Consider the world oil market, in which a cartel (OPEC) and a competitive fringe (rest of the world) are operating. Suppose that global oil demand and the supply of the competitive fringe are given by the following functions: Qw=50PQf=30+P Furthermore, suppose that the cartel is comprised of two countries, and let each country's marginal cost function be as follows: MC1=13+Q1,MC2=13+4Q2. a. Derive the marginal cost function (MCo) of the cartel. (2pt) b. Calculate the price at which the competitive fringe would be driven out of the market (P1) and the price at which the cartel would be driven out of the market c. Due to the presence of the competitive fringe in the market, there will be a kink point in the demand curve of the cartel. Calculate the quantity (Q~) at which this kink occurs. (1pt) d. Derive the demand function of the cartel to the left of the kink point quantity (i.e., for QoQ~ ) and to right of the kink point (i.e., QoQ~ ). e. Using the inverse demand function of the cartel, derive the corresponding marginal revenue function to the left of the kink point and to the right of the kink point. f. Using the marginal revenue, marginal cost, and inverse demand functions obtained above, calculate the cartel's output (Qo) and the price charged per unit of output (Po). (2pt) g. Calculate the output of the fringe (Qf) at this price. (Ipt) h. Calculate the total output (Qo+Qf) supplied in the global oil market. (Ipt) i. Calculate the output of each member of the cartel: Q1 and Q2.(2pt) Consider the world oil market, in which a cartel (OPEC) and a competitive fringe (rest of the world) are operating. Suppose that global oil demand and the supply of the competitive fringe are given by the following functions: Qw=50PQf=30+P Furthermore, suppose that the cartel is comprised of two countries, and let each country's marginal cost function be as follows: MC1=13+Q1,MC2=13+4Q2. a. Derive the marginal cost function (MCo) of the cartel. (2pt) b. Calculate the price at which the competitive fringe would be driven out of the market (P1) and the price at which the cartel would be driven out of the market c. Due to the presence of the competitive fringe in the market, there will be a kink point in the demand curve of the cartel. Calculate the quantity (Q~) at which this kink occurs. (1pt) d. Derive the demand function of the cartel to the left of the kink point quantity (i.e., for QoQ~ ) and to right of the kink point (i.e., QoQ~ ). e. Using the inverse demand function of the cartel, derive the corresponding marginal revenue function to the left of the kink point and to the right of the kink point. f. Using the marginal revenue, marginal cost, and inverse demand functions obtained above, calculate the cartel's output (Qo) and the price charged per unit of output (Po). (2pt) g. Calculate the output of the fringe (Qf) at this price. (Ipt) h. Calculate the total output (Qo+Qf) supplied in the global oil market. (Ipt) i. Calculate the output of each member of the cartel: Q1 and Q2.(2pt)
