I came across another example of this concept in a passage from a paper on the food stamp nutrition cycle. The author's first paragraph, copied below (emphasis mine), discussed the implications of the exponential model, before quickly abandoning it for alternative approaches:
Consider a consumer who is indifferent between enjoying one additional dollar of consumption today and 99.6 additional cents of consumption tomorrow. Such an individual has a daily discount factor of 0.996, and if she is an exponential discounter her annual discount factor will be about 0.23 (corresponding to an annual discount rate of about 146 percent). She would therefore strictly prefer 24 dollars of additional consumption today to 100 dollars of additional consumption one year from now, and would happily accept seven cents today in exchange for 100 dollars in five years.If you ever so slightly prefer consumption today over consumption tomorrow, you'll prefer pennies today over huge amount of money in the far future, according to the model.
What should economists do in the face of such a surprising result? It's a tough question. We could call the conclusion absurd and modify the model until it produces an alternative conclusion that sounds more reasonably. Or we could go against our intuition and attempt to test this result empirically.