Assume a duopoly market (firms 1 and 2) with the following inverse market demand function: = 140 , where Q = q1 + q2. The total cost function for each firm is: = 20 (i = 1, 2). A. Determine the allocatively efficient level of output in this market, . B. Determine the cartel price () and market level of output (). C. Without additional information about the cartel, explain why you cannot calculate the output (1 and 2 ) and profit levels for each firm. D. If firms compete by simultaneously choosing output (i.e., Cournot), determine the Nash equilibrium price ( ) and output levels ( ) for each firm. Illustrate you answer with a graph of the best-reply functions. E. If firms compete by simultaneously choosing price (i.e., Bertrand), determine the equilibrium price ( ) and output levels ( ) for each firm price. F. If firms compete in a dynamic, two-stage, game of perfect and complete information where firm 1 chooses output in the first period and firm 2 chooses output in the second period, determine the subgame-perfect Nash equilibrium (i.e., Stackelberg).