We study supply function competition among conventional power generators with different levels of flexibility and the impact of intermittent renewable power generation on the competition. Inflexible generators commit production before uncertainties are realized, whereas flexible generators can adjust their production after uncertainties are realized. Both types of generators compete in an electricity market by submitting supply functions to a system operator, who solves a two-stage stochastic program to determine the production level for each generator and the corresponding market prices. We aim to gain an understanding of how conventional generators' (in) flexibility and renewable energy's intermittency affect the supply function competition and the market price. We find that the classic supply function equilibrium model overestimates the intensity of the market competition, and even more so when more intermittent generation is introduced into the system. The policy of economically curtailing intermittent generation intensifies the market competition, reduces price volatility, and improves the system's overall efficiency. Furthermore, these benefits of economic curtailment are most significant when the production-based subsidies for renewable energy are absent.