Consider the following Cobb- Douglas production function for the bus transportat

Question

Consider the following Cobb- Douglas production function for the bus transportation system in a particular city: Q= ?L ^?1 F^?2 K^?3. Where L is the labor input in worker hours; F is the fuel input in gallons; K is the capital input in number of buses; and Q is the output measured in millions of bus miles. Suppose that the parameters (?1, ?2, ?3) of this model were estimated using annual data for the past 25 years. The following results were obtained: ?= 0.0012; ?1= 0.45; ?2= 0.20; ?3= 0.30 b). Suppose that labor input (worker hours) is increased by 2 percent next year (other inputs held constant) . Determine the approximate percentage change in output.

Explanation / Answer

a. i The labour Elasticity: let the hypothetical data be as following: a ß1 ß2 ß3 L F K Q = aL ^ß1 F^ß2 K^ß3 0.0012 0.45 0.2 0.3 4000 35000 4000 4.892601548 0.0012 0.45 0.2 0.3 5000 35000 4000 5.409403208 %age Change: (L)25.00% (Q) 10.56% Labour Elasticity = %change in Q / %change in L = 0.42 when the L=4000 changes to L=5000, the Labour Elasticity = 0.42 ii. the Fuel Elasticity: a ß1 ß2 ß3 L F K Q = aL ^ß1 F^ß2 K^ß3 0.0012 0.45 0.2 0.3 4000 35000 4000 4.892601548 0.0012 0.45 0.2 0.3 4000 40000 4000 5.025025128 %age Change: (F)14.29% (Q) 2.71% Fuel Elasticity = %change in Q / %change in F = 0.19 when the F=35000 changes to F=40000, the Fuel Elasticity = 0.19 iii. Capital Elasticity: a ß1 ß2 ß3 L F K Q = aL ^ß1 F^ß2 K^ß3 0.0012 0.45 0.2 0.3 4000 35000 4000 4.892601548 0.0012 0.45 0.2 0.3 4000 35000 5000 5.231338859 %age Change: (K)25.00% (Q) 6.92% Labour Elasticity = %change in Q / %change in K = 0.28 when the K=4000 changes to K=5000, the Fuel Elasticity = 0.28

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