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Developing a Partial Equilibrium Model of an Urban Water System

Staff working paper

This paper by Andrew Barker, Tim Murray and John Salerian was released on 24 March 2010.

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  • Key points
  • Contents
  • A partial equilibrium model of an urban water system is employed to investigate capacity augmentation decisions, pricing policies and the use of water restrictions in the urban water sector.
  • The modelling is based on the solution to a constrained optimisation problem, with the objective to maximise community welfare in the urban water market. The model allows for intertemporal representation of demand and supply; variation in annual inflows to dams; various supply options; and scope to apply policy constraints.
  • The model abstracts from the transaction costs of different policies, institutional settings and incentives. Such considerations could in practice have a significant bearing on outcomes and optimal policies.
  • To illustrate its use, the model is applied to a hypothetical city, which synthesizes features of Australian capital cities. The results therefore are illustrative only, and cannot be used as a template for assessing actual investment and policies.
    • Several possible new supply sources are considered: desalination; groundwater aquifers; household tanks; new dams; and rural-urban trade.
  • The model reinforces the importance of rainfall variability and of making investment decisions regarding new supply sources based on expected returns to investment.
    • Actual payoffs to investment depend on future inflows to dams, as prices respond to demand, supply and storages. If future rainfall is plentiful (scarce), returns to investment are likely to be low (high).
    • Guaranteed investment returns lead to inefficient investment and consumption.
    • The amount of water drawn from new investments should be flexible and respond to rainfall patterns (via their impact on water prices).
  • Pricing based on the relative scarcity of water was the optimised 'base case' against which a range of illustrative policy applications were evaluated.
    • Constraining prices (including through long-run marginal cost pricing) was found in the model to impose costs on the community. Constrained prices are also likely to require restrictions to ration water during times of scarcity because prices are not able to perform a 'rationing' function.
    • The modelling shows large economic costs from imposing water restrictions, which prevent uses of water that consumers would have been willing to pay for. These costs rise as demand becomes less responsive to price or if inflows to dams become lower in the future.
    • A key feature of scarcity-based pricing is the variability in the price of water over time, depending on rainfall. On average, however, prices are lower under scarcity based pricing than under the other policy options modelled.
    • Model results also indicate potentially high costs from ruling out access to particular sources of water (for example, relatively low-cost rural-urban trade using pipelines), or from pursuing supply options that are not least cost.
  • Potential further work using this modelling framework could include its application to specific urban settings.

Background information

John Salerian (Assistant Commissioner) 03 9653 2190

  • Preliminaries
    Cover, Copyright, Contents, Preface and Acknowledgments
  • Overview - including key points
  • Chapter 1 Introduction
    1.1 Existing arrangements
    1.2 Reviews of urban water policy
    1.3 A role for new economic modelling?
  • Chapter 2 Partial equilibrium framework
    2.1 Introduction to the PE framework
    2.2 Stochastic extension: multistage stochastic programming and the probability tree
    2.3 Our application
  • Chapter 3 Results for the core market model
    3.1 Prices and storage
    3.2 Source of supply
    3.3 Sensitivity analysis
  • Chapter 4 Illustrative applications to policy
    4.1 Description of the illustrative applications
    4.2 Impact on net social welfare
    4.3 Pricing
    4.4 Investment in new sources of supply
  • Chapter 5 Opportunities for further work
  • Appendix A Mathematics of the model
  • Appendix B Calibration of the model
  • Appendix C Investment and supply decisions in a simplified model
  • Appendix D Sensitivity analysis
  • References

Model available on request

The GAMS source code for the Urban Water model developed for this paper is available on request by emailing

In order to run the model, a licensed version of GAMS with a linear programming solver is required.

Printed copies

This publication is only available online.

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