The Economics of Conjunctive Groundwater Management with Stochastic Surface Supplies

Knapp, Keith C.; Olson, Lars J.

doi:10.1006/jeem.1995.1022

Cited by 129 publications

(90 citation statements)

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“…Increasing marginal cost is sufficient to mitigate over pumping when demand changes very little. However, for the case of moderate growth, results are consistent with Provencher (1993), Provencher and Burt (1994), and Knapp and Olson (1995) who find that welfare gains approximate 3%, 4% and 3%, respectively. When growth is high, results are consistent with Brill and Burness (1994) who compute gains of approximately 17%.…”

Section: Comparisonsupporting

confidence: 80%

“…The robustness of GSE has been tested repeatedly. Property rights (Provencher 1993;Provencher and Burt 1994), stochastic processes (Knapp and Olson 1995), non-stationary demand (Brill and Burness 1994) and backstop technology (Koundouri 2000;Koundouri and Christou 2006) affect the extent to which GSE persists. See Koundouri (2004a) and Koundouri (2004b) for a thorough review of the groundwater management literature that considers GSE.…”

Section: Introductionmentioning

confidence: 99%

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The economics of optimal urban groundwater management in southwestern USA

Hansen

2012

Hydrogeol J

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Groundwater serves as the primary water source for approximately 80% of public water systems in the United States, and for many more as a secondary source. Traditionally management relies on groundwater to meet rising demand by increasing supply, but climate uncertainty and population growth require more judicious management to achieve efficiency and sustainability. Over-pumping leads to groundwater overdraft and jeopardizes the ability of future users to depend on the resource. Optimal urban groundwater pumping can play a role in solving this conundrum. This paper investigates to what extent and under what circumstances controlled pumping improves social welfare. It considers management in a hydro-economic framework and finds the optimal pumping path and the optimal price path. These allow for the identification of the social benefit of controlled pumping, and the scarcity rent, which is one tool to sustainably manage groundwater resources. The model is numerically illustrated with a case study from Albuquerque, New Mexico (USA). The Albuquerque results indicate that, in the presence of strong demand growth, controlled pumping improves social welfare by 22%, extends use of the resource, and provides planners with a mechanism to advance the economic sustainability of groundwater.

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Section: Comparisonsupporting

confidence: 80%

Section: Introductionmentioning

confidence: 99%

The economics of optimal urban groundwater management in southwestern USA

Hansen

2012

Hydrogeol J

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“…Groundwater management with stochastic surface water is discussed by Tsur and Graham Tomasi [1997], who show that the buffer value of a deterministic groundwater stock is positive, and may be significant in magnitude. Knapp and Olson [1995] consider the relationship between socially optimal and common property withdrawals from groundwater stock. Tsur [1990] discusses the stabilization role of groundwater and implications for the resource development when surface water supplies are uncertain.…”

Section: Introductionmentioning

confidence: 99%

Optimal extraction from a renewable groundwater aquifer with stochastic recharge

Zeitouni

2004

Water Resources Research

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[1] This work considers the management of an aquifer with stochastic recharge and finite boundaries. For a class of such models we show that there is a positive threshold of the water stock that the manager should aim at keeping. Thus, under the optimal extraction regime at a time when the water stock is lower than this threshold, there should be no pumping from the aquifer, while at times when the water stock is greater than the threshold, all water in excess of the threshold level should be pumped. The threshold level happens to coincide with the aquifer boundary for sufficiently high unit cost of pumping, in which case, only the runoff water of excess recharge should be collected.

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“…It is usual to take p = 1, but that is not necessary, so we have left it general. Knapp and Olson (1995) were the first to formulate conjectures (B) and (C) for this problem, but they were unable to prove them. Recently, Huh and Khrisnamurthy have discovered that this is because Knapp and Olsen adopted Burt's model of c(x, y) = c(x)y.…”

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confidence: 99%

ABCs of the bomber problem and its relatives

Weber

2011

Ann Oper Res

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In a classic Markov decision problem of Derman, Lieberman, and Ross (1975) an investor has an initial capital x from which to make investments, the opportunities for which occur randomly over time. An investment of size y results in profit P (y), and the aim is maximize the sum of the profits obtained within a given time t. The problem is similar to a groundwater management problem of Burt (1964), the notorious bomber problem of Klinger and Brown (1968), and types of fighter problems addressed by Weber (1985), Shepp et al (1991) and Bartroff et al (2010a). In all these problems, one is allocating successive portions of a limited resource, optimally allocating y(x, t), as a function of remaining resource x and remaining time t. For their investment problem, Derman et al (1975) proved that an optimal policy has three monotonicity properties: (A) y(x, t) is nonincreasing in t, (B) y(x, t) is nondecreasing in x, and (C) x − y(x, t) is nondecreasing in x. Theirs is the only problem of its type for which all three properties are known to be true.In the bomber problem the status of (B) is unresolved. For the general fighter problem the status of (A) is unresolved. We survey what is known about these exceedingly difficult problems. We show that (A) and (C) remain true in the bomber problem, but that (B) is false if we very slightly relax the assumptions of the usual model. We give other new results, counterexamples and conjectures for these problems.Keywords Bomber problem · fighter problem · groundwater management problem · investment problem · Markov decision problem 1 Stochastic sequential allocation problems An investment problemIn a classic Markov decision problem posed by Derman, Lieberman, and Ross (1975) an investor has initial capital of x dollars, from which he can make withdrawals to fund investments. The opportunities for investment occur randomly as time proceeds. An investment of size y results in profit P (y), and the aim is maximize the sum of the profits obtained within a given time t. Without more ado let us set out this problem's dynamic programming equation. With an eye to variations of this problem to come, we make some notational changes. We take the remaining number of uninvested dollars to be discrete (a nonnegative integer) and denote it by n (= 0, 1, . . .) rather than x. The remaining time is also discrete and denoted by t = 0, 1, . . . . We suppose that an investment opportunity occurs with probability p (= 1 − q), independently at each remaining time step. We replace P (y) with a(k). Let F (n, t) denote the expected total payoff from investments made over t Richard Weber Statistical Laboratory, University of Cambridge, Cambridge CB2 0WB, UK E-mail: rrw1@cam.ac.uk 2 Richard Weber further time steps, given initial capital n, and following an optimal policy. The dynamic programming equations is then F (n, t) = qF (n, t − 1) + p max k∈{0,1,...,n} a(k) + F (n − k, t − 1) ,with F (n, 0) = 0. Let k(n, t) denote a k which is maximizing on the right hand side of (1). We might have chosen to ...

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The Economics of Conjunctive Groundwater Management with Stochastic Surface Supplies

Cited by 129 publications

References 0 publications

The economics of optimal urban groundwater management in southwestern USA

The economics of optimal urban groundwater management in southwestern USA

Optimal extraction from a renewable groundwater aquifer with stochastic recharge

ABCs of the bomber problem and its relatives

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