This is NOT just a "let me google that for you" reply; I selected the search term carefully. (LMGTFY is for when the search is trivially obvious.)
I'd also suggest that the common experience of many professionals in the field matches what the studies show. Note that in theory, the formulation that "A * N_task_1, (1-A) * N_task_2. where A is a number between 0 and 1 representing the percentage of focus on task_1" implies that you must be 100% efficient in task switches, which you can easily disprove simply by trying to switch back and forth every second, or exactly precisely splitting your attention continuously. Again, even computers can "thrash" and spend all their time changing tasks in certain bad cases.
See also "queuing theory", which can put some math on this, and is useful for almost any HN denizen anyhow.
While the JEP study seems to indicate that multitasking isn't very efficient, its findings aren't definitive, according to another study in Psychological Science (Vol. 12, No. 2) by Eric H. Shumacher, PhD, of the University of California, Berkeley, and colleagues. That study found that, under special circumstances, people can do two different tasks at once without much interference--particularly if the tasks are well-practiced and do not physically conflict with each other. "These latter results raise a further question--what causes you to get interference between tasks in some cases but not others?" asks Meyer, a co-author on both studies. "This is a challenging question and one that needs to be answered carefully in order to tell the full story about multitasking and executive control."
Another point is, how fast do you have to switch the tasks to consider it "multitasking." E.g. do you have to switch on a 1-second interval? I would guess that would be much less efficient than something like, grading some papers while waiting for code to compile, which may take a minute to compile/ run some test, and then go back to coding, repeat- I would call that multi-tasking, and would almost guess that would be "more" efficient than actually just doing the coding task or the grading task separately, since it takes advantage of removing useless time.
