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The presence of non-convexities in electricity markets has been an active research area for about two decades. The -- inevitable under current marginal cost pricing -- problem of guaranteeing that no market participant incurs losses in the day-ahead market is addressed in current practice through make-whole payments a.k.a. uplift. Alternative pricing rules have been studied to deal with this problem. Among them, Convex Hull (CH) prices associated with minimum uplift have attracted significant attention. Several US Independent System Operators (ISOs) have considered CH prices but resorted to approximations, mainly because determining exact CH prices is computationally challenging, while providing little intuition about the price formation rationale. In this paper, we describe the CH price estimation problem by relying on Dantzig-Wolfe decomposition and Column Generation, as a tractable, highly paralellizable, and exact method -- i.e., yielding exact, not approximate, CH prices -- with guaranteed finite convergence. Moreover, the approach provides intuition on the underlying price formation rationale. A test bed of stylized examples provide an exposition of the intuition in the CH price formation. In addition, a realistic ISO dataset is used to support scalability and validate the proof-of-concept.