Price controls lead to misallocation of goods and encourage rent-seeking. The misallocation effect alone is enough to ensure that consumer surplus is always reduced by a price control in an otherwise-competitive market with convex demand if supply is more elastic than demand; or when demand is log-convex (e.g., constant-elasticity) even if supply is inelastic. The same results apply both when rationed goods are allocated by costless lottery among interested consumers, and when costly rent-seeking and/or partial de-control mitigates the allocative inefficiency. The results are best understood using the fact that in any market, consumer surplus equals the area between the demand curve and the industry marginal revenue curve.
