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The University of Chicago 4/21/2017 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/r-picker@uchicago.edu Copyright © 2000-12 Randal C. Picker. All Rights Reserved.

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

Copyright © 2000-12 Randal C. Picker 4/21/2017 Integrated Monopoly Marginal Revenue Curve: P = 10 - 2Q Max at MR = MC P Q Demand Curve Marginal Cost CS PM Profits DWL TC QM Marginal Revenue April 21, 2017 Copyright © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 = 10 - 2Q April 21, 2017 Copyright © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker

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 © 2000-12 Randal C. Picker