Consider the following Cobb-Douglas production function for the bus transportation
System in a particular city:
Q=aLb1Fb2Kb3
Where L= labor input in worker hours
F= fuel input in gallons
K= capital input in numbers of buses
Q= output measured in millions of bus miles
Suppose that the parameters (a, B1, B2,, and B3) of this model were estimated using annual data for the past 25 years. The following results were obtained:
a=0.0012 B1= 0.45 B2=0.20 B3=0.30
a. Determine the (i) labor, (ii) fuel, and (iii) capital input production elasticities.
b. Suppose that labor input (worker hours) is increased by 2% next year (with
The other inputs held constant). Determine the approximate percentage change in output.
c. Suppose that capital (number of buses) is decreased by 3% 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.