Consider an industry with two firms, each having marginal costs and total costs equal to zero. The industry demand is P = 100 Q where Q = Q1 + Q2 is total output.

1. Find the cartel output and cartel profits assuming that the firms share the profit equally. In cartels, firms behave as if they are a monopoly. Hence, the cartel quantity is at the point where MR = MC. After finding the quantity, use the demand curve to find the cartel price. And then calculate = T R T C. Divide the total profit by 2 to find each firm's profit.

2. If each firm behaves as a Cournot competitor, what is firm 1's optimal output given firm 2's output? This part is asking the best response function of firm 1. Solve firm 1's profit maximizatin problem by setting its MC = MR. Then, express Q1 as a function of Q2.

3. Calculate the Cournot equilibrium output and profit for each firm. You have already solved firm 1's problem above. Now solve firm 2's problem. Then, solve BR functions simultaneously to get Q1 and Q2. Use the demand function to find the equilibrium price and then calculate = T R T C.