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Unformatted text preview: n consumers buy the socially optimal quantity
(marginal utility equals marginal cost), whereas the
low-valuation consumers buy less than the socially optimal
quantity (marginal utility > marginal cost).
I 2 Low-valuation consumers derive no net surplus, while
high-valuation consumers derive a positive net surplus.
I 3 “E¢ ciency at the top.” “Rent extraction at the bottom.” The relevant personal arbitrage constraint is to prevent
high-valuation consumers from choosing the low-valuation
consumers’bundle. J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘
11 19 / 29 Fully Non-Linear Tari¤: Conclusions (2/3)
Intuition: Why e¢ ciency at the top, but not at the bottom?
Key to the result is that the high type is the one who gets, for
any given q, both:
(i) the highest marginal utility [the “single-crossing condition”] and
(ii) the highest total utility. Because of (ii), the …rm primarily wants to extract the high
type’ surplus (as it’ larger).
I However, if the high type has to pay too much, he can choose
the low type’ bundle instead.
s To prevent this, the monopolist makes the low type’ bundle less
attractive by o¤ering those consumers less.
This works because of (i): The high type su¤ers more from a
reduction in q than the low type.
I See (again) the …gure on the next slide [L2-II, …g. 4]. J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘
11 20 / 29 Fully Non-Linear Tari¤: Conclusions (3/3)
Suppose q stands for quality and the …rm is a railway company.
I Then the di¤erence in service level between …rst- and
second-class is larger under second best than under …rst best:
q-distance under FB q SB !
< q FB < q SB = q FB
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- Spring '11