Question

1. The Petroleum production function in Table 7.4, holding nonproduction workers constant, can be roughly expressed as Q = 100*L^.55*K^.31. Use this function to answer the following. Suppose a firm wishes to produce 1200 units of Q. Use an Excel Spreadsheet to find the MRTS_LK in adding a 10^th unit of Labor. Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. In absolute value terms, the MRTS_LK when we add the 10^th
unit of L is ______.

	A.	84.63.
	B.	20.23.
	C.	14.27.
	D.	10.47.
	E.	7.92.

2. This is a continuation of the previous problem. Suppose a petroleum company’s ratio of P_L
to P_K is 1.40. What is the optimal (cost minimizing) combination of L and K that should be employed by the firm to produce Q = 1200? Conduct your analysis using an Excel Spreadsheet and changing Labor by 1, 2, 3, etc., that is, use integer values of L only. Use a Spreadsheet and not Excel Solver. The optimal L = _____ and K = ______.

	A.	10; 50.94.
	B.	16; 22.13.
	C.	18; 17.95.
	D.	20; 14.89.
	E.	22; 12.58.
	F.	24; 10.78

Answer 1

The left side table shows the calculated values and the right hand side table presents the formula view of the calculations for your reference.

(1) As observed, the marginal rate of technical substitution (MRTS) when we add 10th labor = 10.47 (highlighted with blue)

(2) The optimal L = 20 and K = 14.89. At optimal level MRTS = (P_L/P_K). The closest combination is (L, K) = (20, 14.89) as highlighted in orange).