3. The following Cobb-Douglas production function is used to describe the output

Question

3. The following Cobb-Douglas production function is used to describe the output generated by a local government maintenance agency. Q = ?L?1K?2E?3 Where L represents number of worker hours, K represents number of trucks used, and E represents energy used. Statistical estimated generated the following values for ?, ?1, ?2, and ?3. ? = 0.01; ?1 = 0.5, ?2 = 0.4, and ?3 = 0.2 a. What are the production elasticities of demand for labor, capital (trucks) and energy? b. If worker hours (labor) are increased by 10% next year, how much will output (Q) increase? c. If the number of trucks (K) decreases by 10% next year, how much will output (Q) decrease? d. What type of returns to scale is consistent with the above production function?

Explanation / Answer

1) elasticity will be equal to their powers

so
1 = 0.5

2 = 0.4

and 3 = 0.2 respectively

2)labour increase 10 %

means L must be replaced by 1.01L

putiing in equation

Q'= 1.01^.5Q
=1.005Q

that is increase by 5 % in output

3) summing the powers of each variable =1.1

that is more that 1 so .. it has increasing returns

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