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In the presence of non-convexities, the power market may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, to achieve an economically stable outcome, the uplift payments to the market players are introduced as part of the pricing principle. Given the general pricing principle that involves the lost profit compensation in the form of the uplift payments, we study a question if it is possible to introduce new products/services at the market and the associated prices such that the set of the optimal solutions to the centralized dispatch optimization problem is unaffected, the profit received by each market player at the centralized dispatch schedule is unchanged, and no market player has lost profit. These new products/services and the corresponding prices can be viewed as originating from the Lagrangian relaxation of redundant constraints, which dot not change the centralized dispatch schedule. For any given market price (or a pricing algorithm that sets the producer revenue as a function of its output volume) in a uninode multi-period power market with fixed load, we explicitly construct a family of the redundant constraints that do not change the maximum profit of any producer and result in zero total uplift payment. The analysis can be straightforwardly extended to a multi-node multi-period market with price-sensitive demand.