Stocks and Flows

One major source of confusion about sustainability comes from failing to recognize the distinction between "stocks" and "flows." Any notion of sustainability rests on these two concepts and the relationship between them. A stock, of course, is just a quantity of something (measured in tons, gallons, calories, or dollars) or the "quality" of something (e.g., air pollution levels in parts per million). A flow involves a quantity that "flows" during a period of time (e.g., tons per year or gallons per minute). It can flow in or out and will often be added to or subtracted from a stock. Hicks recognized this distinction and focused on a flow, the amount that could be consumed during a week.

Environmental resources typically involve both a stock and a flow, and there is generally some relationship between the two. For example, the amount of water in a bathtub (in gallons) will be a function of the "inflow" (gallons per minute) from the tap and the "outflow" (gallons per minute) to the drain. If the inflow is greater than the outflow, the stock is increasing over time. If the outflow is two gallons per minute, what must the inflow be in order for the stock in the tub to remain constant? Clearly, two gallons per minute will sustain the tub's fill level.

So can we relate stocks and flows to the idea of sustainabil-ity? In the case of a bathtub, what is it we want to sustain? Is it the stock (fill level) of the tub? Is it the inflow or outflow? If it is the fill level we want to sustain, do we care whether that stock is thirty gallons or one gallon, as long as we sustain it? Already we can see complications. In this particular case involving bathing, it is the stock or fill level that is essential. But we want more than just sustainability. We want the stock to be sufficient for the bather to be able to wash, soak, and rinse.

What about the case of a well where the outflow is the water we draw from the well for use, say, to irrigate a garden. The inflow is a function of the groundwater that seeps from the walls of the well, and the stock of water in the well is the amount available for irrigation at any one time. If we talk about sustainability in this case, is it the stock or flow we want to sustain? Is the answer the same as in the bathtub case? No, in this case, the amount of water we can withdraw from the well is what we want to sustain, and this will depend on the natural seepage inside the well. What matters is whether or not the withdrawals (outflows) for the garden can be sustained.

For these two examples, then, each involving a simple stock-flow relationship for water, we can see that sustainability needs to be applied differently. In the case of a bathtub used for bathing, sustaining an adequate fill level is probably our goal for purposes of bathing. By contrast, in the case of the well, what we want to sustain is our ability to irrigate our garden. So it is a sustainable outflow that is directly important to us: our ability to withdraw the needed quantity of water per week for irrigation. Of course, if the stock of water in the well is declining when in use, we cannot count on a sustainable outflow. What will allow us to achieve sustainability? The inflow must equal the outflow so that the stock of water does not change. Is the stock of water in the well important? In this case, not really. As long as we can dip our bucket into the water, whether the water level is high or low, our ability to water the garden sustainably is not affected. Of course, the stock can be important, for example, if the well goes dry or overflows, flooding our garden.

For most resources, the flow depends on the stock. The bathtub outflow may be higher when the tub is filled due to the added water pressure on a leak or at the drain. This is also true for an important class of resources where the "inflow" is generated from within the resource itself. A fishery grows from within as a result of biological reproduction, and this growth rate (which we can think of as its inflow) is "density dependent" or varies depending on the stock of fish. Biological resources, including forests and wildlife populations, tend to have growth rates that are density dependent. At relatively low stock levels the growth rate may be higher than at high stock levels because of increased competition among fish, trees, and wildlife at higher population densities.

For comparison, consider sustainability of a bank account. It will provide a sustainable flow of services (withdrawals) so long as the inflow (deposits or interest earned) is greater than or equal to the outflow. If we care only about sustainability, then the bank balance is not of direct concern. However, if the inflow is accumulated interest, and the interest is paid as a percentage of the bank balance, then we again have a case where the sustainability of the outflow is dependent on both the stock (bank balance) and the interest rate, which combine to determine the inflow. This relationship comes closest to the one that Hicks had in mind in his definition of income at the start of this chapter: our income from a bank account or other financial asset is only the interest accrued, not the principle. Way back in 1939, when Hicks defined income, he had in mind a definition that implicitly required sustainability.

Okay, at this point the idea of sustainability seems pretty straightforward once we've recognized the importance of stocks and flows and when we're looking at a single resource. But what happens with more than one resource?

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