Suppose you can hire your mechanic for up to six hours. The total benefit and total cost functions are B(H)=420H-40H^2 and C(H)=100H+120H^2. The corresponding formulas for marginal benefit and marginal cost are MB(H)=420-80H and MC(H)=100+240H.
Suppose that in addition to the costs in above.
You have already committed to paying $100 to your mechanic for parts she has ordered.
a. Write out your cost function mathematically and graph it.
b. What is your best choice?
c. Suppose your mechanic tells you that she can return the part she has ordered and you wouldn't need to pay the $100 if you do no repair work at all. What is your cost function now? What is your best choice?(hint: Now if you get no repair work, you can avoid paying the $100- it is no longer a sunk cost.)
d. How would your answers to parts (a)-(c) change if the cost of the parts your mechanic ordered had been $200?