We present a model for the optimal design of an online auction/store by a
seller. The framework we use is a stochastic optimal control problem. In our
setting, the seller wishes to maximize her average wealth level, where she can
control her price per unit via her reputation level. The corresponding
Hamilton-Jacobi-Bellmann equation is analyzed for an introductory case. We then
turn to an empirically justified model, and present introductory analysis. In
both cases, {\em pulsing} advertising strategies are recovered for resource
allocation.