Geomorphology is the study of the shape of the Earth. In this book we take this quite literally, and address the shape of the Earth at many scales. We ask why it is spherical, or not quite spherical, why it has a distribution of elevations that is bimodal, one mode characterizing a quite well-organized set of ocean basins, another the terrestrial landscape. At smaller scales, we address why hilltops are convex, why glacial troughs are U-shaped, why rivers are concave up. At yet smaller scales, sand is rippled, beaches are cusped, hillslopes are striped, and mud is cracked. These are some of nature's most remarkable and visible examples of self-organizing systems. Each cries out for both explanation and appreciation.

Goals

We wrote this textbook to provide modern teachers and students of geomorphology with a formal treatment of geomorphic processes that acknowledges the blossoming of this field within the last two decades. It brings together between two covers the background that serves to attach our field with those of geophysics, atmospheric sciences, geochemistry, and geochronology. It honors the heightened importance of geomorphology in understanding the environment and its changes, with an attendant need to pose these problems more formally.

The book is intended to be used in an introductory geomorphology course in which the attention is more on the processes that shape landscapes than on the cataloging of landforms. Most likely such a course will fit into a third and fourth year undergraduate or an introductory graduate curriculum.

RENEWABLE, NONRENEWABLE, AND ENVIRONMENTAL RESOURCES

Economics might be defined as the study of how society allocates scarce resources. The field of resource economics, would then be the study of how society allocates scarce natural resources, such as stocks of fish, stands of trees, fresh water, oil, and other naturally occurring resources. A distinction is sometimes made between resource and environmental economics, where the latter field is concerned with the way wastes are disposed and the resulting quality of air, water, and soil serving as waste receptors. In addition, environmental economics is concerned with the conservation of natural environments and biodiversity.

Natural resources are often categorized as being renewable or nonrenewable. A renewable resource must display a significant rate of growth or renewal on a relevant economic time scale. An economic time scale is a time interval for which planning and management are meaningful. The notion of an economic time scale can make the classification of natural resources a bit tricky. For example, how should we classify a stand of old-growth coast redwood or an aquifer with an insignificant rate of recharge? While the redwood tree is a plant and can be grown commercially, old-growth redwoods may be 800 to 1,000 years old, and the remaining stands may be more appropriately viewed as a nonrenewable resource.

INTRODUCTION AND OVERVIEW

In the preceding chapters I have presented economic models for the management of fisheries, forests, nonrenewable resources, and stock pollutants. For renewable resources and stock pollutants, the possibility of achieving and maintaining a steady state might correspond to the now ubiquitous term sustainability. The term sustainable development became prominent in the lexicon of resource and development agencies following the Earth Summit in Rio de Janeiro in 1992. The United Nation's World Commission on Environment and Development defined sustainable development as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs…. At a minimum, sustainable development must not endanger the natural systems that support life on Earth.”

Since 1992, sustainability has been broadly adopted as a goal by individuals and governments. Making the concept operational and implementing policies that would lead to sustainable lifestyles for individuals and sustainable production and consumption in the global economy have proved difficult. If the global economy critically depends on nonrenewable resources, long-term sustainability may be open to question. Interestingly, the notion of sustainability in a macroeconomic model with a nonrenewable resource was examined by several economists in the early 1970s. Perhaps the most famous article was by Robert M. Solow, entitled, “Intergenerational Equity and Exhaustible Resources,” which appeared in a special symposium issue of the Review of Economic Studies in 1974.

INTRODUCTION AND OVERVIEW

Nonrenewable resources do not exhibit significant growth or renewal over an economic time scale. Examples include coal, oil, natural gas, and metals such as copper, tin, iron, silver, and gold. I noted in Chapter 1 that a plant or animal species might be more appropriately viewed as a nonrenewable, as in Chapter 4, where the stock of old-growth forest was modeled as a nonrenewable resource. In Chapter 2, in the mine manager's problem, I developed a finite-horizon model of a nonrenewable resource to show how Solver might be used to determine the optimal extraction path.

