$($Continuing with the situation described in the preceding question.$)$ Consider the model of a schoolteacher's labor supply

decision that we discussed in class. Teachers can work up to $180$ days in a school 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, and teachers are free to take as much leave as they

want. Also assume that teachers have no nonlabor income $($i$.$e$.,Y=0).$ In terms of notation,

E represents the teacher's annual earnings

$L$ represents annual days of sick leave taken by the teacher

w represents the wage that the teacher earns for each day of work

$U(E,L)$ represents the teacher's utility function

Assume that $E$ and $L$ are normal goods. Whenever graphing the model, put $E$ on the vertical axis and $L$ on the horizontal axis.

Finally, assume that teachers receive sick pay according to the following policy. For the school year, each teacher is given $20$

fully$-$paid sick days, and after these have been used up$,$ each teacher receives an additional $60$ days of sick leave at two$-$thirds

of their normal pay.

Before the sick pay policy was instituted, teachers received no pay for days that they did not work. Consider a teacher who,

prior to the introduction of sick pay, took $50$ days of sick leave. According to labor supply theory, how will introduction of the

sick pay policy described above change the amount of sick leave that this teacher takes?

Sick leave will increase because of an income effect.

Sick leave will increase because of a substitution effect.

Sick leave will increase because of substitution and income effects that reinforce each other.

Sick leave will not change.

The change in sick leave is indeterminate because of conflicting substitution and income effects.