Economics question

A homogeneous products duopoly faces a market demand function given by P = 500 10Q . Both rms have a constant marginal cost of M C = 200. a. What would the equilibrium price in this market be if it were perfectly com- petitive? (5 points) b. What are the rm's outputs in a Nash equilibrium of Cournot's model? (5 points) c. What is the market price in a Nash equilibrium of Cournot's model? (5 points) d. What would the equilibrium price in this market be if the two rms coliuded to set the monopoly price? (5 points)