Adventures in high theory

Sometimes an economist, in analyzing an esoteric question with a highly mathematical model, will stumble upon a result that turns out to have applications to a wide range of practical policy issues. Sometimes it's the opposite.

From Ricardo Reis, "When Should Policymakers Make Announcements?":

An interesting result that should be useful to future models of rational inattention in continuous time is that, in spite of their apparent complexity, they reduce to optimal control problems without uncertainty that are part of the standard tool kit of economists. The particular optimal control problem that arises is interesting in its own right and may be useful in other applications.[FN]

[FN] The optimal control problem in this paper can be described as follows. Imgaine a person who has the view from her window blocked by two trees, that grow exogenously at different rates. The person has a fixed amount of effort every instant that she can devote to chop down the two trees. How should she split her effort between the two trees over time, and how does their height optimally evolve?