The Time Value of Energy

So Adam and i walked into the Stanford Law Library this afternoon, whereupon each of us maneuvered so as to align the respective pockets of our jeans (in which our respective ID cards were located) with the proximity sensor. We each proceeded to the reserve desk to check out materials that would require our IDs to be scanned. Adam pointed out to me that, assuming any efficiency loss in thrusting our hips at the machine rather than removing our IDs and passing them in front of the machine (or even a nonzero probability of positive efficiency loss), we had each wasted some effort by waiting until we got to the reserve desk to pull our IDs out of our pockets. In other words, why did we wait to pull our IDs out of our pockets when doing so prior to entering the library would have saved some energy?

i agree with Adam in principle, so long as we neglect what i call the time value of energy. Consider briefly an analogy to the time value of money. What if we had been required to pay a dollar either upon entering the library or checking out a book? Obviously a rational actor would prefer to pay the dollar later rather than sooner, all other things being equal. Given the continuous nature of the depreciation of the dollar versus the discrete efficiency loss at the door if we chose to wait (the analog here is to imagine that the proximity reader is designed to detect the presence of a dollar in your pocket, but this is not the relevant issue here), and assuming complete and instantaneous liquidity of the dollar (essentially postulating my pocket as an interest-bearing account), we could construct a breakeven point at which the loss of efficiency would be compensated exactly by retaining the dollar for that additional length of time. On one side of this line, it would make sense to pay the dollar upon entry; but on the other side, it would be rational to save the dollar..

Yes, i've made some pretty absurd leaps here, but those were only by way of fitting the theoretical question raised to an actual event that occurred. Any economist would agree axiomatically with my analysis above. If a loss of efficiency can be averted by paying a dollar earlier rather than later, we can use a quantitative measure of that savings to compute exactly how long we would need to be able to hold the dollar in order to break even. The real question is what the economic implications are of considering the time value of energy in the same way. Is there a break even point at which retaining the energy in my body exactly compensates for any inefficiency of the proximity reader? Is the time value of energy even a valid concept? Would i rather expend the same energy later rather than now? If so, is that just because i am lazy or is there some economic value in a body's energy stores?

Perhaps more poignantly, does the time value of energy even operate the same way as it does with money? Maybe it operates in reverse! Maybe a rational operator would prefer to make an energy expenditure now rather than in the future. Consider: If bodily energy can be converted effectively to cash (through labor or whatever), any energy stores i have in my body represent a potential for cash generation. Any energy stores that are not immediately converted to cash represent an economic loss to me. Let's say i can convert the energy expenditure required to pull out my ID into a dollar. Wouldn't i rather expend the energy now to convert it into a dollar, invest the dollar, and convert the dollar back to energy (who knows, maybe i buy a muffin) at the moment i need to expend the energy to pull out my ID? If this is true, then even if the proximity reader is perfectly efficient, Adam is unilaterally correct in that we should have expended the energy to pull out our IDs earlier rather than later..