Question

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=80-P

Qf=-60+p

suppose the cartel is comprised of 2 countries, let each countries marginal cost function be as follows:

MC1=5+2Q2

MC2=5+2Q2

1. Derive the marginal cost function (?C?) of the cartel. (2 pt)

2. Calculate the price at which the competitive fringe would be driven out of the

market (?1) and the price at which the cartel would be driven out of the market

(?2). (2 pt)

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 price (?) and quantity (?) at

which this kink occurs. (2 pt)

d. Derive the demand function of the cartel to the left of the kink point quantity (i.e.,

for ?? ≤ ??�) and to right of the kink point (i.e., ?? ≥ ?). (2 pt) ????

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. (2 pt)

f. Using the inverse demand and marginal revenue functions that you obtained in parts d. and e., calculate the cartel’s output (?? ) and the price charged per unit of output (??). ?? (2 pt)

7. Calculate the output of the fringe (?f ) at this price, along with the total output (?? + ?? ) supplied in the global oil market. (2 pt)

8. Calculate the output of each of the two members of the cartel; Q1 and Q2

Answer 1

a) The marginal cost function (?C?) of the cartel is derived through horizontal summation of firm's individual Marginal Cost curves.

Therefore, MCo =  MC₁ + MC₂ = 5+2Q₂ + 5+2Q₂ = 10 + 4Q₂

b) The price at which competitive fringe is driven out of the market, is when Qf=0, that is,

-60 + p = 0

which implies p=60

Therefore, the price at which the competitive fringe would be driven out of the market (?1) is $60

The price at which the cartel would be driven out of the market is when Qw=Qf

80-p = -60 +p

140 = 2p

p = 70

Therefore, the price at which the cartel would be driven out of the market (?2) is $70.

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 as shown in the graph below. The price (?) and quantity (?) at which this kink occurs is P1= $60 and Q= Qw at P1. therefore, Q_kink = 80-60 = 20 the kink occurs at (20, 60)

d) Demand curve to the left of Q= 20 i.e. Q<20, is cartels demand curve derived by subtracting Qf from Qw between price p=70 to p=60.

therefore, Qc = Qw-Qf = (80-p) - (-60+p) = 140-2p

Demand curve to the right of Q=20, i.e. Q>20, is the world demand curve, i.e. Qw= 80-p