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Undiscounted optimal growth with consumable capital: Application to water


  • Sherif Khalifa

    (California State University, Fullerton)

  • Ihsan Kaler Hurcan

    (Mitsui & Co. Europe)


This paper utilizes the geometric techniques developed in Khan and Mitra (2005, 2007) to analyze the optimal intertemporal allocation of water resources in a dynamic setup without discounting. The framework features two sectors: the first uses labor to purify water, while the second uses labor and purified water for irrigation to produce an agricultural consumption good. Purified water can also be used as potable water for drinking purposes. The planner allocates the available factors of production between the two sectors every period, and determines the optimal amounts of purified water, potable water, and irrigation water. The geometry characterizes the optimal path depending on whether the irrigation sector is more labor intensive than the purification sector. When the irrigation sector is labor intensive, the optimal path is a non converging cycle around the golden rule stock of purified water, while if the purification sector is labor intensive, there is a damped cyclical convergence to the go lden rule stock.

Suggested Citation

  • Sherif Khalifa & Ihsan Kaler Hurcan, 2011. "Undiscounted optimal growth with consumable capital: Application to water," Journal of Applied Economics, Universidad del CEMA, vol. 14, pages 145-166, May.
  • Handle: RePEc:cem:jaecon:v:14:y:2011:n:1:p:145-166

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    More about this item


    water resources; overtaking criterion; golden rule stock;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • Q25 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Water


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