Microeconomic Theory: Lecture 4 Monopoly

1 Monopoly Price Discrimination Double Marginalization Microeconomic theory : Lecture 4. Monopoly Parikshit Ghosh Delhi School of Economics Summer Semester, 2014. Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist The Monopolist's Problem I The monopolist realizes his quantity choice a ects market price through the demand function. I Monopolist's problem can be described either as one of choosing optimal price or optimal quantity. I Inverse demand function p (q ) and cost function c (q ).

2 I Maximizing pro ts: max p (q )q c (q ). q I First order condition: p (q m ) + qp 0 (q m ) = c 0 (q m ). | {z } | {z }. marginal revenue = marginal cost Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Monopolist's Optimum: Another Look I The FOC can be rewritten as qm dp pm 1 + . = c 0 (qm ). pm dq 1. or, pm 1 = c 0 (qm ). e (qm ). I e (q ) is the elasticity of demand at quantity q. The monopolist never operates on the inelastic part of the demand curve. I Yet another way to write it: pm c 0 (qm ) 1.

3 =. pm e (qm ). I The mark-up is equal to the inverse of demand elasticity. Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Comparison With Competitive Markets I Competitive output level: p (q ) = c 0 (q ). I The monopolist produces less than the competitive market. I Suppose q m q ) p (q m ) p (q ) and c 0 (q m ) c 0 (q ). I Subtracting the 's yields a contradiction: p (q m ) p (q ) + qp 0 (q m ) = c 0 (q m ) c 0 (q ). | {z } | {z } | {z }. = +. I Unlike a competitive rm, when a monopolist raises output, he earns lower revenue on previous units.

4 Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Monopoly in Pictures Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Monopoly in Pictures Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Monopoly in Pictures Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Non-Discriminating Monopolist Monopoly in Pictures Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Price Discrimination: First Degree I Each consumer buys 0 or 1 unit and is willing to pay up to v.

5 I There is a continuum of consumers whose v follow a distribution with F (v ). I The monopolist can charge each consumer his personal v . I Must choose a cuto v above which to sell: Z . max vf (v )dv c (1 F (v )). v v I First-order condition (using Leibnitz Rule) implies absence of ine ciency: v f (v ) + c 0 (1 F (v ))f (v ) = 0. v |{z} = c 0 (1 F (v )). | {z }. price to marginal customer = marginal cost Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Price Discrimination: Second and Third Degree I Second degree price discrimination arises when the monopolist can charge di erent prices for di erent quantities.

6 I , bulk discounts, multi-packs, frequent- yer miles, buy-one-get-50%-o on next purchase, etc. I A way to extract consumer's surplus from a single consumer. I Third degree price discrimination arises when observably di erent groups are charged di erent prices. I , student/senior citizen discounts, country speci c prices. I A cruder form of rst degree price discrimination using group identity as a predictor of individual traits. I A common instrument of price discrimination: screening. Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly

7 Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Second Degree Price Discrimination Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Two Part Tari.

8 Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Two Part Tari . Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Two Part Tari . I Suppose a single consumer with income y has quasi-linear utility: u (q, m ) = (q ) + m. I The monopolist can charge an entry fee (f ) and a price (p). per unit of consumption. I Consumer's optimum quantity choice (if she subscribes): 1. max (q ) + y f pq ) q (p ) = 0 (p ).

9 Q I Consumer subscribes if (participation constraint): (q (p )) + y f pq (p ) y Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Types of Price Discrimination Two Part Tari . I The monopolist's problem: max pq (p ) + f c (q (p )). f ,p subject to (q (p )) + y f pq (p ) y I Participation constraint must be binding at optimum (otherwise simply increase f ). max (q (p )) c (q (p )) ) 0 (q b) = c 0 (q b). p I If the market were competitive (price taking behaviour): 0 (q ) = c 0 (q ). I Again, two-part tari s remove the monopolistic distortion.

10 Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Monopolistic Screening Airfares: More Than 2 Weeks Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Monopolistic Screening Airfares: Less Than 2 Weeks Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Monopolistic Screening Hardcover vs. Paperback: Prices Parikshit Ghosh Delhi School of Economics Monopoly Monopoly Price Discrimination Double Marginalization Monopolistic Screening Hardcover vs.