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 by 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 Bayesian models. We then extend this order from the 'total' to the 'marginal value of information' --- i.e. the value of an additional signal. We show that it is eventually exponentially falling in quantity, and is higher for lower quality signals. We exploit this result to provide a precise formula for the information demand, valid at low prices: q=[log p+(1/2)log (-log p)]C + D where the constants C and D depend on the underlying signal, and D also depends on preferences. So demand is logarithmic, falling in the price, and falling in the signal quality for a given price