In the subsidised housing sector, building corporations can use their market power as purchasers to raise output of subsidised housing to a level higher than it is with perfect competition on both sides of the market. This holds true if the building society is perfectly X-efficient. The proposition is not necessarily true if the corporation maximises a utility function in which discretionary profit, or organisational slack, is an argument. The X-inefficient building society may set output higher or lower than with perfect competition. If the government grants a fixed subsidy per house and tries to constrain X-inefficiency by imposing a maximum price, this might be an incentive for the building corporation to maintain a planned shortage of subsidised houses. However, housing shortages will be smaller and welfare possibly greater than it is with perfect competition. The existence of a perfectly competitive non-subsidised housing sector is for the building corporation an incentive to increase strategically the output of subsidised housing and reduce planned shortages; but it does not necessarily eliminate such shortages.