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Adaptation with an Envelope

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Economists like to emphasize how people and businesses will adapt to climate change.  On a geological scale the world is warming very fast.  But on a human scale it is warming slowly, so we can easily adjust infrastructure and management decisions to the gradually changing climate.  For example, in agriculture farmers can gradually adjust planting times, cultivars, and locations where we grow crops, and so on. So how much does adaptation really buy us?  As it turns out, probably very little, at least in most contexts.  Since it is economists who often emphasize this point, sometimes even intimating that otherwise negative impacts could turn positive with adaptation, perhaps we should pause for a moment to consider what basic microeconomic theory says about it.  And we have a ready-made tool for the job, called the envelope theorem  (or here ), that provides essential insight. I'll try to make this intuitive, but it helps to be a little formal.  Suppose agricultural