This study investigates the existence of a dominant producer in the world crude oil market for the period 1973 to 1994. Contrary to the literature, the results show that neither OPEC nor the OPEC core can be characterized as a dominant producer. Using statistical tests, we also investigate whether OPEC, the OPEC core, or Saudi Arabia fit the competitive model or the Cournot model. The statistical results reject all models except the dominant firm model for Saudi Arabia. New user cost estimates are introduced and included in the models. An alternative explanation of high OPEC profits in the 1973-82 period is also developed as part of a statistical test of the effect of the US oil price regulation on world oil demand and supply. An estimate of the wealth transfer from price regulation is also calculated.