Explicit investment rules with time-to-build and uncertainty

by René Aïd, Salvatore Federico, Huyên Pham & Bertrand Villeneuve

We establish explicit socially optimal rules for an irreversible investment decision  with time-to-build and uncertainty. Assuming a price sensitive demand function  with a random intercept, we provide comparative statics and economic interpretations  for three models of demand (arithmetic Brownian, geometric Brownian, and the  Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the investment  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.

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