This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf (1994).Economics, Equilibrium Pricing; MIP models of markets, MIP Applications

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Abstract-This paper decomposes the effects of the transition from an average cost distribution tariff to a cost causation based distribution tariff, in terms of time and location, that uses nodal prices to recover losses and an "extent-of-use" method to recover fixed network costs based on use at coincident peak.Our decomposition is designed so that the effects of using coincident peak and location for fixed network charges, as well as using marginal losses under constraints recovering the exact amount of losses, and recovering exactly the cost of network service in total can be isolated and analyzed separately.We apply our tariff transition and decomposition method to an example network with data from Uruguay to isolate the various effects with and without a distributed generation (DG) resource. We show moving to coincident peak charges and to fully charging for marginal losses while rebating the merchandising surplus through the fixed charges have the greatest effects on changes in distribution tariff charges. DG provides countervailing cost changes to distribution tariffs for loads through loss reductions and the implicit "creation" of new network capacity for which it is paid. The interaction of all these effects may lead to outcomes that are counter-intuitive, which further supports the need to decompose the tariff changes to fully understand the reasons for the direction and magnitude of changes in tariff charges in the transition to tariffs based more on cost causation.