Session Questions
Pleaseaddress the following questions after reading the session notes below. Inaddition, perform additional research if possible and list all references.
1.Thissession’s lecture strongly suggests that the economically efficient rate ofharvest is less than the maximum sustainable yield. Compare and contrast these two criteria.
2.Canyou find an example of natural resource policies (in the USA or elsewhere)that attempt to achieve efficient rates of harvest for renewable resources?
SessionNotes
Renewable resources generally involvebiological populations that continually replenish themselves (e.g., forests andfisheries). These resources are oftendescribed as interactive since a given population is jointlydetermined by both biological and social considerations. As a biological consideration, the growth ordecline of a biological population generally depends on the size of thatpopulation. For example, a populationthat is reduced below a critical level may be unable to sustain itself andtherefore becomes extinct. An obvioussocial consideration is the rate of harvest, which affects the biologicalpopulation size. In turn, the currentbiological population size influences future rates of harvest. Thus, our allocation decisions (how much toharvest and when) determine the flow of these renewable resources over time.
Thisinterrelationship raises at least two interesting questions.
·Whatis the economically efficient rate of harvest for a renewable resource?·Canmarkets achieve that efficient rate of harvest?
First we describe a basic model ofpopulation dynamics. Then we explore theeconomic efficiency implications that arise from that model.
A Basic Model of Population Dynamics
A generally accepted model ofpopulation dynamics was originally proposed by Schaefer in 1957. While more sophisticated models have beendeveloped since then, Schaefer’s model first described the essential populationresponses to alternative harvest decisions.It is useful to us because it describes the average growth of apopulation without introducing the confounding influences of variouscounteracting forces that affect real populations. This model is graphically illustrated below.
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It is important to realize that thismodel describes a long-term relationship that abstracts from the effects offood supply, competition, predation, and other short-term influences. Accordingly, the rate of population growth(vertical axis) is simply a function of population size (horizontal axis). This model suggests that the rate of growthincreases with population up to a certain point (S*), and decreases withpopulation beyond that point.
The population Sâ€_x009d_ is known as the naturalequilibrium. This is thepopulation size that would persist through time given no outside influencessuch as harvesting. Sâ€_x009d_ is an equilibriumbecause its rate of growth is zero, where births exactly offset deaths. This equilibrium is also stable. A temporary decrease in population from Sâ€_x009d_would result in a positive rate of growth that would eventually return thepopulation back to Sâ€_x009d_. Conversely, atemporary increase in population from Sâ€_x009d_ would result in a negative rate ofgrowth that would eventually return the population back to Sâ€_x009d_. The stable nature of this equilibrium allowsit to persist through time through various natural perturbations.
The population S’ is also anequilibrium since its rate of growth is zero.However, this equilibrium is not stable.Any decrease in population below S’ would result in negative rates ofgrowth that would eventually cause extinction.Therefore, this level is known as the minimum viable population. On the other hand, any increase in populationfrom S’ would cause positive rates of growth that would eventually drive thepopulation to its natural equilibrium at Sâ€_x009d_.
We have discussed only some biologicalconsiderations that influence the availability of renewable resources. We now turn to some social considerations inthe form of harvest. We harvest lumberfrom forests and fish from oceans. But howdo these harvest activities influence the availability of renewableresources? The simple model ofpopulation dynamics presented above provides an analytical structure to answerthis question. We begin by describing a sustainableyield as a level of harvest that equals the growth rate of apopulation. If only the growth of agiven population is harvested, then that population size will remain constant,neither increasing nor decreasing.Therefore, the rate of growth illustrated in the graph above alsodescribes the sustainable yield for various population levels. Given that, one can easily see that the maximumsustainable yield is the rate of growth associated with populationS*. In other words, S* is the populationthat yields the maximum growth that can be harvested repeatedly on asustainable basis. Larger levels ofharvest are possible, but they cannot be sustained since they would lead tolower population sizes and eventually extinction.
We often hear of managing renewableresources for maximum sustainable yield as one allocation criterion. It sounds intuitive since society wouldproduce more of the resource over time.But is it economically efficient?
