THE SUPPLY OF INFORMATION BY A CONCERNED EXPERT* Andrew Caplin and John Leahy How much information should a policy maker pass on to an ill-informed citizen? In this paper, we address this classic question of Crawford and Sobel (1982) in a setting in which beliefs impact utility, as in Kreps and Porteus (1978). We show that this question cannot be answered using a utility function with standard revealed preference foundations. To solve the model, we go beyond the classical model in two respects, relying on the psychological expected utility model of Caplin and Leahy (2001) to capture preferences, and the psychological game model of Geanakoplos et al. (1989) to capture strategic interactions. How much information should a policy maker pass on to a currently ill-informed citizen? This question was first posed formally in the classic sender-receiver game of Crawford and Sobel (1982). In that model, the citizen in question had standard expected utility preferences. In this paper, we enrich the question by allowing for a broader class of preferences, in particular preferences over the timing of resolu- tion of uncertainty. 1 This amendment allows us to address such questions as whether or not a doctor should reveal the truth to a terminally ill patient who is naively optimistic, and whether or not parents should tell their children the truth about Santa Claus. Larger scale policy issues of this form concern the optimal use of warning codes concerning terrorist threats and whether or not bank regulators should immediately pass on new information about systemic credit risk to a worried public. Given our focus on the resolution of uncertainty, it would be natural to assume that the receiver in our game has Kreps-Porteus preferences (Kreps and Porteus, 1978: henceforth KP). As opposed to the classical expected utility model, these preferences allow individuals to prefer later rather than earlier resolution of uncertainty. The natural modelling procedure would seem to be to append these preferences to a variant of the classical sender-receiver model. The central point of this paper is that such a mix and match procedure is doomed to failure. The fact that beliefs may impact utility raises a fundamental theoretical issue that cannot be answered using any standard model of individual preferences, including the KP model. The issue is simple, yet profound. Standard models of individual preferences, including the KP model, are based on the principle of revealed preference. Yet there are no private choices that can guide the policy maker in our policy problem. In technical terms, revealed preference cannot tell us whether in a particular state s a decision maker prefers to believe * We thank Nico Frijda, George Loewenstein, and Bob Rosenthal for valuable comments on an early draft, and Kfir Eliaz and David de Meza for equally valuable comments on a later draft. Caplin thanks the C.V. Starr Center at NYU and Leahy thanks the National Science Foundation and the Sloan Foundation for financial support. 1 To reduce the number of equilibria, we move away from the cheap talk assumption of Crawford and Sobel by assuming that all information is verifiable. The Economic Journal, 114 (July), 487–505. Ó Royal Economic Society 2004. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. [ 487 ]