A major law firm that uses associates and partners to provide legal services to its clients. To some degree both classes of employee are substitutable for each other. Indeed the firm has discovered that its clients' current needs can be satisfied using any of the combinations of person/hours for the year listed below:

Partners	Associates
13000	95750
14000	92750
15000	90000
16000	87500
17000	85250
18000	83250
19000	81500
20000	80000

Current wage for partners is $100,000 and $50,000 for associates. The firm has had a staffing policy of six to one. That is, for every partner, there are six associates. The current situation thus finds the firm using 15,000 partner hours and 90,000 associate hours.

a) What is the marginal rate of technical substitution between partners and associates (i.e. MP_Partners/MP_Associates) for the range between 13,000 and 14,000 partner hours? (20 points)

b) What happens to the marginal rate of technical substitution between partners and associates as one moves down the table and considers more partners and fewer associates? (One or two words will suffice.) (10 points)

c) If you were the legal administrator in charge of hiring and staffing, would you regard the current ratio of partners to associates as optimal? Why or why not? (10 points)

d) What would be the best mix of the two classes of personnel and why? (20 points)