This article in Hydrology and Earth System Sciences (which is open access) is a great simulation-based study of how natural resource scarcity, the economy and technological change interact. First, they take an economic production function and add water to it as a factor of production. Then, they simultaneously allow population growth, increasing water scarcity, and technological innovation. Technological innovation is driven by scarcity, the level of investment the society chooses to make in innovation activities, and an assumed success rate. To invest more in innovation activities, the society has to save more, which means incomes have to decline in the short term.

So, this model answers the criticism economists often make that other models have ignored the effects of scarcity on innovation. With reasonable inputs the simulation always ends in declining water consumption, declining incomes, and eventually declining population. They relate this to real case studies from Australia where drought did drive innovation (for example drip irrigation), but ultimately it was not enough – agricultural output declined, incomes declined, and eventually population declined (they didn’t die of thirst, they just moved away).