Lectures%2022%2B23%20Price%20Discrimination

Lectures%2022%2B23%20Price%20Discrimination - If we can...

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1 If we can distinguish every single consumer and know his demand: ± Perfect price discrimination (“First Degree Price Discrimination”) ± Efficient ± But : Are we satisfied with a solution where all the gains from trade go to one party? A = Consumer Surplus ± Fixed fee A that extracts consumer surplus Non-linear Prices in the Demand - Supply Diagram MC q p p=c q* ± p=c efficient production Pricing scheme: Demand Aggregation Model 1 p q Downward sloping individual demand Reservation price for one good unit demanded Aggregation Model 2 Model 2 q 1 r p p q 1 r 1 p q = 1 2 p + q 1 r 2
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2 Elasticity ± Measure of relative changes instead of absolute changes: ± The Elasticity measures the percentage change in demand (supply) induced by a percentage change in price. p p q q Δ Δ = ε > 2 1 Demand D 1 is more elastic than D 2 ± q p D(p) Elasticity ± Linear Demand D(p) = a - b · p bp a bp = b a 2 2 a | ε | > 1 | ε | < 1 0 | ε | = 0 a b a | ε | = | ε | = 1 ± The monopolist’s maximization problem: Optimum: Marginal Revenue = Marginal Cost ± How is this different from perfect competition? Firm takes into account the impact of a marginal sale on the revenue from inframarginal units Monopoly C(q) R(q) q max (q) C (q) R = Monopoly: q q p p (q) R + = p (q) R = Perfect Competition:
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3 A Linear Example C, Π , R q C(q) R(q) q ^ q Demand: bq - a P(q) = Cost: 2 q 2 c C(q) = 2 bq - aq R(q) : Revenue = ^ ^ q R MAX 1 maximized is Revenue : q ˆ ˆ At = ±
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Lectures%2022%2B23%20Price%20Discrimination - If we can...

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