The law of large demand for information

An unresolved problem in Bayesian decision theory is how to value and price information., This paper resolves both problems assuming inexpensive information. Building on Large Deviation Theory, we produce a generically complete asymptotic order on samples of i.i.d. signals in finite-state, finite-action models. Computing the marginal value of an additional signal, we find it is eventually exponentially falling in quantity, and higher for lower quality signals. We provide a precise formula for the information demand, valid at low prices: asymptotically a constant times the log price, and falling in the signal quality for a given price.