Neoclassical Growth and the 'Trivial' Steady State

If capital is an essential input, the neoclassical growth model has a steady state with zero capital. From this, one is inclined to conclude that an economy starting without capital can never grow. We challenge this view and claim that, if the production function satisfies the Inada conditions, a take-off is possible even though the initial capital stock is zero and capital is essential. Since the marginal product of capital is initially infinite, the ‘trivial’ steady state becomes so unstable that the solution to the equation of motion involves the possibility of a take-off, even without capital. When it happens, the take-off is spontaneous; there is no causality.