. Aliyah earns $15 per hour for up to 40 hours of work per week. She is paid double time for every hour worked beyond 40 per week. Suppose she can work anywhere between 0 and 112 hours per week. She faces a 20% marginal tax rate on earned income and pays $5 per hour in child care expenses for every hour she works. She receives $100 (untaxed) for child support every week regardless of whether she works.

a) Calculate the following for herweeklybudget line:

Kink point (hours, $) when she starts working: ___________________________

Slope of budget line right after she starts working: _______________

Kink point (hours, $) when she starts earning double time: _________________________

Slope of budget line after she starts earning double time: _______________

Vertical intercept (hours, $): __________________________

b) Graph her weeklybudget line, clearly labeling the axes, intercept values and kink points.

c) Suppose Aliyah's child support now falls by $10 for every hour she works. Add her new budget line to your earlier diagram, either as a dotted line or in a different color, again clearly labeling everything. Before drawing it, calculate:

Slope of budget line right after she starts working: _______________

Kink point (hours, $) when she stops earning child support: _________________________

Slope of budget line after she stops earning child support: _______________

Kink point (hours, $) when she starts earning double time: _________________________

Slope of budget line after she starts earning double time: _______________

Vertical intercept (hours, $): __________________________

d) What is the expected effect of the change in child support on Aliyah's hours of work if she initially worked 30 hours per week? Explain your answer.

e) Would your answer be different if she initially worked 5 hours per week? Explain why or why not.