For risk assessment purposes, we study how economic dispatch decisions vary with the uncertain input factors that may arise, e.g., from the use of variable renewable energies. Given a known random input distribution and linear programming (LP)-based dispatch, we aim to describe the distribution of the resulting variables and objective values. Relying on Monte Carlo simulation (MCS) is computationally expensive, especially if the uncertain factors are high dimensional. In this paper we evaluate an algorithm using multiparametric linear programming (MPLP) for this purpose. It avoids solving an LP for every sample of the random vector by characterizing the parametric LP solution as a piece-wise linear function whose pieces can be stored for repeated use. We compare the algorithm with MCS and other quasi-Monte Carlo sampling approaches for three economic dispatch use cases with varying complexity. The MPLP approach is as accurate as MCS, but up to 300 times faster for the merit order use case.