Uzawa's theorem, also known as the steady-state growth theorem, is a theorem in economic growth that identifies the necessary functional form of technological change for achieving a balanced growth path in the Solow–Swan and Ramsey–Cass–Koopmans growth models. It was proved by Japanese economist Hirofumi Uzawa in 1961. A general version of the theorem consists of two parts. The first states that, under 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. The second part asserts that, within such a balanced growth path, the production function$Y = \tilde{F}(\tilde{A},K,L)$$A$$K$$L$$Y = F(K,AL)$) a property known as labor-augmenting or Harrod-neutral technological change. Uzawa's theorem demonstrates a limitation of the Solow-Swan and Ramsey models. Imposing the assumption of balanced growth within such models requires that technological change be labor-augmenting. Conversely, a production function that cannot represent the effect of technology as a scalar augmentation of labor cannot produce a balanced growth path. ## Statement $\dot{X}(t)\equiv {d