Course Objectives: · Critique a peer’s e-portfolio and pitch by providing feedback using the assigned rubric. Prompt Examine the work of one of the peers with which you linked to in Week 5. You will
Running head: Week 2 Math Assignment 1
Week 2 Math Assignment
Steven C. Higgs
TLMT601 Transportation Economics
American Public University
Dr. Wallace Burns
08 July 2019
Assignment Questions:
Please show all work for this quiz and explain your derivations. Lack of step-by-step work will not be credited. Partial credit will be given for step-by-step description of answer.
a. In trip calculation, it is observed that a Wal-Mart store driver successfully made a total of 120 trips in a given period of time. During field calculation, it is shown that the calculated number of trips is actually 144. What is the value of the adjustment factor? ____ (14 points)
Kij=Tij(observed)/Tij(calculated)
Tij(observed) = 120
Tij(calculated)= 144
Kij = 120/144
Kij= 0.8333
b. It is shown that the population of New York City, NY is much greater than that of Irvington, NJ. Employment opportunities, malls, social activities and tourist sites in New York City are therefore more than that in Irvington. If attractiveness for New York and Irvington are therefore 1,600 and 160 respectively and if the calculated impedance of migration is known to be 1.57, based on Gravity-Based model, estimate in demands, the number of people who travel between Irvington, NJ and New York City per week. ____ (14 points)
VAB=NA*NB*IAB
Vab=demand for transportation between New York City, NY and Irvington, NJ
NA=Impedance of Migration for New York City, NY=1,600
NB=Impedance of Migration for Irvington, NJ=160
IAB=Calculated impedance of migration as per the Gravity-Based Model
Vab=1600*160*1.57
Vab=401,920 people/week
c. Elasticity can be defined as percentage change in demand for a 1% change in decision attribute. For linear aggregate demand, what is the mathematical representation/formula for this statement? You must define the parameters you choose to use for this answer. ____ (14 points)
ex(V)=Linear Aggregate Demand
x= mode type, trip purpose, time of day, trip length, trip-maker characteristics, existing level of factor
V= the point elasticity of travel demand
ex(V)= x/V
d. In the City of Joplin, due to weather devastation and hurricane effects, the cost of parking in the local Square has increased by 15%. This change has not only reduced the number of vehicles that travel to the Square by 10%, but it has also forced the inhabitants of Joplin to use buses. Bus trips have therefore increased to 25%. With respect to the cost of parking in the local Square, determine the elasticity of vehicle traffic. ____ (14 points)
Where:
initial parking price = p1
final parking price = 1.15p1
initial transit demand = Vt1
final transit demand = Vt2=1.25Vt1
initial auto demand = Va1
final auto demand = Va2=.90Va1
eTP=(Va2-Va1)(p1+p2)/2(p2-p1)(Va1+Va2)/2
=(.90Va1-Va1)(p1+1.15p1)/2[(1.15p1-p1)(Va1+.9Va1)/2]
=(-0.1)(2.15)/2[(0.15)(1.9)/2]
=-0.215/2(0.1425)
=-0.215/0.285
=-0.75
e. In your own words, describe the meaning of average cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk informs you that the same crate of wine now costs $82. However, there are 10 bottles in a crate. To the nearest cent, determine the average cost of the crate from last month to now. ____ (14 points)
Average Costs: The Average Total Cost, ATC, is the total cost associated with 1 unit of output. It is calculated as the ratio of the total cost to the output: ATC = TC /V , where TC is the total cost and V is the volume (output). The Average Fixed Cost, AFC, is the fixed cost associated with 1 unit of output and is calculated as the ratio of the fixed cost to the output, AFC = FC /V . Similarly, the Average Variable Cost is the cost of 1 unit of output and is calculated as the ratio of the variable cost to the output, AVC = VC /V. Average costs help in establishing the relationship of supply and demand in relation to supply chain economics.
75/8=$9.375 per bottle
82/10= $8.20 per bottle
$9.375-$8.20=$1.18 difference in bottle cost
75-82=-7, or a case has increased in cost by $7.00
f. In your own words, describe the meaning of marginal cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk informs you that the same crate of wine now costs $82. However, there are 10 bottles in a crate. To the nearest cent, determine the marginal cost for one additional bottle of wine now. (15 points)
Marginal Cost: The marginal cost of a transportation good or service is the incremental cost of producing an additional unit of output. The terms of incremental cost, differential cost, and marginal cost have essentially similar meaning but typically are used in contexts that have very subtle differences. Incremental cost is a small increase in cost. Differential cost is the ratio of a small increment of cost to a small increase in production output. Marginal cost analysis is relevant in transportation system evaluation because an agency may seek the incremental cost changes in response to planned or hypothetical production of an additional unit of output with respect to facility construction, preservation, or operations. Marginal cost and average cost can differ significantly. For example, suppose that an agency spends $10 million to build a 10-mile highway and $10.5 million to build a similar 11-mile highway, the average costs are $1 million and $0.954 million, respectively, but the marginal cost of the additional mile is $0.5 million. The expressions related to marginal cost are as follows: Marginal Variable Cost: MVC = ∂VC ∂V Marginal Total Cost: MTC = ∂TC ∂V = ∂ FC ∂V + ∂ VC ∂V = ∂ VC ∂V = MVC Like average cost, marginal cost concepts help an agency or shipper to evaluate the cost impacts of various levels of output or the additional cost impact of moving from a certain output level to another.
$9.375-$8.20=$1.18 difference in bottle cost
75-82=-7, or a case has increased in cost by $7.00
g. In your own words, describe the meaning of unit travel. When traveling on a Greyhound bus, without intervention or obstruction, it is important to determine the unit travel time. If you leave Cleveland in a bus full of 30 passengers and arrive Cincinnati in 4 hours, what will be the average unit travel time in person minutes? ____ (15 points)
Unit travel: Unit in-vehicle travel time per traveler, U1 = OCC × TT V where TT V is the average vehicular operating travel time and OCC is the average vehicle occupancy. In cases where the travel speeds of trucks and other commercial vehicles are significantly different from passenger vehicles, separate travel time estimates should be made for each vehicle class.
Assuming that 30 passengers include me, the average unit travel time will be 30 x 240 = 7200 without interruption. 4 hours = 240 minutes multiplied by 30 passengers.
References
Sinha, K. C., & Labi, S. (2007). Transportation decision making: Principles of project evaluation and programming. Hoboken, NJ: John Wiley & Sons, Inc.
