L2p2 - Microeconomics(Mikk 3 Lecture 2 Part II Monopoly...

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Microeconomics (Mik°k) 3 Lecture 2, Part II: Monopoly Pricing and Adverse Selection Johan N. M. Lagerl±f Dept. of Economics, U. of Copenhagen Email: [email protected] Website: www.johanlagerlof.org January 31, 2011 J. Lagerl±f (U of Copenhagen) Microeconomics (Mik°k) 3: L2-II Spring ²11 1 / 29
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Agenda Non-linear monopoly pricing Fully non-linear tari/s. J. Lagerl±f (U of Copenhagen) Microeconomics (Mik°k) 3: L2-II Spring ²11 2 / 29
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Fully Non-Linear Tari/: Intro (1/1) Now suppose the ³rm can choose any non-linear tari/ , not necessarily a TPT. In particular, suppose that the ³rm o/ers two price-quantity (or price- quality ) bundles to the consumers: I ° q , t ± is directed to the low-valuation consumers. I ( q , t ) is directed to the high-valuation consumers. This structure allows for a two-part tari/ as a special case. I Therefore, if we now ³nd that this special case is not optimal, it´s a con³rmation that using a two-part tari/ is indeed restrictive. Assumptions: 1 The parameters are such that it is optimal for the ³rm to sell to both consumer types, rather than focusing on only the high-valuation consumers. 2 µBunching¶ (the same contract to both types) not considered · we will show later in a problem set that this is never optimal with two types. J. Lagerl±f (U of Copenhagen) Microeconomics (Mik°k) 3: L2-II Spring ²11 3 / 29
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Fully Non-Linear Tari/: The problem (1/1) The ³rm chooses ° q , q , t , t ± so as to max. its expected pro³t, V ° q , q , t , t ± = ν ° t ° cq ± + ( 1 ° ν ) ( t ° c q ) , subject to four constraints: I Low types must prefer their bundle to no bundle at all: θ u ° q ± ° t ± 0 . (IR-L) I High types must prefer their bundle to no bundle at all: θ u ( q ) ° t ± 0 . (IR-H) I Low types must prefer their bundle to the high types´bundle: θ u ° q ± ° t ± θ u ( q ) ° t . (IC-L) I High types must prefer their bundle to the low types´bundle: θ u ( q ) ° t ± θ u ° q ± ° t . (IC-H) J. Lagerl±f (U of Copenhagen) Microeconomics (Mik°k) 3: L2-II Spring ²11 4 / 29
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Fully Non-linear Tari/: Graphical analysis (1/5) An allocation that does NOT solve the maximization problem What would be the ideal solution for the ³rm? I That would be to let the two types consume their ³rst-best levels q FB and q FB , and then choose some payments · call them t FB and t FB · such that neither type gets any rents (their IR constraints are binding). Is that allocation (and the associated pro³t level for the ³rm) achievable? I No, it would not be incentive compatible · it would violate the high type´s IC constraint. I See ³gure [L2-II, ³g. 1]! J. Lagerl±f (U of Copenhagen) Microeconomics (Mik°k) 3: L2-II Spring ²11 5 / 29
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Fully Non-Linear Tari/: Graphical analysis (2/5) Possible ways of making the allocation incentive compatible Adjusting the prices (see °gure [L2-II, °g. 2] on next slide) Make the low type´s bundle more expensive. [ B FB !
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