The characteristics of the Optimal Posted Price (OPP) are considered in the search model of \textit{G. Stigler} [J. Political Econ. 69, 213-225 (1961)] and \textit{McCall} (1967). Many facts valid for the more familiar reservation price regime do not hold in the posted price setting. E.g., an increase in buyer valuation always leads to an increase in the Optimal Reservation Price (ORP), while it can lead to a reduction in the OPP. However, sufficient conditions on the hazard rate function \(h\) are given which ensure that an increase in demand induces an increase in the OPP. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium. The analytical properties of \(h\) are crucial in the analysis of the OPP while \(h\) plays almost no role in the analysis of the ORP.