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…