# The Demand for Information: More Heat than Light

*Jussi Keppo* (),
*Giuseppe Moscarini* and
*Lones Smith*

Additional contact information

Jussi Keppo: University of Michigan

No 1498, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

**Abstract:**
This paper produces a comprehensive theory of the value of Bayesian information and its static demand. Our key insight is to assume 'natural units' corresponding to the sample size of conditionally i.i.d. signals -- focusing on the smooth nearby model of the precision of an observation of a Brownian motion with uncertain drift. In a two state world, this produces the heat equation from physics, and leads to a tractable theory. We derive explicit formulas that harmonize the known small and large sample properties of information, and reveal some fundamental properties of demand: (a) Value 'non-concavity': The marginal value of information is initially zero; (b) The marginal value is convex/rising, concave/peaking, then convex/falling; (c) 'Lumpiness': As prices rise, demand suddenly chokes off (drops to 0); (d) The minimum information costs on average exceed 2.5% of the payoff stakes; (e) Information demand is hill-shaped in beliefs, highest when most uncertain; (f) Information demand is initially elastic at interior beliefs; (g) Demand elasticity is globally falling in price, and approaches 0 as prices vanish; and (h) The marginal value vanishes exponentially fast in price, yielding log demand. Our results are exact for the Brownian case, and approximately true for weak discrete informative signals. We prove this with a new Bayesian approximation result.

**Keywords:** Value of information; Non-concavity; Heat equation; Demand; Bayesian analysis (search for similar items in EconPapers)

**JEL-codes:** D81 D83 (search for similar items in EconPapers)

**Pages:** 36 pages

**Date:** 2005-01

**New Economics Papers:** this item is included in nep-mic

**Note:** CFP 1258.

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (1)

**Published** in Journal of Economic Theory (January 2008), 138(1): 21-50

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**Related works:**

Journal Article: The demand for information: More heat than light (2008)

Working Paper: The Demand for Information: More Heat than Light (2005)

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**Persistent link:** https://EconPapers.repec.org/RePEc:cwl:cwldpp:1498

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