This paper measures the unilateral incentive each of the five largest electricity suppliers in the California had to exercise market power in the state's wholesale market during the five month period June 1 to September 30 of 1998, 1999 and 2000. Using the actual bids submitted to the California Independent System Operator's (CAISO) real-time energy market, I compute the hourly price elasticity of the ex post residual demand curve faced by each supplier evaluated at the market-clearing price for that hour. The inverse of this hourly ex post residual demand elasticity quantifies the extent to which that supplier is able to raise the hourly real-time energy price above its marginal cost of supplying the last megawatt-hour (MWh) it sells in the CAISO's real-time energy market. I use the average hourly value of the inverse of the firm-level residual demand elasticity over the four month sample period of each year as a summary measure of the extent of unilateral market power possessed by each supplier. For each firm, this measure of unilateral market power is significantly higher in 2000 relative to the corresponding firm-level values in 1998 and 1999. For each of the five firms, this measure is slightly higher in 1998 than 1999. The firm-level results presented below are consistent with the view that the enormous increase in the amount market power exercised in the California market beginning in June of 2000 documented in Borenstein, Bushnell and Wolak (2002) was due to a substantial increase in the amount of unilateral market power possessed each of the five large suppliers in California.