Download Standard Setting in High

Class 9 Whiteboard
Antitrust, Fall, 2012
Vertical Restraints: Double
Marginalization
Randal C. Picker
Leffmann Professor of Commercial Law
The Law School
The University of Chicago
773.702.0864/[email protected]
Copyright © 2000-12 Randal C. Picker. All Rights
Reserved.
Demand and Costs

Production
Produced
by Manufacturer and sold by
Retailer.

Demand Curve
P

= 10 - Q
Marginal Costs
MC
of production (incurred by M) = 2
MC of distribution (incurred by R) = 2
May 23, 2017
Copyright © 2000-12 Randal C. Picker
2
Finding Marginal Revenue
PxQ

D. Curve: P = 10 - Q
Price
10
9
8
7
6
5
4
3
2
1
0
May 23, 2017
RC[-1] – R[-1]C[-1]
Quantity Total Rev Rev Diff Marg Rev
0
0
1
9
9
8
16
2
7
6
21
3
5
4
24
4
3
2
25
5
1
0
24
-1
-2
6
21
-3
-4
7
16
-5
-6
8
-7
-8
9
9
-4.5
10
-9
0
Copyright © 2000-12 Randal C. Picker
(RC[-1] +
R[+1]C[-1])/2
Formula:
MR = 10 – 2Q
3
Deriving Marginal Revenue


TR = P x Q = (10 – Q) x Q = 10Q – QxQ
Differentiate TR with respect to Q:
TR
 10  2Q
Q
May 23, 2017
Copyright © 2000-12 Randal C. Picker
4
Integrated Monopoly


Marginal Revenue Curve: P = 10 - 2Q
Max at MR = MC
P
CS
Demand Curve
PM
Profits
DWL
Marginal Cost
TC
QM
May 23, 2017
Marginal Revenue
Q
Copyright © 2000-12 Randal C. Picker
5
Stacked Monopolies


Suppose that we separate manufacturing
and retail.
Retailer Demand and Costs
The
retailer faces the same demand curve
as before.
As to costs, the retailer buys the good at
wholesale from M at a price of Pw.
This means that the retailer faces total per
unit costs of Pw + marginal cost of
distribution, which is 2.
May 23, 2017
Copyright © 2000-12 Randal C. Picker
6
Derived Demand Curves

Retailer Decisionmaking
Our
monopolist retailer will maximize by
equating its costs with marginal revenues,
so
Pw + 2 = 10 - 2Q
May 23, 2017
Copyright © 2000-12 Randal C. Picker
7
Deriving Demand Curves

Derived Demand Curve for Manufacturer
Rearranging
Pw = 8 - 2Q.
This looks like a relationship between
wholesale prices and the quantity that will
be demanded, meaning that we have
created the demand curve faced by the
manufacturer.
May 23, 2017
Copyright © 2000-12 Randal C. Picker
8
Finding Marginal Revenue
PxQ

D. Curve: Pw = 8 - 2Q
Price
8
7
6
5
4
3
2
1
0
May 23, 2017
RC[-1] – R[-1]C[-1]
Quantity Total Rev Rev Diff Marg Rev
0
0
0.5
3.5
3.5
6
1
6
2.5
4
1.5
7.5
1.5
2
2
8
0.5
0
2.5
7.5
-0.5
-2
3
6
-1.5
-4
3.5
3.5
-2.5
-6
4
0
-3.5
Copyright © 2000-12 Randal C. Picker
((RC[-1] +
R[+1]C[-1])/2)*2
(units rising in half
unit increments)
Formula:
MR = 8 – 4Q
9
Deriving Marginal Revenue


TR = P x Q = (8 – 2Q) x Q = 8Q – 2QxQ
Differentiate TR with respect to Q:
TR
 8  4Q
Q
May 23, 2017
Copyright © 2000-12 Randal C. Picker
10
M Decisionmaking

Marginal Revenue
We
need to derive the marginal revenue
curve from this demand curve, and it is MR
= 8 - 4Q.

Max by equating MC and MR
2

= 8 - 4Q, or Q = 1.5.
This gives us Pw = 5 and P = 8.5.
May 23, 2017
Copyright © 2000-12 Randal C. Picker
11
Stacked Monopolies


Derived Demand: Pw = 8 - 2Q
M MR Curve: MR = 8 - 4Q
P
P2
Derived DC
PM
PW
CS
Demand Curve
Profits
DWL
M MR
Marginal Cost
TC
Q2 QM
May 23, 2017
M MC
Marginal Revenue
Q
Copyright © 2000-12 Randal C. Picker
12
Double Marginalization

Two Monopolies Are Worse Than One
This
is the harm of stacked monopolies, or
of double marginalization.
What drives this is that the retailer makes its
decisions based on the costs it faces—the
wholesale price plus its marginal retail
costs—rather than the actual cost of
producing a unit of the good.
May 23, 2017
Copyright © 2000-12 Randal C. Picker
13
Double Marginalization
It
ignores the profits that that difference
creates for the monopolist manufacturer
when it makes its purchasing decisions.
May 23, 2017
Copyright © 2000-12 Randal C. Picker
14