The following questions concern the "pure" Bertrand model. Assume there are two firms. Explain your answers.

a. What are the assumptions of the pure Bertrand model? b. Under the assumptions of the pure Bertrand model, what are the equilibrium prices? c. Which assumption would you change if you wanted to alter the pure Bertrand model to exhibit cycles in prices? Give your answer, and then explain your reasoning in detail. d. Would price behavior in these cycles imply illegal collusion?