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Class 9 WhiteboardAntitrust, Fall, 2012
Vertical Restraints: Double Marginalization
Randal C. PickerLeffmann Professor of Commercial Law
The Law School
The University of Chicago773.702.0864/[email protected] © 2000-12 Randal C. Picker. All Rights Reserved.
April 19, 2023 Copyright © 2000-12 Randal C. Picker 2
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 19, 2023 Copyright © 2000-12 Randal C. Picker 3
Finding Marginal Revenue
D. Curve: P = 10 - QPrice
109876543210
Quantity012345678910
Total Rev091621242524211690
Rev Diff
97531-1-3-5-7-9
Marg Rev
86420-2-4-6-8
-4.5
P x Q RC[-1] – R[-1]C[-1]
(RC[-1] + R[+1]C[-1])/2
Formula:MR = 10 – 2Q
April 19, 2023 Copyright © 2000-12 Randal C. Picker 4
Deriving Marginal Revenue
TR = P x Q = (10 – Q) x Q = 10Q – QxQ Differentiate TR with respect to Q:
TR210
April 19, 2023 Copyright © 2000-12 Randal C. Picker 5
Integrated Monopoly
Marginal Revenue Curve: P = 10 - 2Q Max at MR = MC
Marginal RevenueQM
PM
TC
Profits
CS
DWL
P
Q
Demand Curve
Marginal Cost
April 19, 2023 Copyright © 2000-12 Randal C. Picker 6
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 19, 2023 Copyright © 2000-12 Randal C. Picker 7
Derived Demand Curves
Retailer Decisionmaking Our monopolist retailer will maximize by
equating its costs with marginal revenues, so
Pw + 2 = 10 - 2Q
April 19, 2023 Copyright © 2000-12 Randal C. Picker 8
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 19, 2023 Copyright © 2000-12 Randal C. Picker 9
Finding Marginal Revenue
D. Curve: Pw = 8 - 2QP x Q RC[-1] – R[-1]C[-1]
((RC[-1] + R[+1]C[-1])/2)*2
(units rising in half unit increments)
Formula:MR = 8 – 4Q
Price Quantity Total Rev8 0 07 0.5 3.56 1 65 1.5 7.54 2 83 2.5 7.52 3 61 3.5 3.50 4 0
Rev Diff
3.52.51.50.5-0.5-1.5-2.5-3.5
Marg Rev
6420-2-4-6
April 19, 2023 Copyright © 2000-12 Randal C. Picker 10
Deriving Marginal Revenue
TR = P x Q = (8 – 2Q) x Q = 8Q – 2QxQ Differentiate TR with respect to Q:
TR48
April 19, 2023 Copyright © 2000-12 Randal C. Picker 11
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 19, 2023 Copyright © 2000-12 Randal C. Picker 12
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
Q2
PW
P2
M MC
M MR
Derived DC
April 19, 2023 Copyright © 2000-12 Randal C. Picker 13
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 19, 2023 Copyright © 2000-12 Randal C. Picker 14
Double Marginalization
It ignores the profits that that difference creates for the monopolist manufacturer when it makes its purchasing decisions.