If the initial reserves of a nonrenewable resource are known, the question becomes, “How should they be extracted over time?” Is complete depletion (exhaustion) ever optimal? Is it ever optimal to abandon a mine or well with positive reserves? Does the time path of extraction by a competitive firm differ from that of a price-making monopolist or cartel? If exploration allows a firm to find (acquire) more reserves, what is the optimal risky investment in exploration?

In working through the various models of this chapter, an economic measure of resource scarcity will emerge that is different from standard measures based on physical abundance. From an economic perspective, scarcity should reflect net marginal value (marginal value less the marginal cost of extraction).

INTRODUCTION AND OVERVIEW

In this chapter we will explore, in greater detail, the general renewable-resource model used to introduce the method of Lagrange multipliers in Chapter 1. This model will serve as a vehicle to compare managed and unmanaged fisheries and to analyze policies that have been employed in an attempt to correct for overfishing and stock depletion. Overfishing often will result when a fishery resource is both common property and open access. Biological overfishing has been defined as harvesting that reduces a fish stock to a level below the stock level that supports maximum sustainable yield or, in the notation of previous chapters, Xt < X MSY (Clark, 1990). By a common-property resource, I mean a resource that is not recognized as “private property” until it is captured. Open access is a situation in which fishers face no regulations in terms of either their level of harvest or entry or exit to or from the fishery.

Overfishing has been the usual result when a common-property fishery is harvested under conditions of open access. It has occurred on fishing, sealing, and whaling “grounds” going back to the seventeenth century, if not before. In the nineteenth century one sees the first attempts by individual nation states or two or more nations via international treaty to implement management policies in the hopes of avoiding severe overfishing.

INTRODUCTION AND OVERVIEW

This chapter is concerned with the wastes from production or consumption that might accumulate over time. I will refer to any accumulated waste as a stock pollutant. Returning to Figure 1.1, extracted ore qt was seen to generate a waste flow αqt that might accumulate as the stock pollutant Zt , where α > 0 was a coefficient (parameter) with a dimension that converted the units used to measure qt into the units used to measure Zt . For example, if qt were measured in metric tons (mt) and Zt were measured in parts per million (ppm), then α would have the dimension of ppm/mt.

For degradable wastes, there is often a biological or chemical process where a portion of the pollution stock is decomposed (degraded) into constituent compounds that might pose little or no threat to the environment. In Figure 1.1, the rate at which the stock pollutant degrades is γZt , where 1 > γ > 0 is a degradation coefficient indicating the fraction of the pollution stock degraded during period t. The net effect of the rates of waste flow and degradation will determine the change in the stock pollutant as given by the difference equation

As noted in Chapter 1, if the rate of waste flow exceeds the rate of degradation, the stock pollutant will increase, whereas if the degradation rate exceeds the flow of new waste, the stock pollutant will decrease.

INTRODUCTION AND OVERVIEW

This chapter will examine the economics of even-aged forestry and the optimal inventory of old-growth forest. By an even-aged forest, I mean a forest consisting of trees of the same species and age. Such a forest might be established by a lightning-induced fire or by humans after clearcutting a stand of trees. The first nonnative settlers in western Washington and Oregon encountered vast stretches of even-aged forest (predominantly Douglas fir) that had been established by natural (“volunteer”) reseeding following a fire. Today, silvicultural practices by forest firms are specifically designed to establish an age-structured forest inventory, or synchronized forest, where tracts of land contain cohorts ranging in age from seedlings to “financially mature” trees, that provides the forest firm with a more or less steady flow of timber to its mills.

In western Washington and Oregon in the mid-1800s, most forest stands contained trees over 200 years old with diameters in excess of five feet. Collectively, these forests constituted a huge inventory of old-growth timber that was used in the construction of houses and commercial buildings, the building of ships, and the manufacture of railroad ties, telegraph poles, furniture, musical instruments, and a plethora of other items. In the 1850s, the old-growth forests of the Pacific North-west must have seemed limitless and inexhaustible, but by the 1920s, foresters were already contemplating the end of this period of “old-growth mining” and the establishment of a forest economy based on the sustainable harvest of timber from even-aged forest “plantations.”

