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Economics 1480
Answer key #2
1) Rosen Chapter 4: problem 11
a.
Zach’s marginal benefit schedule shows that the marginal benefit of a
lighthouse starts at $90 and declines, and Jacob’s marginal benefit starts at
$40 and declines. Neither person values the first lighthouse at its marginal
cost of $100, so neither person would be willing to pay for a lighthouse
acting alone.
b.
Zach’s marginal benefit is MB
ZACH
=90Q, and Jacob’s is MB
JACOB
=40Q.
The marginal benefit for society as a whole is the sum of the two marginal
benefits, or MB=1302Q (for Q
≤
40), and is equal to Zach’s marginal
benefit schedule afterwards (for Q>40). The marginal cost is constant at
MC=100, so the intersection of aggregate marginal benefit and marginal
cost occurs at a quantity less than 40.
Setting MB=MC gives 130
2Q=100, or Q=15.
Net benefit can be measured as the area between the
demand curve and the marginal benefit of the 15
th
unit.
The net benefit is
$112.5 for each person, for a total of $225.
2) Rosen Chapter 4: problem 13
Britney’s marginal benefit is MB
BRITNEY
=12Z, and Paris’s is MB
PARIS
=82Z.
The marginal benefit for society as a whole is the sum of the two marginal
benefits, or MB=203Z (for Z
≤
4), and is equal to Britney’s marginal benefit
schedule afterwards (for Z>4).
The marginal cost is constant at MC=16.
Setting
MB=MC along the first segment gives 203Z=16, or Z=4/3, which is the efficient
level of snowplowing.
Note that if either Britney or Paris had to pay for the entire
cost herself, no snowplowing would occur since the marginal cost of $16 exceeds
either of their individual marginal benefits from the first unit ($12 or $8).
Thus,
this is clearly a situation when the private market does not work very well.
Also
note, however, that if the marginal cost were somewhat lower, (e.g., MC
≤
8), then
it is possible that Paris could credibly free ride, and Britney would provide the
efficient allocation.
This occurs because if Britney believes that Paris will free
ride, Britney provides her optimal allocation, which occurs on the second segment
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 Spring '10
 Knight
 Economics

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