The Law of Large Demand for Information

Abstract

A longstanding unresolved problem in Bayesian economics is how to value and price information. This paper resolves both problems for the case of inexpensive information. We build on Chernoff's (1952) asymptotic efficiency of simple hypothesis tests to produce a generically complete order on signals in finite-state finite-action Bayesian models --- assuming a large enough i.i.d. sample of such signals.

In our main novel results, we use large deviation theory from Cramer (1938) to extend this order on the 'total value of information' to the 'marginal value of information' --- i.e. the value of an additional signal. We show that the marginal value schedule is eventually exponentially falling in quantity, and is higher for lower quality signals. This yields our 'Law of Large Demand' for information: For all low enough prices, information demand rises as the price falls, and falls in the signal quality, for a given price. We then derive this asymptotic demand function --- logarithmic for small enough prices. We also explore some surprising implications of our theory for the monopoly pricing of information.

JEL Classification: D81