Complementary Goods

1
Complementary Goods

• Complementary goods are goods that are consumed
  together
• nuts and bolts
• PC monitors and computer processors
• How should these goods be produced?
• How should they be priced?
• Take the example of nuts and bolts
• these are perfect complements need one of each!
• Assume that demand for nut/bolt pairs is

Q A - (PB PN)
2
Complementary goods (cont.)
This demand curve can be written individually for
nuts and bolts
For bolts QB A - (PB PN)
For nuts QN A - (PB PN)
These give the inverse demands PB (A - PN) - QB
PN (A - PB) - QN
These allow us to calculate profit maximizing
prices
Assume that nuts and bolts are produced by
independent firms
Each sets MR MC to maximize profits
MRB (A - PN) - 2QB
Assume MCB MCN 0
MRN (A - PB) - 2QN
3
Complementary goods (cont.)
Therefore QB (A - PN)/2
and PB (A - PN) - QB (A - PN)/2
by a symmetric argument PN (A - PB)/2
The price set by each firm is affected by the
price set by the other firm
In equilibrium the price set by the two firms
must be consistent
4
Complementary goods (cont.)
PB (A - PN)/2
PN (A - PB)/2
Pricing rule for the Nut Producer PN (A - PB)/2
PB
? PN A/2 - (A - PN)/4
Equilibrium is where these two pricing
rules intersect
A
A/4 PN/4
Pricing rule for the Bolt Producer PB (A -
PN)/2
? 3PN/4 A/4
? PN A/3
? PB A/3
A/2
? PB PN 2A/3
A/3
? Q A - (PBPN) A/3
Profit of the Bolt Producer PBQB A2/9
PN
A
A/2
A/3
Profit of the Nut Producer PNQN A2/9
5
Complementary goods (cont.)
Merger of the two firms results in consumers
being charged lower prices and the firm making
greater profits
What happens if the two goods are produced by the
same firm?
The firm will set a price PNB for a nut/bolt pair.
Why? Because the merged firm is able to
coordinate the prices of the two goods
Demand is now QNB A - PNB so that PNB A - QNB

? MRNB A - 2QNB
MR MC 0
A
? QNB A /2
? PNB A /2
A/2
Profit of the nut/bolt producer is PNBQNB A2/4
Demand
MR
Quantity
A
A/2