Under binding ceilings, cost-minimizing suppliers drive allocations to corners rather than Harberger or random benchmarks, producing larger losses and discontinuous welfare jumps.

We show that equilibrium generically occurs at neither the Harberger nor Glaeser-Luttmer benchmark. Cost-minimizing suppliers drive allocations to vertices, not interiors. Corners are not an assumption but an outcome about what cost-minimizing suppliers choose. The correct benchmark is corners, not random, and corners generate qualitatively different welfare properties: losses far larger than either efficient or random distributions, and discontinuous jumps from small parameter perturbations.