Dan is a single dad. In order to work, he has to place his $3-$year$-$old daughter, Taylor, in daycare. Daycare costs $$10000$ per year. If he works, his wage rate is $$40$ hour and he can work up to $2000$ hours a year. His non$-$labour incorne is $$30000.$

$($a$)$ Carefully drawn Dan's budget line. As he only requires daycare if he works, this can be treated as a work expense rather than spending on consumption; as a result, his income and consumption should be treated as net of daycare expenses $($and he does not incur this expense if he elects to not work$).$

$($b$)$ With the addition of an indifference curve, illustrate the case where Dan clects to be a stay$-$at$-$home dad rather than working.

$($c$)$ On the same diagram, draw the budget line for the case where the wage rate is just high enough that he is indifferent between continuing to stay at home and joining the work force.

$($d$)$ Suppose that the wage rate is high enough that Dan chooses to work and the provincial government subsequently introduces a daycare subsidy that reduces Dan's day care expenses by $$5000.$ Under what circumstances would this policy increase Dan's hours worked per year? Explain.