Isaac Sonin, UNC Charlotte

*Title: *Water Puzzle and Marginal Utility Optimization

Abstract. There are two cups of tea on a table, each with a two-unit capacity. Cup 1 has one unit of tea at 80% concentration, and cup 2 has one unit with 25% concentration. You have one unit of hot water in your own cup, which you should distribute between these two cups, say volume x into cup 1 and the rest, i.e., 1-x, into cup 2. After that, the volume x is returned to you from cup 1, and the volume 1-x from cup 2, i.e., you get back one unit in total. Now you are ready to drink your tea. The question is, what should be the value of x such that your tea is as strong as possible? Is x=1 or x<1? Strangely enough, this simple problem leads to the maximization problem with a transparent socio-economic interpretation, related to so-called marginal utility, one of the fundamental concepts in Economics. Calculus 1 is the only prerequisite for this talk.