Question
Consider the Cobb–Douglas production function \(Q=AK^{\alpha}L^{\beta}\), with A, α and β positive constants and both K and L freely variable. Which statements are true? (a) This is a long-run production specification.
(b) This specification holds one input fixed as in the short run.
(c) This function necessarily has increasing returns to scale.
(d) Its output elasticities with respect to the two factors are constant.
The correct answer is
(a) and (d)
(a) and (d) are true. Both factors can vary, and their output elasticities are α and β. Returns to scale are increasing, constant or decreasing according as α + β is greater than, equal to or less than 1.
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