Question

Suppose Standard OIl consists of two firms with marginal costs MC1(Q1) = 6+Q1 and MC2(Q2) = 6+2Q2. The inverse demand function would be P(Q) = 194-2Q, where Q=Q1+Q2 Suppose that standard oil is a dominant firm with a competitive fringe given by Qf(P)=-6+P/2.

1) How much oil will standard oil produce in the prescence of a competitive fringe

2) How much oil will the competitive fringe produce

3) What will be the market price for a barrel of oil?

4) How much oil will firm 1 of standard oil produce?

5) How much oil will firm 2 of standard oil produce?

Answer 1

Find the residual demand. Here demand function is converted to P = 194 – 2Q or 2Q = 194 – P or Q = 194/2 – P/2. This implies the demand is Q = 97 – 0.5P.

RD = Market demand – fringe supply

= 97 – 0.5P + 6 – 0.5P

= 103 – P

Find the aggregate marginal cost for Q1 + Q2

Q1 = MC – 6, Q2 = 0.5MC – 3

Q = Q1 + Q2 = MC – 6 + 0.5MC – 3

Q = 1.5MC – 9

1.5MC = Q + 9

MC = 6 + 0.67Q

Now from the demand function we have P = 103 – Q. MR = 103 – 0.5Q. Standard oil will use MR = MC

103 – 0.5Q = 6 + 0.67Q

97 = 1.167Q

Q = 83 (approximately)

MC = 61.5

P = 103 – 83 = $20.

Q1 = 61.5 – 6 = 55.5

Q2 = 0.5*61.5 – 3 = 27.5

Fringe supply = - 6 + 20/2 = 4 units.

1) How much oil will standard oil produce in the prescence of a competitive fringe

87 units

2) How much oil will the competitive fringe produce

4 units

3) What will be the market price for a barrel of oil?

$20

4) How much oil will firm 1 of standard oil produce?

55.5 units

5) How much oil will firm 2 of standard oil produce?

27.5 units