Shoe leather cost refers to the cost of time and effort (more specifically the opportunity cost of time and energy) that people spend trying to counter-act the effects of inflation, such as holding less cash and having to make additional trips to the bank. The term comes from the fact that more walking is required (historically, although the rise of the Internet has reduced it) to go to the bank and get cash and spend it, thus wearing out shoes more quickly. Further, with the advent of sneakers, the shoe leather cost has been significantly reduced as well. The actual cost of reducing money holdings is the additional time and convenience that must be sacrificed to keep less money on hand than would be required if there were no inflation.
Sources
http://www.andrew.cmu.edu/course/88-301/data_of_macro/shoe_leather.html
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