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 her weekly budget 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 weekly budget 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.