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This paper discusses the problem of defining marginal costs when integer variables are present, in the context of short-term power auctions. Most of the proposals for price computation existing in the literature are concerned with short-term competitive equilibrium (generators should not be willing to change the dispatch assigned to them by the auctioneer), which implies operational-cost recovery for all of the generators accepted in the auction. However, this is in general not enough to choose between the different pricing schemes. We propose to include an additional criterion in order to discriminate among different pricing schemes: prices have to be also signals for generation expansion. Using this condition, we arrive to a single solution to the problem of defining prices, where they are computed as the shadow prices of the balance equations in a linear version of the unit commitment problem. Importantly, not every linearization of the unit commitment is valid; we develop the conditions for this linear model to provide adequate investment signals. Compared to other proposals in the literature, our results provide a strong motivation for the pricing scheme and a simple method for price computation.