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With the introduction of enhanced metering and communication capabilities in smart grids, utility companies will have the ability to extend Demand Response (DR) to small customers through Time-Dependent Pricing (TDP). By using pricing signals that more accurately reflect the demand-supply situation of an electricity network, utility companies can induce customers to shift their consumptions to off-peak periods, thus reducing the cost and improving the reliability of the network. Despite its promises, large scale deployment of DR still faces many obstacles, in particular, resistance from customers due to concerns over cost, uncertain price and privacy issues. In this paper, we propose a dual-price DR scheme to overcome some of these issues. The proposed scheme offers both regulated flat price and TDP to customers to meet their different risk-taking profiles. The TDP rates are computed from a cost minimization problem considering both consumption behaviours of customers and generation cost. We also present an analysis for solving the optimization problem and find a closed form solution for TDP. It is shown that the proposed scheme is effective in inducing the desired consumption behaviours. In addition, it is found that with proper price signals, the proposed scheme can provide incentives to both utility companies and TDP customers, thus encouraging the adoption of TDP. Theoretical results from this paper are illustrated using numerical examples.