The following Cobb-Douglas production function is used to describe the output generated by a local government maintenance agency.
Q = αL^{β1}K^{β2}E^{β3}
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 α, β1, β2, and β3.
Α = 0.01; β1 = 0.5, β2 = 0.4, and β3 = 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?