1. The University of Chicago
4/21/2017
Class 9 Whiteboard Antitrust, Fall, Vertical Restraints: Double Marginalization
Randal C. Picker
Leffmann Professor of Commercial Law
The Law School
The University of Chicago
Copyright © Randal C. Picker. All Rights Reserved.

2. Copyright © 2000-12 Randal C. Picker
4/21/2017
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
April 21, 2017
Copyright © Randal C. Picker

3. Finding Marginal Revenue
4/21/2017
Finding Marginal Revenue
P x Q
RC[-1] – R[-1]C[-1]
D. Curve: P = 10 - Q
(RC[-1] + R[+1]C[-1])/2
Formula:
MR = 10 – 2Q
April 21, 2017
Copyright © Randal C. Picker

4. Deriving Marginal Revenue
4/21/2017
Deriving Marginal Revenue
TR = P x Q = (10 – Q) x Q = 10Q – QxQ
Differentiate TR with respect to Q:
April 21, 2017
Copyright © Randal C. Picker

5. Copyright © 2000-12 Randal C. Picker
4/21/2017
Integrated Monopoly
Marginal Revenue Curve: P = Q
Max at MR = MC P Q
Demand Curve
Marginal Cost CS PM
Profits
DWL TC QM
Marginal Revenue
April 21, 2017
Copyright © Randal C. Picker

6. Copyright © 2000-12 Randal C. Picker
4/21/2017
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.
April 21, 2017
Copyright © Randal C. Picker

7. Copyright © 2000-12 Randal C. Picker
4/21/2017
Derived Demand Curves
Retailer Decisionmaking
Our monopolist retailer will maximize by equating its costs with marginal revenues, so
Pw + 2 = Q
April 21, 2017
Copyright © Randal C. Picker

8. Deriving Demand Curves
4/21/2017
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.
April 21, 2017
Copyright © Randal C. Picker

9. Finding Marginal Revenue
4/21/2017
Finding Marginal Revenue
P x Q
RC[-1] – R[-1]C[-1]
D. Curve: Pw = 8 - 2Q
((RC[-1] + R[+1]C[-1])/2)*2
(units rising in half unit increments)
Formula:
MR = 8 – 4Q
April 21, 2017
Copyright © Randal C. Picker

10. Deriving Marginal Revenue
4/21/2017
Deriving Marginal Revenue
TR = P x Q = (8 – 2Q) x Q = 8Q – 2QxQ
Differentiate TR with respect to Q:
April 21, 2017
Copyright © Randal C. Picker

11. Copyright © 2000-12 Randal C. Picker
4/21/2017
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.
April 21, 2017
Copyright © Randal C. Picker

12. Copyright © 2000-12 Randal C. Picker
4/21/2017
Stacked Monopolies
Derived Demand: Pw = 8 - 2Q
M MR Curve: MR = 8 - 4Q QM PM TC
Profits CS
DWL
Marginal Revenue P Q
Demand Curve
Marginal Cost P2
Derived DC PW
M MR
M MC Q2
April 21, 2017
Copyright © Randal C. Picker

13. Double Marginalization
4/21/2017
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.
April 21, 2017
Copyright © Randal C. Picker

14. Double Marginalization
4/21/2017
Double Marginalization
It ignores the profits that that difference creates for the monopolist manufacturer when it makes its purchasing decisions.
April 21, 2017
Copyright © Randal C. Picker