Why you’re encouraged to take sick leaves?
Imagine your company allows you to take sick leaves for a maximum of S bar days and annual leaves for a maximum of A bar days.
The benefit of taking leaves is getting higher utility from leisure time, which represents in L(.), we assume that the utility you gain from leisure time is proportional to the leaves you take. And you can choose to take sick leaves and/or annual leaves.
So as a utility-maximized agent, you may decide to take annual leaves or sick leaves.
Assuming your company offers half compensation for sick leaves, and offers pro-rate payment for annual leaves not being taken, here’s the utility maximization
where the m bar indicates your monthly salary, and M is the marginal utility you get per unit salary.
Notice that we suggest a cap for both annual leaves and sick leaves.
You can see that the marginal utility for taking a day off sick leave is always higher than one of the annual leaves.
The result suggests that you should always take sick leave first.