Problems such as price volatility have been observed in electric power markets. Demand-side participation is often offered as a potential solution by promising to increase market efficiency when hockey-stick type offer curves are present. However, individual end-consumer will surely value electricity differently, which makes demand-side participation as a group and at a bus difficult. In this paper demand is categorized into two groups: one that highly values reliability and the other that does not. The two types are modeled separately and a new optimal bidding function is developed and tested based on this model.