Question

The Organization of Petroleum Exporting Countries (OPEC), in its heyday, could be considered as a cartel operating with a fringe of price-taking smaller firms. Suppose the world demand for oil is given by p = 400-Q , with p in dollars per barrel of oil and Q in millions of barrels per month. The fringe marginal cost curve is MCf = 40+0.5Qf (with Qf and MCf also in millions of barrels and dollars per barrel, respectively), and OPEC’s cost of producing oil is constant at $20 per barrel.

a) Determine the residual demand OPEC faces after accounting for the quantity supplied by the competitive fringe for any level of price.

b) How many barrels of oil will OPEC supply per month?

c) What is the resulting world oil price?

d) How many barrels of oil are supplied by the competitive fringe?

Answer 1

Marginal cost of dominant firm is 20 and that of competitive fringe is MC = 40 + 0.5Qf. This gives the fringe supply function as P = MC or P = 40 + 0.5Qf or Qf = (P – 40)/0.5. Market Supply is Qs = 2P - 80.

a) Residual demand is given by Qd – Qs or Qd = 400 – P – 2P + 80 or Qd = 480 – 3P. Inverse demand is given by P = 160 – Q/3.

b) Marginal revenue is MR = 160 – 2Q/3 and so we have dominant firms quantity as

MR = MC

160 – 2Q/3 = 20

2Q/3 = 140

Q = 140*3/2

Q = 210 units

c) World price of oil is P = 160 – 210/3 = $90. This is also the price charged by dominant firm OPEC.

d) Fringe will supply Q = 2*90 – 80 = 100 units.