Q. Consider the following Cobb-Douglas production function for the bus transportation system in a particular city:
Q = αLβ 1Fβ 2Kβ 3
where L = labor input in worker hours
F = fuel input in gallons
K = capital input in number of buses
Q = output measured in millions of bus miles
Suppose that the parameters (α, β1, β2, and β3) of this model were estimated using
annual data for the past 25 years. The following results were obtained:
α = 0.0012 β1 = 0.45 β2 = 0.20 β3 = 0.30
a. Determine the (i) labor, (ii) fuel, and (iii) capital input production elasticity.
b. Suppose that labor input (worker hours) is increased by 2 percent next year (with the other inputs held constant). Establish the estimated percentage change in output.
c. Suppose that capital input (number of buses) is decreased by 3 percent next year (when certain older buses are taken out of service). Assuming that the other inputs are held constant, determine the approximate percentage change in output.
d. What type of returns to scale appears to characterize this bus transportation system? (Ignore the issue of statistical significance.)
e. Discuss some of the methodological and measurement problems one might encounter in using time-series data to estimate the parameters of this model.