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One of the main challenges in the emerging smart grid is the integration of renewable energy resources (RER). The latter introduces both intermittency and uncertainty into the grid, both of which can affect the underlying energy market. An interesting concept that is being explored for mitigating the integration cost of RERs is demand response (DR). Beginning with an overall model of the major market participants with RER and DR, together with the constraints of transmission and generation, we analyze the energy market in this paper and derive conditions for existence and uniqueness of the competitive market equilibrium using standard Karush-Kuhn-Tucker (KKT) criteria. The effect of wind uncertainty on the competitive market equilibrium is then quantified. Perturbation analysis methods are used to compare the equilibria in the nominal and perturbed markets. This analysis is used to quantify the effect of RERs uncertainty and its possible mitigation using DR. Finally numerical studies are reported using an IEEE 30-bus to validate the theoretical results.