consider the following cobb-douglas production function for the bus transportati

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consider the following cobb-douglas production function for the bus transportation system in a particular city: Q = aL(B1)F(B2)K(B3) where L = labor input in worker hours F = fuel input in gallons K = capital input in munber of buses Q = output measured in millions of bus miles. suppose that the parameters (a,B1,B2,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 percent next year ( with the other inputs held constant ). determine the approximate percentage change in output. c. suppose that capital input ( number of buses) is decreasd 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.

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