On the Possibility of Informationally Inefficient Markets Without Noise

Noise traders can be dispensed with entirely. Partial revelation of information through prices arises under any non-exponential expected utility preference, including CRRA, without noise traders, random endowments, supply shocks, hedging motives, or behavioral biases. The model contains zero exogenous noise. The mechanism is a mismatch between the space in which market clearing aggregates signals and the Bayesian sufficient statistic. CARA demand is linear in log-odds, so prices aggregate in log-odds space and reveal the statistic exactly. Every other preference aggregates differently; the resulting Jensen gap makes revelation partial. I prove that CARA is the unique fully revealing preference class, characterize the rational expectations equilibrium via a contour integration fixed point, and verify that partial revelation survives learning from prices. The Grossman-Stiglitz paradox is resolved: information acquisition has positive value within the rational class. Numerical solution of the rational expectations fixed point at K = 3 confirms partial revelation, positive trade volume, and positive value of information across the full range of CRRA risk aversion, vanishing only in the CARA limit.