Because there is no organized market for wetland services, we can use the marginal productivity method to assess the external economic benefits that accrue to commercial fishermen from Florida wetlands. This theory is based on the premise that the value or price in an organized market is the sum of the marginal contribution of each of the factors of production such as capital and labor. The harvesting of fish, for example, involves vessels, deckhands and, of course, wetlands. According to marginal productiv- ity theory, a wetland or saltwater marsh is a third factor of production for those species of fish that depend on the marsh for food and protection during at least some of their lifetime. More than 90 percent of the commercial species harvested in Florida depend on wetland habitats at some time in their life cycle (Bell 1989). We first give a sketch of
the theory and then progress to more complex expressions that are actually used in obtaining the results.
According to marginal productivity theory, the combination of labor and capital (i.e., fishing effort) by harvesters with fish habitat services determines the number of fish caught. Consider the following linear production function, equation, which relates harvests to effort and wetland productivity:
Q(i) = c(o) + c(l) E(i) + c(2) W(i), where (1)
Q(i) = harvest (pounds) of the i’th estuarine-dependent fish species E(i) = fishing effort applied to the i’th species in question (e.g.,
standardized fishing days)
W(i) = wetland acres (e.g., saltwater marsh) affording services to the i’th, species in question,
c(l), c(2) = positive coefficients
We begin with the assumption that the coefficient c(2) = 10. This means that an increase (or decrease) in one acre of wetland will increase (or decrease) the catch by 10 pounds, if fishing effort and other environmental factors are held constant. To arrive at an esti- mate of the value of one more acre, we ask what consumers are willing to pay for the additional 10 pounds of fish. Assuming the additional 10 pounds do not depress ex- vessel price (because it is a very small addition to the entire market), the marginal value product of wetlands (MVPW) may be calculated as:
MVPW = P X MPW, where (2)
P = Ex-vessel value of a pound of fish
MPW = Marginal productivity of saltwater marsh
Assuming that P = $2, then for an MPW of 10 pounds, the MVPW = $20. In effect, the $20 represents the marginal fish value for the i’th species from adding one single acre of wetlands. This is a simplified example and does not account for such complexities as the relation between fish catch and fishing effort, which has been assumed to be linear.
In any ecosystem, a biomass of the i’th estuarine-dependent species is limited to some maximum size such as “B.” Space, predators and, of course, the abundance of wetlands providing food and protection services limit the size of any biomass. So a bio- mass will usually grow rapidly if relatively small, but slowly if relatively large. If we eliminate some saltwater marsh or mangroves from the ecosystem, this will potentially reduce the maximum size of the biomass or B*. Thus, there are two relationships to consider. How does fishing effort impact the fish harvest when the size of the habitat or wetlands is held constant? If the size of the wetlands changes, what is the effect on the maximum value for B*? Using the Schaefer (1954) model of population dynamics for fish, we have the following expression for the catch function for fish:
Q(i) = B* {AE(i) - C E(i) }2, where (3)
Q(i) = harvest (pounds) of the i’th estuarine-dependent fish species E(i) = fishing effort applied to the i’th species in question (e.g.,
standardized fishing days)
B* = the maximum size of the i’th fish population given a fixed or constant amount of wetlands.
A, C = constants that are parameters of the production function (see page 48)
This Schaefer catch function is parabolic in nature and has a maximum sustainable yield at the peak of the function. This function is depicted in Figure 5.1. Notice that if the biomass B* is increased, then the fish yield function will shift upward; if it is decreased, the fish yield function will shift downward. Thus, at any level of fishing effort, E(l), the catch will be higher the greater the biomass (B*), or lower the smaller the biomass. The upper level of the potential biomass is determined by how favorable or unfavorable environmental conditions are.
As wetlands or saltwater marsh are increased, the potential upper limit of the biomass would be expected to increase; conversely, if the wetlands decreased, the bio- mass would likely decrease. Not knowing what this functional form is from either a theoretical or empirical basis, we use a simple equation:
B* = DlnM, where (4)
ln M = the natural logarithm of saltwater marsh D = a positive coefficient
The equation indicates that B* will rise as the natural logarithm of M increases. By using the logarithm, the function and other functions derived from this relationship will be non-linear, which has been suggested by some as the approximate relationship. The last step in getting the fishery yield curve is to substitute the above equation into the traditional Schaefer yield curve, which leads to the following function:
Q(i) = DlnM { AE(i) - CE(i) }2 (5)
The marginal productivity of saltwater marsh (MPW) is simply the first derivative of the above function with respect to lnM, holding the level of fishing effort constant. This is nothing more than the incremental contribution of one acre of saltwater marsh to the production of the i’th species of commercial fish and represents the external economic benefit of wetlands to fishers.
Owners of saltwater marsh cannot easily charge for such benefits because of the market failure discussed earlier. The marginal productivity of saltwater marsh (MPW) will vary with the level of marshland and fishing effort. If fishing effort is held con-
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stant, while aggregate marshland is increased, the MPW will decrease in a nonlinear fashion, illustrating the principle of diminishing returns to more and more marshland. In other words, the fish catch or harvest will rise as marshland is increased, but by decreasing increments. When the change in catch induced by a change in marshland, or the MPW is multiplied by the ex-vessel price for the i’th species, we have the marginal value product or MVPM(i) as discussed earlier. In this next section, we turn from theory to application.