The Law of Large Demand for Information

21 Pages Posted: 9 Jun 2000

See all articles by Lones Smith

Lones Smith

University of Wisconsin at Madison - Department of Economics

Giuseppe Moscarini

Cowles Foundation for Research in Economics; Yale University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: April 2000

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

Suggested Citation

Smith, Lones and Moscarini, Giuseppe, The Law of Large Demand for Information (April 2000). Available at SSRN: https://ssrn.com/abstract=223531 or http://dx.doi.org/10.2139/ssrn.223531

Lones Smith (Contact Author)

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

Giuseppe Moscarini

Cowles Foundation for Research in Economics ( email )

Box 208281
New Haven, CT 06520-8281
United States

HOME PAGE: http://economics.yale.edu/people/giuseppe-moscarini

Yale University - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3596 (Phone)

HOME PAGE: http://www.econ.yale.edu/~mosca/mosca.html

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