea dictates
 territorial/sovereign territorial waters exxtend 13.8miles from shore
 exclusive economic zones (EEZ) extend 230 miles, where countries have rights over resourcs (house more than 80% of fish)
 As such nonmigratory species/fisheries can be regulated by national governments, reducing the need for international regulation.
 territorial/sovereign territorial waters exxtend 13.8miles from shore
 exclusive economic zones (EEZ) extend 230 miles, where countries have rights over resourcs (house more than 80% of fish)
How can government regulate open access fisheries using traditional policies? What are the problem related to each policy?
 Restrict length of fishing season
 Problem: push to supersize ships to max catch during shorter season
 Restrict technology e.g. min fish net size to allow young fish to escape
 Problem: Average fish size decreases as it adapts (Darwin)
 Restrict fishing areas
 Problem: fishermen will relocate effort around reserves to catch fish as they leave the reserve
 Make effort more costly
 Advantage: leads to higher fish stock
 Disadvantage: zero profits = wasted resources
 Problem: push to supersize ships to max catch during shorter season
 Problem: Average fish size decreases as it adapts (Darwin)
 Problem: fishermen will relocate effort around reserves to catch fish as they leave the reserve
 Advantage: leads to higher fish stock
 Disadvantage: zero profits = wasted resources
Since the problem of open access are caused by imperfect property rights what are economic incentives to address open access problems?
 Institute property rights
 Individual transferable quotas (ITQ), which allocate shares to fishermen based onthe total allowable catch (TAC).
 Every fish caught requires and ITQ and ITQs can be freely traded.
 To maximize the value of the ITQ, the value of the fishery need to be maximized, thus giving fishermen an incentive to reach an optimal level of fishing.
 Problem: bycatch (other species that may be discarded)
 Territorial Use Rights Fisheries (TURF)
 grants local monopolies to fishermen, who now get rewarded for optimally managing the fishery
 Problem: does not work for migratory species

 Individual transferable quotas (ITQ), which allocate shares to fishermen based onthe total allowable catch (TAC).
 Every fish caught requires and ITQ and ITQs can be freely traded.
 To maximize the value of the ITQ, the value of the fishery need to be maximized, thus giving fishermen an incentive to reach an optimal level of fishing.
 Problem: bycatch (other species that may be discarded)
 grants local monopolies to fishermen, who now get rewarded for optimally managing the fishery
 Problem: does not work for migratory species
Case study: Atlantic sea scallop fisheries
 US implemented mix of size, effort and area controls > saw a decrease in catch per day
 Canada implemented ITQs resulting in higher overall abundance and bette protection of undersized scallops > 7fold increase in catch per day
 equity concerns were unfounded as
 65% of quota's still held by original owners (no crowding out of smaller fishers
 boats operate under lay system under which crews get a percentage
 equity concerns were unfounded as
 65% of quota's still held by original owners (no crowding out of smaller fishers
 boats operate under lay system under which crews get a percentage
Case study: Fishery collapse and ITQs study
 Study found that instituting ITQs reverse the trend of fisheries on the path to collapse
Case study: US rebuilding program study