American Airlines produces round-trip transportation between Dallas and San Jose using three inputs: capital (planes), labor (pilots, flight attendants, and so on), and fuel. Suppose that American's production function has the following Cobb-Douglas form:
T=aK^b L^c F^d = 0.02K^.25 L^.2 F^.55
Where T is the number of seat-miles produced annually, K is capital, L is labor, and F is fuel.
a. If currently American employs K=100, L=500, and F=20,000, calculate the marginal products associated with K, L, F.
b. What is American's MRTS between K and L? MRTS between K and F? Should American try to ensure that all its MRTSs are equal? Explain.
c. Does American's production function exhibit constant, increasing, or decreasing returns to scale? Explain. How would your answer change if c=-0.2?
d. Does the law of diminishing returns imply decreasing returns to scale? Explain.