Helen makes pies using equipment that she rents for $50 and pecans and other ingredients that cost $4.66 a pie. She hires workers and finds that they produce pies according to the following schedule:

Pies Workers
1 0.25
2 0.58
3 1.02
4 1.61
5 2.40
6 3.44
7 4.82
8 6.66
9 9.11
10 12.36
11 16.69
12 22.45
13 30.11
14 40.30

Workers are paid $12/hour.

a. find out and graph the marginal cost of each pie. Show your calculations! Why does the MC curve have the slope (up, down, or flat) that it does?
b. find out and graph the marginal cost of each pie if workers become 25% more productive, that is to say, if each pie can be made with only 75% as much labor. Show your calculations! find out and graph marginal cost if workers get a raise to $18/hour, with the old productivity.