  In this paper we introduce the problem of dynamic pricing of power for
smart-grid networks. This is studied within a network utility maximization
(NUM) framework in a deterministic setting with a single provider, multiple
users and a finite horizon. The provider produces power or buys power in a
(deterministic) spot market, and determines a dynamic price to charge the
users. The users then adjust their demand in response to the time-varying
prices. This is typically categorized as the demand response problem, and we
study a progression of related models by focusing on two aspects: 1) the
characterization of the structure of the optimal dynamic prices in the Smart
Grid and the optimal demand and supply under various interaction with a spot
market; 2) a greedy approach to facilitate the solution process of the
aggregate NUM problem and the optimality gap between the greedy solution and
the optimal one.
