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Consider the global market for crude oil, consisting of Saudi Arabia, Iran, and the rest of the world. Suppose that price-taking consumers in the rest of the world have demand for crude oil given by: P = 500 - 0.75Q. Assume that price-taking fringe suppliers of crude oil in the rest of the world have marginal costs given by: P = 400 + 0.6Q. Suppose that Saudi Arabia has marginal costs given by: P = 50 + 0.25Q, And that Iran has marginal costs given by: P = 50 + 0.5Q. Assume that neither Iran nor Saudi Arabia has demand of their own. Suppose that Saudi Arabia and Iran are contemplating forming a Cournot duopoly cartel. (Hint: assume residual demand reflects case 3). a. What is the optimal amount of crude oil that Saudi Arabia, Iran, and the rest of the world produces? b. What is the equilibrium price of crude oil in the market? c. What is the mark-up charged by Saudi Arabia and Iran? d. What are the profits to Saudi Arabia and Iran? e. What is the share of Saudi Arabia's production to total duopoly production? f. How does the Cournot mark-ups compare to the full enforcement (multi-plant monopoly consisting of Saudi Arabia and Iran) mark-ups? Now suppose instead that rest of world fringe supply is given by: P = 150 + 0.60. Suppose that Saudi Arabia and Iran are again contemplating forming a Cournot duopoly cartel (Hint: assume residual demand reflects case 1). g. What is the optimal amount of crude oil that Saudi Arabia, Iran, and the rest of the world produces? h. What is the equilibrium price of crude oil in the market? i. What is the mark-up charged by Saudi Arabia and Iran? j. What are the profits to Saudi Arabia and Iran? k. What is the share of Saudi Arabia's production to total duopoly production? 1. How does the Cournot mark-ups compare to the full enforcement (multi-plant monopoly consisting of Saudi Arabia and Iran) mark-ups? m. Compare your results for these two cases. What insights might this question have for the OPEC strategy game