Statically Efficient Sustainable Yield
The short answer is no – maximum sustainableyield is not economically efficient. Thereason is that maximum sustainable yield as a criterion only considers thebenefits of harvest and not its costs.Economic efficiency, on the other hand, is concerned with maximizing netbenefits, which are benefits minus costs.
Let’s take a closer look. Consider the following graph whichillustrates the concept of statically efficient sustainable yield. The statically efficient sustainable yield isthe level of harvest that, if maintained indefinitely, would produce thelargest net benefit year after year.This concept illustrates the basic idea of efficiency withoutcomplications involving discounting.
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The following simplifying assumptionsare made.
Theprice received for the resource (e.g., price per ton of fish in acommercial fishery) is constant – it does not vary with the total amountsold.Themarginal cost of harvest effort (e.g., cost per vessel-day of fishing) isalso constant – it does not vary with the total level of effort expended.Theyield per unit of harvest effort (e.g., tons of fish per vessel-day) isproportional to the resource population size – larger populations yieldmore per unit of harvest effort than smaller populations.
Given these assumptions, the totalrevenue and total cost of sustainable levels of effort arerepresented in the graph above. Notethat the horizontal axis of this graph is effort, not population. A sustainable level of effort produces asustainable yield year after year. Considerthe following.
Theshape of the total revenue curve obtains directly from the shape of thelong-term population growth curve.It reflects the assumptions of a constant resource price and aproportional yield per unit of harvest effort.Thelinear shape of the total cost curve derives directly from the assumptionof a constant marginal cost of harvest effort.Anincrease in harvest effort obviously results in a reduced resourcepopulation. This is represented bya leftward move along the long-term population growth curve.
E* is the level of harvest effort thatproduces the maximum sustainable yield.The net benefit generated by that level of effort is given by thevertical distance on the graph between the associated levels of total revenueand total cost (i.e., total revenue minus total cost). But that distance is not maximized at E* (youmight have to use a ruler to tell from this graph). Rather, net benefit is maximized at E’. That point also happens to be where the slopeof the total revenue curve (i.e., marginal revenue) equals the slope of thetotal cost curve (i.e., marginal cost).In other words, net benefit is maximized where marginal revenue equalsmarginal cost (i.e., the equi-marginal condition). Notice that the slope of the total revenuecurve is positive only for levels of effort that are strictly less thanE*. Therefore, since marginal costs arealways positive, the statically efficient level of harvest is always lessthan the maximum sustainable yield.
This analysis demonstrates thatmaximum sustainable yield can never be statically efficient given a positivemarginal cost of harvest effort. Onlywhen the marginal cost of harvest effort is zero (i.e., a perfectly horizontaltotal cost curve) would the slope of the total revenue curve equal the slope ofthe total cost curve at E*, the level of effort that produces the maximumsustainable yield. That whollyunrealistic situation (zero marginal cost) illustrates why the maximumsustainable yield is never statically efficient. Technological improvements in harvesttechniques might rotate the total cost curve downward, and thereby reduce themarginal cost of harvest effort. But acomplete reduction of marginal costs to zero is not reasonable.
The question of whether markets can achievethe efficient rate of harvest depends on the same considerations we discussedearlier this semester. For example, ifthe biological population is also a common property resource such as mostcommercial fisheries, then individuals will not have incentives to constraintheir harvest activities in order to maximize their long-term net benefit. Moreover, if the harvest activity alsoinvolves a negative externality, then individuals will not be responding to thefull scope of costs associated with their harvest activities. Therefore, to the extent that these marketfailures are significant issues for renewable resources, normal market forcescannot be expected to achieve efficient rates of harvest.
Conclusion
Renewable resources generally involvebiological populations that continually (or potentially) replenishthemselves. The maximum sustainableyield of a biological population is the largest rate of harvest that can bemaintained year after year. However,that rate of harvest is not economically efficient. Positive marginal costs of harvest effortimply an efficient rate of harvest that is less than the maximumsustainable yield. Normal market forcescannot be expected to achieve efficient harvest levels of renewable resourcesif market failures such as common property and externalities are present.