Suppose that Drexenture, a new consulting company, has the following production function: q=2c+4e+.5c*e where q is the number of reports produced, c denotes the number of fresh college graduates, and e denotes the number of experienced consultants.
a. What is the marginal product of college graduates? What is the marginal product of experienced consultants?
b. Calculate the marginal rate of technical substitution (MRTS) between college graduates and experienced consultants for Drexenture.
c. Suppose that college graduates cost $60K per year and experienced consultants cost $120K per year. Also assume that Drexenture has fixed costs amounting to $50K (including rent on office space, utilities, etc.). Given these costs and the production function above, determine the optimal production ratio; i.e., the optimal number of college graduates per experienced consultant Drexenture has on staff.
d. Given the optimal production ratio, determine the cost-minimizing numbers of college graduates and experienced consultants Drexenture should use to produce any given amount of output q; i.e., determine c and e as a function of q. Hint: you will need the quadratic formula to solve this; Only the positive square root will be relevant in this case.
e. Using your solutions for c and e, derive Drexenture’s optimal total cost function.
f. Suppose that Drexenture wants to produce 65 reports in the next year. Given your answers above, what are the optimal numbers of c and e to employ to produce 65 reports? What is the total cost of producing this number of reports given that you are producing it as efficiently as possible?
g. Suppose that Drexenture wants to produce 240 reports in the next year. Given your answers above, what are the optimal numbers of c and e to employ to produce 240 reports? What is the total cost of producing this number of reports given that you are producing it as efficiently as possible?
h. Using the total cost function derived in part (e), derive the marginal cost function. How much does the 65th report cost to produce? How much does the 240th report cost to produce?
i. Explain if and why there is (or is not) a difference in the cost of producing the 65th report as compared to the cost of producing the 240th report.