Cobb-Douglas production functions can be formulated using expenditures rather than physical units
While production functions theoretically relate physical inputs and outputs, economic literature and practice frequently formulate and estimate them using monetary values and expenditures.
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en.wikipedia.org: Cobb–Douglas production function. en.wikipedia.org. https://en.wikipedia.org/wiki/Cobb%E2%80%93Douglas_production_function
Defines the standard Cobb-Douglas production function using physical units like labor and capital.
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doi.org: The Estimation of Production Functions with Monetary Values. doi.org. https://doi.org/10.2139/ssrn.4687937
Notes that in practice, production functions are estimated using monetary values for output and capital.
ar5iv.labs.arxiv.org: [1711.10031] Constructive Identification of Heterogeneous Elasticities in the Cobb-Douglas Production Function. ar5iv.labs.arxiv.org. https://ar5iv.labs.arxiv.org/html/1711.10031
Shows that input costs and cost shares are used in identifying elasticities in Cobb-Douglas functions.
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