Find labor-fuel and capital input production elasticities

Question

Consider the following Cobb-Douglas production function for the bus transportation system in a particular city

                                  Q=aL_B1F_B2K_B3

 Where L= labor input in workers hours

             F= fuel input in gallons

            K=Capital input in number of buses

            Q= output measure in millions of bus miles

Suppose that 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

1. Determine the (i) labor, ( ii) fuel, (iii) capital input production elasticities.
2. Suppose that labor input (worker hours) is increased by 2 percent next year (with the other input held constant). Determine the approximate percentage change in output
3. Suppose that capital input (number of buses) is decrease by 3 percent next year ( when certain older buses are taken out of service). Assuming that the other input are held constant, determine the approximate percentage changes in output.
4. What type of returns to scale appears to characterize this bus transportation system? (Ignore the issue of statistical significance)
5. Discuss some of the methodological and measurement problems one might encounter in using time -series data to estimate the parameters of this model.