Price controls lead to misallocation of goods and encourage rent seeking. The misallocation effect alone ensures that a price control always reduces consumer surplus in an otherwise-competitive market with convex demand if supply is more elastic than demand or with log-convex demand (e.g., constant elasticity) even if supply is inelastic. The same results apply whether rationed goods are allocated by costless lottery or whether costly rent seeking and/or partial decontrol mitigates the inefficiency. Our analysis exploits the observation that in any market, consumer surplus equals the area between the demand curve and the industry marginal revenue curve.
