Chaos and Misallocation under Price Controls

TL;DR

This paper proves a Chaos Theorem showing how price controls lead to arbitrary allocation outcomes and significant misallocations, with welfare losses calibrated to historical data.

Contribution

It introduces a Chaos Theorem for price-controlled markets, revealing how small differences cause large misallocations and welfare jumps, and derives bounds on these effects.

Findings

Price controls cause arbitrarily small cost differences to determine allocations.

Misallocation losses can be 1 to 9 times the Harberger triangle.

Sharp bounds on misallocation are derived without parametric assumptions.

Abstract

Price controls kill the incentive for arbitrage. We prove a Chaos Theorem: under a binding price ceiling, suppliers are indifferent across destinations, so arbitrarily small cost differences can determine the entire allocation. The economy tips to corner outcomes in which some markets are fully served while others are starved; small parameter changes flip the identity of the corners, generating discontinuous welfare jumps. These corner allocations create a distinct source of cross-market misallocation, separate from the aggregate quantity loss (the Harberger triangle) and from within-market misallocation emphasized in prior work. They also create an identification problem: welfare depends on demand far from the observed equilibrium. We derive sharp bounds on misallocation that require no parametric assumptions. In an efficient allocation, shadow prices are equalized across markets; combined with the adding-up constraint, this collapses the infinite-dimensional welfare problem to a one-dimensional search over a common shadow price, with extremal losses achieved by piecewise-linear demand schedules. Calibrating the bounds to station-level AAA survey data from the 1973--74 U.S. gasoline crisis, misallocation losses range from roughly 1 to 9 times the Harberger triangle.