Above graph is very informative; for example, if you spend around $4500 yearly on drugs it makes sense that you die in June. On the other hand, if you spend around $6750 yearly on drugs your death in April is a better deal while your death in September makes no sense at all.

If you are on Medicare, right now you are bombarded with leaflets and booklets about the new (next) big step: Medicare Prescription Drug Coverage. You may immediately notice that two levels of drug costs, $2250 and $5100 (=2250+ 2850), are of special importance: they divide the coverage into notably different sections of coverage. Sharp transitions between sections of a particular model are usually a sign of either primitive modeling or hidden intentions or both.

Let’s first find out at what yearly drug cost (YDC₀) your payments under the coverage, at monthly premium of $37, equal the drug costs:

YDC₀ = 250 + 0.25*(YDC₀ - 250) + 12*37

The result is YDC₀ = $842, which is 37.42% of the reference value of $2250. So, if you spend less than $842 yearly ($70 monthly) for drugs, you pay more under coverage than the real drug costs; see the graph on the left where uniform spending over 12 months is assumed. If you spend from 50% to 100% of the $2250 reference value, your actual benefits range from 19% to 47% of the drug costs although you may be under the impression that the benefit is 75% in that section of the coverage. It becomes even trickier in the section from $2250 to $5100 where $2850 of your expenses do not draw any benefit. At this point you may realize that private companies which provide the coverage under the Medicare shield are not humanitarian organizations. A thought may cross your mind that these companies know of many old people spending from $2250 to $5100 yearly on drugs.

Of course, the above mentioned companies have an incentive for you if your current drug costs are low and you would like to ignore them; it is called a penalty: