Chaos and Misallocation under Price Controls

TL;DR

The paper analyzes how binding price ceilings eliminate arbitrage, pushing allocations to corner solutions that respond discontinuously to small changes in costs or frictions. It introduces the Chaos Theorem, showing that under price controls the allocation is determined by cost-ordering across segments, not by a common shadow price, producing large, non-smooth welfare losses beyond the Harberger triangle. It develops robust, nonparametric bounds that identify the possible range of misallocation using only observed allocations, a controlled price, and slope/bounds on demand, and applies this to the 1973–74 U.S. gasoline crisis with AAA data to quantify misallocation that can exceed several times the Harberger triangle. The results imply that price controls generate substantial, patchy misallocation across space, time, and product mix, and that these effects persist even when smoothing mechanisms or partial liberalizations are present; robust bounds provide policy-relevant welfare measures in the face of unknown demand forms.

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.

Figures (8)

• Figure 1: Percentage of gasoline stations rationing fuel by state, February 1974. Rationing includes stations completely out of fuel and those limiting purchases (e.g., maximum gallons per customer). Data are from AAA surveys of sampled stations aaa_aaa_1974.
• Figure 2: Two-Market Misallocation under Price Ceiling. Panel A: efficient allocation with equalized shadow prices; $a + b = c$. Panel B: corner allocation where Market 1 receives full demand; shadow prices diverge and $a + b > c$.
• Figure 3: The feasible set is a line segment. Corners $E_1$ and $E_2$ are the only generic equilibria under price controls.
• Figure 4: Allocation of a fixed supply ($\bar{Q} = 150$) across 100 cities under free markets (top) versus price controls (bottom). Each column is a different random draw of delivery costs. Under free markets, quantities vary smoothly. Under price controls, low-cost cities fill to capacity while approximately 30 cities go unserved.
• Figure 5: Station-Level Demand Curves Without Choke. The two panels show high-loss and low-loss demand configurations consistent with observed open and closed/limiting station quantities when no choke cap is imposed, using the baseline calibration $q_O=1.06$ and $q_C=0.66$. Solid segments are identified by the observed allocations and slope bounds; dashed segments are admissible extensions.

Theorems & Definitions (35)

• Definition 1
• Definition 2
• Proposition 1
• Definition 3
• Theorem 1
• Theorem 2: Chaos
• Corollary 1
• Proposition 2: Informal
• Theorem 3: Informal
• Corollary 2