Differential Privacy protects individuals' data when statistical queries are\npublished from aggregated databases: applying "obfuscating" mechanisms to the\nquery results makes the released information less specific but, unavoidably,\nalso decreases its utility. Yet it has been shown that for discrete data (e.g.\ncounting queries), a mandated degree of privacy and a reasonable interpretation\nof loss of utility, the Geometric obfuscating mechanism is optimal: it loses as\nlittle utility as possible. For continuous query results however (e.g. real\nnumbers) the optimality result does not hold. Our contribution here is to show\nthat optimality is regained by using the Laplace mechanism for the obfuscation.\nThe technical apparatus involved includes the earlier discrete result by Ghosh\net al., recent work on abstract channels and their geometric representation as\nhyper-distributions, and the dual interpretations of distance between\ndistributions provided by the Kantorovich-Rubinstein Theorem.\n