The key assumption here is that only a shift along the time preference schedule happens while his time preference schedule per se remains the same (e.g., the following quote from Rothbard). But in reality, the schedule can and does shift—and what brings about the increased saving is the shift in the time-preference schedule per se.

“Here, one element, a man’s money stock, is varied and his value scale is otherwise assumed to remain constant. It is not his money stock that is relevant to his time preferences, but the real value of his money stock. In the ERE, of course, where the purchasing power of the money unit remains unchanged, the two are identical. Ceteris paribus, an increase in his real income—real additions to his money stock—will lower the time-preference rate on his schedule.” (p. 444)

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