Working Paper: CEPR ID: DP4943
Authors: Hendrik Hakenes; Andreas Irmen
Abstract: 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.
Keywords: capital accumulation; industrialization; neoclassical growth model
JEL Codes: N60; O11; O14; O41
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| trivial steady state with zero capital (D25) | no income, savings, or investment (D14) |
| Inada conditions (C62) | spontaneous takeoff even with zero initial capital (D25) |
| infinite marginal product of capital at initial zero capital (D24) | instability in steady state (C62) |
| capital's essentiality vs Inada condition (P11) | multiple outcomes for capital accumulation (E22) |
| trivial steady state is unstable (C62) | possibility of capital accumulation without initial capital stock (E22) |
| Cobb-Douglas production function (E23) | non-uniqueness of solutions when capital is zero (D59) |