Critical Review of Pricing Schemes in Markets with Non-Convex Costs

We consider a market in which suppliers with asymmetric capacities and asymmetric marginal and fixed costs compete to satisfy a deterministic and inelastic demand of a commodity in a single period. The suppliers bid their costs to an auctioneer who determines the optimal allocation and the resulting payments, a typical situation in deregulated electricity markets. Under classical marginal-cost pricing, the nonconvexity of the total cost may result in losses for some suppliers because they may fail to recover their fixed cost through commodity payments only. To address this problem, various pricing schemes that lift the price above marginal cost and/or provide side-payments (uplifts) have been proposed in the literature. We review several of these schemes, also proposing a new variant, in a two-supplier setting. We derive closed-form expressions for the price, uplifts, and profits that each scheme generates that enable us to analytically compare these schemes along these three dimensions. Our analysis complements known numerical comparisons available in the literature. We extend some of our analytical comparisons to the case of more than two suppliers and discuss extant numerical comparisons for this case. Further, we present known results concerning the potential for supplier strategic bidding behavior in the context of the considered pricing schemes, emphasizing when possibilities for market manipulation exist.