A 19th-century amateur mathematician, William Forster Lloyd, modeled the fate of a common pasture shared among rational, utility-maximizing herdsmen. He showed that as the population increased the pasture would inevitably be destroyed. This tragedy may be the fate of all sorts of common resources, because no individual, firm or group has meaningful property rights that would make them think twice about using so much of it that it is destroyed. Once a resource is being used at a rate near its sustainable capacity, any additional use will reduce its value to its current users. Thus they will increase their usage to maintain the value of the resource to them, resulting in a further deterioration in its value, and so on, until no value remains. Contemporary examples include overfishing and the polluting of the atmosphere. (See public goods and externality. )