Something Out of Nothing? Neoclassical Growth and the 'Trivial' Steady State

A common perception about the neoclassical growth model is that an economy devoid of capital cannot evolve to strictly positive levels of output if capital is essential. We challenge this view by positing a broad class of production functions, encompassing the neoclassical production function, that - surprisingly - show that 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. When it happens, the take-off is spontaneous: there is no causality, not even randomness