Uzawa's theorem, also called the steady-state growth theorem, was proved by the Japanese economist Hirofumi Uzawa in 1961 and identifies the functional form technological change must take for the Solow-Swan and Ramsey-Cass-Koopmans growth models to admit a balanced growth path. It shows first that on such a path capital, investment, consumption and output must all grow at the same constant exponential rate, and second that the production function can then always be rewritten so that technological change enters only as a multiplier on labor, a property called labor-augmenting or Harrod-neutral technological change. The theorem is often read as exposing a limitation of these growth models, since it forces modelers to assume labor-augmenting technical change even though that assumption sits awkwardly with the observed long-run decline in the relative price of capital goods.
Facts
StatementUnder the normal assumptions of the Solow-Swan and Ramsey models, if capital, investment, consumption, and output are increasing at constant exponential rates, these rates must be equivalent. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Uzawa's theorem - Wikipedia
Introduction, paragraph 2, first part of the theorem
if capital, investment, consumption, and output are increasing at constant exponential rates, these rates must be equivalent.
Introduction, paragraph 1, last sentence
It was proved by Japanese economist Hirofumi Uzawa in 1961.
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