In many countries, electricity demand increases very steeply during the morning hours, and decreases steeply during the evening hours. A steep change in electricity demand incurs considerable costs for ramping up and down electric power equipment, and raises the possibility of a large-scale blackout. This paper gives new insights into classical real-time pricing (RTP) by considering the case in which demand changes very steeply. We generalize the concept of the ramping costs, and derive an extended form of RTP that achieves the optimal rate of change in quantity demanded by explicitly taking the ramping costs into account. Under the optimal pricing policy, the prices are dramatically reduced during the period corresponding to the lower end of the slope of the load curve. In contrast, the prices are dramatically raised during the period corresponding to the upper end of the slope of the load curve. As a result, the steepness of the load curve will be remarkably controlled, which will reduce both the ramping costs and the possibility of a large-scale blackout. (c) 2005 Elsevier Ltd. All rights reserved.