INTRODUCTION AND OVERVIEW

Numerical allocation problems can serve at least two functions. First, they can make theory and methods less abstract and more meaningful. Second, they can serve as a useful bridge from theory and general models to the actual analysis of “real world” resource-allocation problems. By a numerical problem, I mean a problem where functional forms have been specified, and all relevant parameters and initial conditions have been estimated or assigned values. For example, in Section 1.4, the general net-benefit function took the form πt = π(Xt , Yt ). A specific functional form, used in Exercises E1.1 through E1.3, was, where p > 0 was a parameter denoting the per-unit price for fish on the dock, Yt was the level of harvest in period t, c > 0 was a cost parameter, and Xt was the fish stock in period t. In a numerical problem, we would need values for p > 0 and c > 0, which might be estimated econometrically or simply assigned values based on a knowledge of current market prices and the cost of operating a fishing vessel.

Numerical analysis might involve solving an implicit equation for the steady-state value of a resource stock, the deterministic or stochastic simulation of a harvest or extraction policy, or the selection of escapement, harvest, or extraction rates to maximize some measure of present value.

The second edition of Resource Economics has expanded the first six chapters of the first edition, added an entirely new Chapter 7 (“Maximin Utility with Renewable and Nonrenewable Resources”), and deleted Chapter 7 (“Option Value and Risky Development”) and Chapter 8 (“Sustainable Development”) from the first edition. Most of the exercises at the end of each chapter are new. In Chapter 1, “Basic Concepts,” separate sections have been added on simulation, steady state, and local stability (1.1); extraction of a nonrenewable resource (1.2); asymptotic depletion of a nonrenewable resource (1.5); the maximum principle and dynamic programming in discrete time (1.6); dynamic programming in a two-period, two-state model (1.7); and the Markov decision model and stochastic dynamic programming (1.8). The last three sections in Chapter 1 were designed to introduce students to more advanced methods of dynamic optimization that would be encountered in a graduate program.

Chapter 2, “Solving Numerical Allocation Problems Using Excel's Solver,” has been significantly expanded and now presents 11 problems to show how Excel's Solver can be used to find the optimal rotation for an even-aged stand of trees (2.1); the steady-state optimal fish stock (2.2); the optimal date of exhaustion for a nonrenewable resource (2.3); the optimal first-period harvest in a two-period, two-state fishery (2.4); the optimal linear harvest policy in a finite-horizon fishery (2.5); the optimal escapement in a finite-horizon fishery (2.6); the optimal escapement for one “realization” in a stochastic fishery (2.7); the minemanager's problem (2.8); approximating the asymptotic approach to a steady-state optimum (2.9); the most rapid approach to an optimal pollution stock (2.10); and optimal escapement with stochastic growth (2.11).

Homer's Odyssey tells a familiar story: a hero, a veteran of the Trojan War, returns home after ten trial-filled years of wandering in exotic lands only to find his halls occupied by 108 carousing youths who court his wife in the hope that the lawful husband and master has perished abroad. And yet for all the simplicity of its tale, the poet's technique is brilliantly intricate; from the notorious tease of the opening line which hides the epic hero's name, to the sudden threat of retaliation from the dead suitors' kin in the closing episode, the composition uses flashbacks and internal narratives, dramatic irony, doubling, and retardation devices to keep us wondering how exactly affairs in Ithaca will be resolved. It is a work that, not surprisingly, has exercised a lasting fascination from archaic through to contemporary times, and that has been re-imagined in countless forms, visual, verbal and musical among them.

If another study of the Odyssey needs no justification, then the choice to focus on books 17 and 18 may prompt the question ‘why these?’ One reason is the sheer diversity and tonal range of the two books' contents, which run from the burlesque comedy of the boxing match between the disguised Odysseus and the parasite Irus to the charged moment when the hero re-enters his home after his twenty years' absence and first sets eyes on his wife.