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Water Resource Use and Competition in an Evolutionary Model

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Over the last few years water scarcity and pollution have been rapidly growing at both regional and global level. This has generated in many cases increasing intersectoral competition over the use of a limited amount of water resources. To examine the dynamics that such competition may generate in the economy, the present paper proposes a simple dynamic evolutionary model in which two sectors (A and B) compete for the use of water and studies the impact of water pricing on the dynamics of the two sectors in the presence of a population of interacting economic agents characterized by imitative behaviors. As it emerges from the model, when water is underpriced a self-enforcing process may be observed driving the economy towards a Pareto-dominated equilibrium. In such equilibrium the economy fully specializes in sector A, characterized by the highest negative impact on the water resource, at the expenses of sector B. The paper shows that a policy of fine tuning that increases water price through the endogenous water pricing mechanism examined in the model can inhibit the convergence of the economy to such an equilibrium point and can progressively shift the system towards the less water-consuming sector. Finally, assuming a Leontief production function and performing numerical simulations, it is shown how a change in water price can affect the dynamics of the model, and that the same results hold also in a more general, three-sector context.

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  1. The first WTP markets date back to 1979 in Chile and to the early 1980s’ in some States of the USA (Idaho, Wisconsin, Colorado). In Australia water consumption permits were introduced in 1989 in the Murray-Darling Basin. The Australian regulator then decided to extend the application of water markets and implemented also a a system of water pollution permits in the same basin three years later. See Borghesi (2013) for a discussion of these applications.

  2. See Borghesi (2013) for an in-depth discussion of the factors of success/failures of WTP that distinguishes between general issues that are common to both TWPR and TWAR and application problems that are specific to each of them.

  3. The latter contribute to pollute water therefore both water consumption and water pollution problems can be simultaneously taken into account in the model.

  4. See also Bebbington and Williams (2008) for a discussion of the conflicts between the mining companies and the local community in the Yanacocha gold mine site in Northern Peru.

  5. As pointed out before, the model can be easily adapted to examine water pollution rather than consumption problems. If so, the terms \(\overline {W}_{i}\) (i = A, B) can be interpreted as measures of water quality (rather than quantity), while the parameters α, β, γ, δ measure the effect that the polluting activities of sectors A and B have on water quality. In what follows, however, we will generally refer to water consumption rather than pollution problems as the former have more immediate and evident consequences on the production capacity of the economic sectors.

  6. The same results on dynamics, in this one-dimensional context, would be obtained under every sign-preserving adoption dynamics (see Weibull 1995) according to which: \(\overset {\cdot } {x}\gtreqless 0\) if \(\widetilde {\Pi }_{A}(x)\gtreqless \widetilde {\Pi }_{B}(x)\) for every x ∈ (0, 1).

  7. The slope of the graphs \(\widetilde {\Pi }_{i}(x)\) (i = A, B) are equal to \( \frac {d\widetilde {\Pi }_{A}(x)}{dx}=\frac {d{\Pi }_{A}\left [ W_{A}(x)\right ]} { dW_{A}}(\beta -\alpha )\overline {N}-\mu (\alpha +\gamma )\overline {N}\) and \( \frac {d\widetilde {\Pi }_{B}(x)}{dx}=\frac {d{\Pi }_{B}\left [ W_{B}(x)\right ]} { dW_{B}}(\delta -\gamma )\overline {N}-\mu (\beta +\delta )\overline {N}\). In what follows the slope of the graph of \(\widetilde {\Pi }_{A}(x)\) is said to be lower (respectively higher) than that of the graph of \(\widetilde {\Pi } _{B}(x)\), if \(\frac {d\widetilde {\Pi }_{A}(x)}{dx}<\frac {d\widetilde {\Pi }_{B}(x)}{dx}\) (respectively \(\frac {d\widetilde {\Pi }_{A}(x)}{dx}>\frac {d \widetilde {\Pi }_{B}(x)}{dx}\)) ∀x ∈ (0, 1). Notice that, if μ = 0 , the slopes of the graphs of \({\Pi }_{A}\left [ W_{A}(x)\right ] \) and \({\Pi }_{B}\left [ W_{B}(x)\right ] \) coincide with those of the graphs of \( \widetilde {\Pi }_{A}(x)\) and \(\widetilde {\Pi }_{B}(x)\), respectively.

  8. Although a zero-price scenario is admittedly less frequent, one can find specific examples in which water is free. Think, for instance, of common-pool water resources in some African countries that are freely available to the inhabitants of the surrounding villages, causing women to walk long distances to get the available water and provoking well-known free-riding problems. As pointed out above, however, all dynamic regimes of Figs. 16 apply even if water price is strictly positive but sufficiently low.

  9. The parameter values underlying Figs. 7 and 8 are: α = 0.73, β = 0.62, γ = 1.94, δ = 0.41, \(\overline {W}_{A}=8.4\) , \(\overline {W}_{B}=6\) , w = 0.8, a = b = d = 1, c = 1.5.

  10. This simulation is obtained setting:

    α = 0.83, β = 0.2, γ = 0.94, δ = 0.41, ε = 0.1, ζ = 0.21, η = 0.7, 𝜃 = 0.41, λ = 0.01, μ = 0 , σ = 0,\(\overline {W}_{A}=10\), \(\overline {W}_{B}=6\), \(\overline {W}_{C}=3\), \(\overline {p}=0.21\), w = 0.8, a = 1, b = 1, c = 1.5, d = 1, e = 2.7 , f = 1.


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The authors would like to thank two anonymous referees and seminar participants to the Fourth Annual Conference of IAERE (Italian Association of Environmental and Resource Economists, Bologna, 2016) and to the Workshop ”European Water Utility Management: Promoting Efficiency, Innovation and Knowledge in the Water Industry”, 2015 held at University of Pisa (Italy) for helpful comments and suggestions on a preliminary version of the paper. The usual disclaimer applies.

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Antoci, A., Borghesi, S. & Sodini, M. Water Resource Use and Competition in an Evolutionary Model. Water Resour Manage 31, 2523–2543 (2017).

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