Question 2)
Consider a three-mode choice situation in which a worker must choose between auto,
bus, and walking for the journey to work.
The systematic utility functions for the
alternatives are :
V
auto
= 1.0-0.1(TT
auto
)-0.05(TC
auto
)
V
bus
= -0.1(TT
bus
)-0.05(TC
bus
)
V
walk
= -0.5-0.1(TT
walk
)
Where :
TT
i
= travel time by mode i, minutes
TC
i
= out-of-pocket travel cost by mode i, dollars
A person is faced with travel times of 8, 14 and 24 minutes for the auto, bus and walk
modes, respectively.
Similarly, out-of-pocket travel costs by auto and bus are $2.00 and
$1.80, respectively.
a) Calculate the probability of auto, bus, and walk for this person.
b) The buses in this example are operated by the Red Bus Transit Co.
Assume that a
new operator, Blue Coach Lines, introduces a service that is identical to that of the Red
Bus Transit Co.
(i.e. 14 minute travel time, $1.80 fare, and follows the same utility
function shown above), except that the buses are blue instead of red.
We now have
four modes being chosen. Calculate the probabilities of each of these four modes.
c) Compare the results to those of the three-mode example.
Are the results reasonable,
especially given that the model ignores the frequency of service?
Why or why not?
d) Compute the following point elasticities:
i) The direct elasticity of the
person’s
probability of using the auto drive
mode with respect to auto out-of-pocket travel cost.
ii) The cross elasticity of the
person’s
probability of using the bus mode
with respect to auto out-of-pocket cost.
iii) The cross elasticity of the
person’s
probability of using the auto mode
with respect to bus out-of-pocket cost/fare.
Compare the results of parts (ii) and (iii) above. Briefly discuss the reasonableness of
these results.
Given that auto travel cost is essentially determined by the price of gasoline, briefly
discuss the implications for the use of gasoline taxes as a means for reducing auto
usage.
