We characterize the optimal investment and production path in a project characterized by indivisible capacity and stochastic inverse demand curve. At first best (without budget requirements), the investment is made earlier the lower the price elasticity of demand, causing the trajectory of production to be below the trajectory of capacity. At second best (when the investor is required to break even), the investment delay is upward distorted, the distortion being larger the lower the price elasticity of demand. Moreover, in the particular case of constant elasticity demand, investment is delayed but production remains at its first-best level.