Price caps are often used by policy makers to "regulate markets". Previous analyses have focussed on the "supply side" impact of these caps, and derived the optimal price cap, which maximizes investment and welfare. This article expands the analysis to include the "demand side" impact of price caps: when prices can no longer rise, customers must be rationed to adjust demand to available supply. This yields two new findings, that contradict previous analyses. First, the welfare-maximizing cap is higher than the capacity-maximizing cap, since increasing the cap increases gross surplus when customers are rationed. Second, in somes cases, the capacity-maximizing cap leads to lower capacity and welfare than no cap. These findings underscores the...