My limited time spent in Economics lectures was anything but pleasant. But in due course I managed to put that to fair use. The idea is hardly original. It is a way of proving that time travel is possible. I used this analogy during a presentation in journalism school.
The way our professor told us, the law of diminishing marginal utility works like this: You pay a fruit seller five bucks for an apple the first time. Then you get partially full and are not willing to pay five for the next one you buy. You pay four.
The seller keeps shoving apples into your hands and you pay less each time. He eventually gives you apples for free. When you can’t take any more apples, he pays you to eat apples. Eventually you start charging five bucks for every apple you take.
Now, look this way. If you were to run to the end of the street, touch the telephone pole, and run back to your starting point, you would finish it in, say, five seconds. Assuming that the amount of energy available to you is infinite and that you go faster each time you run to the pole and back, you finish the next trip in four, then three and then two seconds.
Going on, you eventually get to zero (thoretically possible) and then enter negative time. This means, in simple terms, you get back to your starting point even before you leave it.
Yeah yeah, paradox and all. Infinite energy is a farther than the farthest cry. Even energy worth the speed of light is something we may not lay claim to unless we have a black hole or two at our command. That will take some time.
In the meantime all our grandmothers can sleep in peace in their childhoods. No mean murderous time travelling grandsons / daughters coming their way!