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Economic Quarterly

Winter 1997

Algebraic Production Functions and Their Uses Before Cobb-Douglas

Thomas M. Humphrey

The notion of a production function relating output to its underlying factor inputs has a long history. From A. R. J. Turgot in 1767 to Knut Wicksell in the early 1900s, economists used the concept to explain phenomena ranging from diminishing returns to product exhaustion under marginal productivity. Malthus's iron law of wages, Ricardo's rent theory, the trend of relative income shares in a growing economy, the first-order conditions of optimal factor hire, Euler's theorem on adding-up--all revealed their secrets through the production function. Moreover, J. H. von Th√ľnen and Knut Wicksell discovered the Cobb-Douglas function long before Charles Cobb and Paul Douglas.

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