Suppose that different levels of service can be provided by a docking station, resulting in different probabilities that
Posted: Tue Apr 26, 2022 3:57 pm
Suppose that different levels of service can be provided by a
docking station, resulting in
different probabilities that a boat will be warned of its nearness
to the rock. For
example, the more powerful the beacon (or signal) emitted by the
docking station, the
higher the probability that a boat will receive the warning.
However, once the light is
turned on, all boats in the area benefit.
The marginal cost (MC) of attaining various probabilities (Q) is MC
= 2Q. There
are two boats in the area, one owned by the pirate
captain Lucille, and the
other owned by the pirate captain Aurora. Their individual demand
functions for
the service is:
Lucille : P = 10 − Q
Aurora : P = 10 −1/2Q
(a) What is the socially optimal level of service, and how much is
it worth to each
pirate captain? Carefully draw relevant equations on a diagram with
the price on the
vertical axis and level of service (Q) on the horizontal
axis.
(b) The docking station is privately owned, however. Assume
that each pirate captain
will willingly pay to the lighthouse owner the value he, the
captain, gets from
the service, and not try to free-ride. What level of service will
the free market
provide, and how much will each pirate captain pay? Add relevant
information
to the diagram from a).
docking station, resulting in
different probabilities that a boat will be warned of its nearness
to the rock. For
example, the more powerful the beacon (or signal) emitted by the
docking station, the
higher the probability that a boat will receive the warning.
However, once the light is
turned on, all boats in the area benefit.
The marginal cost (MC) of attaining various probabilities (Q) is MC
= 2Q. There
are two boats in the area, one owned by the pirate
captain Lucille, and the
other owned by the pirate captain Aurora. Their individual demand
functions for
the service is:
Lucille : P = 10 − Q
Aurora : P = 10 −1/2Q
(a) What is the socially optimal level of service, and how much is
it worth to each
pirate captain? Carefully draw relevant equations on a diagram with
the price on the
vertical axis and level of service (Q) on the horizontal
axis.
(b) The docking station is privately owned, however. Assume
that each pirate captain
will willingly pay to the lighthouse owner the value he, the
captain, gets from
the service, and not try to free-ride. What level of service will
the free market
provide, and how much will each pirate captain pay? Add relevant
information
to the diagram from a).