The Economics of Lossy Compression

The price system is a lossy codec. It compresses the high-dimensional judgments of economic agents into scalar signals, destroying information in the process. This paper formalizes the claim by applying rate-distortion theory to price formation within a multivariate Gaussian framework. The main result: the excess distortion - the gap between the price system's actual distortion and the information-theoretic minimum at the same compression rate - is strictly positive whenever the price is informative enough for the optimal codec to reach the constraint dimensions, strictly increasing in constraint-dimension variance, and convergent to the total constraint variance in the limit of perfect market efficiency. The result extends to general (non-diagonal) source covariance. On its own dimension, the price system is an optimal codec; the excess distortion arises entirely from concentrating all compression capacity on the consensus value while leaving the constraint dimensions uncompressed. This is a structural mismatch, not a correctable design flaw - no improvement to the price system can deliver constraint information through the price channel. Supplementary disclosure channels that target uncompressed dimensions produce strictly higher marginal distortion reduction than additional price precision. The framework complements Sims's (2003) rational inattention program: where rational inattention explains why agents underprocess available signals, the present analysis explains why the signals themselves are degraded.

From the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics by Gregory Caldwell Beier (forthcoming 2026).