  We establish explicit socially optimal rules for an irreversible investment
deci- sion with time-to-build and uncertainty. Assuming a price sensitive
demand function with a random intercept, we provide comparative statics and
economic interpreta- tions for three models of demand (arithmetic Brownian,
geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is,
the installed capacity plus the in- vestment in the pipeline, must never drop
below the best predictor of future demand, minus two biases. The discounting
bias takes into account the fact that investment is paid upfront for future
use; the precautionary bias multiplies a type of risk aversion index by the
local volatility. Relying on the analytical forms, we discuss in detail the
economic effects.
