Production Function Estimation
Consider the following Cobb-Douglas production func- tion for bus service in a typical metropolitan area:
where
Q = b0Lb1Kb2Fb3
Q = output in millions of passenger miles
L = labor input in worker hours
K = capital input in bus transit hours
F = fuel input in gallons
Each of the parameters of this model was estimated by regression analysis using monthly data over a recent 3-year period. Results obtained were as follows (standard errors in paren- theses):
ˆb0 = 1.2; ˆb1 = 0.28; ˆb2 = 0.63; ˆb3 = 0.12
The standard error estimates for each coefficient are
ˆb0 = 0.4; ˆb1 = 0.15; ˆb2 = 0.12; ˆb3 = 0.07
A. Estimate the effect on output of a 4% decline in worker hours (holding K and F constant).
B. Estimate the effect on output of a 3% reduction in fuel availability accompanied by a 4% decline in bus transit hours (holding L constant).
C. Estimate the returns to scale for this production system.