Irreversible investment with uncertainty and scale economies

This paper analyses optimal irreversible investment policy when profits are subject to a multiplicative geometric Brownian motion shock. The marginal product of capital is increasing initially and decreasing thereafter. In the latter range, optimal policy is familiar: capacity is added gradually as the shock rises to a threshold where the expected return on the marginal unit is a required multiple of the cost of capital. The multiple reflects the option value of waiting. The optimal policy in the increasing marginal product range obeys the same multiple, now applied to the total return on the discrete increase in capital. Implications for economic growth, and suboptimal equilibria under external economies, are examined.