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Locational marginal prices (LMPs) are influenced by various factors such as load uncertainty, thermal limit, capacity reserve, and market power. We build a system model to quantitatively analyze the effects of these individual factors and their interactions on the mean and standard deviation of the LMPs, assuming that the factors are either active or inactive. According to the sensitivity analysis results from convex quadratic programming, LMPs are piecewise linear functions of demand variation, which is a key property used in the computation. This paper attempts to answer the following types of questions: (1) To what extent does market power raise the LMPs above the marginal cost? (2) What effects will generation or transmission capacity expansion have on relieving high LMPs under high demand scenarios? An IEEE 30-bus test system is used as an example to demonstrate our approach. Index Terms--Capacity expansion, load flow analysis, locational marginal price (LMP), power system planning, probability, quadratic programming, sensitivity analysis.