This paper produces a theory of value for Gaussian information with two states and two actions, tracing the solution of the option pricing formula, but for the process of beliefs. We derive explicit formulas for the value of information. The marginal value is convex and rising, concave and peaking, and finally convex and falling. As the price falls, demand is initially zero, and eventually logarithmic. Its elasticity exceeds one, and falls to zero with the price. Demand is hill-shaped in beliefs, zero at extremes. Our results approximate models where information means the sample size for weak discrete informative signals.
See the companion paper on discrete information that is closer to an extension of Blackwell’s Theorem: “The Law of Large Demand for Information“.