Consider the following Cobb-Douglas function for the bus transportation system i

Question

Consider the following Cobb-Douglas function for the bus transportation system in a particular city: Q=aLb1Fb2Kb3 Where: L = labor input in workers hours F = fuel input in gallons K = capital input in number 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. (i). EL = b1 = .45; (ii). EF = b2 = .20; (iii). EB = b3 = .30. 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 decreased 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. 8. Based on the production function parameter estimates reported in table 7.4: a. Which industry (or industries) appears to exhibit decreasing returns to scale? (Ignore the issue of statistical significance)

Explanation / Answer

the powers of the corresponding components are the output elasticities of the corresponding variables i.e. a)labour=0.45 b)fuel=0.20 c)capital input=0.30 from the definition the %age change in the output is just the corresponding power of the variable thus a 2%increase in labour hour will lead to 0.30 % increase in output :) using same concept once again poutput increase due to 3%increase in no. of buses=0.9%=3*0.3% thats all ii could help u with :\

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