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.