Over-exploitation of natural resources is followed by inevitable declines in economic growth and discount rate

Abstract

A major challenge in environmental policymaking is determining whether and how fast our society should adopt sustainable management methods. These decisions may have long-lasting effects on the environment, and therefore, they depend critically on the discount factor, which determines the relative values given to future environmental goods compared to present ones. The discount factor has been a major focus of debate in recent decades, and nevertheless, the potential effect of the environment and its management on the discount factor has been largely ignored. Here we show that to maximize social welfare, policymakers need to consider discount factors that depend on changes in natural resource harvest at the global scale. Particularly, the more our society over-harvests today, the more policymakers should discount the near future, but the less they should discount the far future. This results in a novel discount formula that implies significantly higher values for future environmental goods.

Fig. 1

Schematic illustration of the model. Demonstrated is the state of the system at the global scale (e.g., the entire planet’s marine area, forest area, or agricultural area) in a given year. The dark-gray area characterizes the part of the system that is degraded due to former non-sustainable harvesting. The light gray area with the arrows characterizes the part of the system that is being harvested non-sustainably and will be degraded starting next year (total dark-gray area is given by H_n). The green area with the fishing vessels characterizes the part of the system that is being harvested sustainably and will remain non-degraded next year (total green area is given by H_s). (Note that the total area under harvest, H, is given by the green and the light gray areas combined, H = H_n + H_s). The blue area characterizes the part of the system that is not degraded but is still not being harvested. We assume that the spatial scale of the system is very large, and therefore, the recovery of the degraded areas due to migrating biota from other regions is negligible and the total degraded area increases over time. Each year, H_n and H_s are determined by the aggregate management by all the managers. We assume that managers may be subject to different externalities in distinct regions, e.g., some regions are managed by a single manager that dictates the harvest method, while some regions are shared (open-access), and all managers are free to harvest in them (rightmost region). The variables x₁ and x₂ (Eqs. 7 and 8) characterize the total non-degraded areas (blue, green, and light gray) in the managed and in the shared regions, respectively

Fig. 2

Over-harvesting extends the period during which the discount rate is high, but it is followed by sharp declines in the discount rate and the cumulative discount. Panels a and b demonstrate the optimal harvest of the natural resource from a social planner’s perspective, where the natural resource and the other goods are either non-substitutable (a, Eq. B2) or partially substitutable (b, Eq. B10). In the early stages, harvesting activity increases exponentially and the discount rate is high. Approximately at time t₀, when harvesting is occurring in the whole system (H_s + H_n = x₁ + x₂), the total harvest stops increasing and the discount rate decreases. Next, panels c and d demonstrate harvesting in a competitive market in which some of the regions are shared. The parameters and utility functions used in panels c and d are identical to those used in panels a and b, respectively. The period during which the discount rate is high is extended until t = t₁ due to over-harvesting of the natural resource in the shared regions (compare panel a with panel c, and compare panel b with panel d). However, this period is followed by a rebound in which harvesting declines and the discount rate and the cumulative discount drop. In addition, around t = t₁, the price of the natural resource increases and the total product decreases. Note that, in accordance with the theorem, the cumulative discount approaches lower values if the harvest is determined by the market. Scaling: the harvest rates are given in (years)⁻¹, the total non-degraded areas are given in units showing the maximal annual sustainable yield (ax₁ and ax₂), and Δ is given by 100 times the value on the y-axis. The parameter values used are within their realistic ranges (Methods). Parameter values and Source data are provided as a Source Data file

Fig. 3

Social welfare and the cumulative discount are ultimately lower if the transition to sustainable harvest is more gradual. Demonstrated are the aggregate non-sustainable harvest, H_n(t) (solid lines); the aggregate sustainable harvest, H_s(t) (dashed lines); and the cumulative discount, Δ (dotted lines), for two systems. System 1 (blue) follows the market solution, in which society abruptly stops harvesting non-sustainably at t = t₁. System 2 (purple) follows the same dynamics until t = t₁, but then, society gradually shifts to sustainable harvest. The gradual transition postpones the decline in the cumulative discount, but ultimately, it declines to an even lower value than its value in system 1. Moreover, the cumulative welfare, U^t, in system 1 is initially smaller, but it ultimately becomes greater compared to system 2 (gray). Harvest rates are given in units of (years)⁻¹, and Δ is given by 100 times the value on the y-axis. The parameters are the same as in Fig. 2c (Parameter values and Source data are provided as a Source Data file)

Fig. 4

The decline in the cumulative discount is unavoidable (demonstration of the theorem). At some point in time, −t₀, some planetary boundaries for harvest have been approached, and the rate of discount that would have occurred if managers used only sustainable harvesting has decreased from δ_today to δ_sus (blue lines, Δ_sus). Nevertheless, due to over-harvesting, the economy grew faster and the cumulative discount, $\mathrm{\Delta }\left(t\right)={\int }_0^t\delta \left(t\prime \right)\mathrm{d}t\prime$, continued to grow at a higher rate, δ_today (solid orange lines), at least until today (t = 0). In turn, the future value of Δ(t) depends on the future harvest patterns. If over-harvesting continues, the discount rate might remain close to δ_today for several years or decades (dotted orange lines). But in the longer run, according to the theorem, Δ has to decrease below the blue curve that characterizes Δ_sus, regardless of how the resource is being harvested. This is also demonstrated for three scenarios in panel a: In scenario 1, the non-sustainable harvest stops today, while in scenarios 2 and 3, the non-sustainable harvest continues for a few decades and then declines gradually. Also, note that Δ_sus increases at a rate δ_sus, so if one assumes that the discount rate remains δ_today for the next τ years and becomes δ_sus afterward, then he/she needs to subtract at least ϕ_τ to obtain the correct Δ (Eqs. 2 and 3). (The value of ϕ_τ is demonstrated in Fig. 5.) We assume that u(c, f) is given by Eq.  B5 (non-substitutable goods) in panels a and c, and by Eq.  B12 (partially substitutable goods) in panels b and d. In turn, the scenarios are calculated for three different choices of H_n(t), where the dynamics follow Eqs. 6–9 with H(t) = x₁(t) + x₂(t) for all t. The parameter values used are within their realistic ranges (Methods). Parameter values and Source data are provided as a Source Data file

Fig. 5

Endogenizing changes in harvest patterns implies a larger discount factor and higher values for future environmental goods. If a policymaker considers a gradual transition to sustainable harvest that would occur within τ years, then he/she may consider a sustainable discount rate, δ_sus, starting from year τ. In addition, however, he/she needs to add to Δ another factor, ϕ_τ, that accounts for the decline in the cumulative discount that will follow due to over-harvesting prior to time τ (Eqs. 2, 3 and Fig. 4). This factor may impose significantly higher values on future goods, e.g., over two times higher if τ = 50 years and g_f = 1% year⁻¹ (exp(ϕ_τ) > 2 in both panels a and b) and even significantly higher for higher values of τ or lower values of g_f. However, if the long-term provision of the natural resource continues to increase at the same rate as the other goods, i.e., g_f = g_c = 2% year⁻¹, then δ_sus = δ_today and ϕ_τ = 0 (Eq. 3). The other parameter values are the same as in Fig. 4 (Parameter values and Source data are provided as a Source Data file)