5. (21 points total) Consider the labor supply decision of schoolteachers. Teachers can work up to 180 days in a year, and they earn the wage w for each day that they work. Assume that sick leave is at the discretion of each individual teacher. In other words, the school does not ask for proof of illness, so teachers can take leave even when they are not sick, teachers are free to take as much leave as they want. Finally, assume that teachers have no nonlabor income (i.e., Y=0). a. (10 points) Initially assume that teachers are not paid anything for the days of sick leave that they take. With annual earnings (E) on the vertical axis and annual days of leave (L) on the horizontal axis, graph the budget constraint faced by a typical teacher. Label the intercepts and slope of this budget constraint. Now consider the following sick pay policy: teachers are given 20 fully-paid sick days a year, and after they have used these up, they receive an additional 60 days of sick leave at two-thirds of their normal pay. On the same graph you used before, draw the budget constraint that corresponds to this new situation, labeling as many points as you can, including the relevant slopes