Question

4. Modes of Transit

As seen in class, the average cost per commuter depends on the number of commuters and the mode of transportation. Assume that in the town of Mos-Espa the average cost per commuter for each respective transportation mode is given by the following functions, where n is the number of commuters using that mode per day:

AC Auto, Private = 3 AC Auto, External = 0 1-2+ 100 if n < 200 if n > 200 ACbus = 2 + 1600 ACtrain = 5+ 2400

(A) Given these functions, fill the cells of the table below. Round Any Decimals to two place.

To receive full credit you need to show your work for all of the cells of at least

one row. (2 points)

(B) Referring to part (a), plot the values and draw the functions for the average cost per

commuter for automobiles (private), automobiles (social), bus, and train on the graph

below. I encourage you to use graphing software to assist with this problem. (1 point)

(C) Referring to parts (a) or (b), at what threshold number of commuters per day will buses

begin to have a lower average cost than average cost of automobiles from a private per-

spective (that is, ignoring the external costs)? No explanation is required. (1 point)

(D) Referring to parts (a) or (b), at what threshold number of commuters per day will buses

begin to have a lower average cost than average cost of automobiles from a social per-

spective (that is, including the external costs)? No explanation is required. (2 points)

(E) Referring to parts (a) or (b), at what threshold number of commuters per day will trains

begin to have a lower average cost than average cost of automobiles from a social perspec-

tive (that is, including the external costs)? No explanation is required. (2 points)

Answer 1

A)

Private All Autombile) External All Autombily) ACLAM Social ACCAMO 3. Bus AL 10 To A 17 200 you 3 0 bou 7 4.66. 9 4 800 - 1000 8 11 3.6 7.4

B)

Acom AC(Truen) AllBus) -Alpha CAM 200 yoo 800 1000 600 h

C)3=2+1600/n

1=1600/n

n=1600

After 1600 commuters average bus cost will get lower than average private cost of automobile

D) 3-2+n/100=2+1600/n

-1=1600/n-n/100

After solving,

n~453

E)3-2+n/100=5+2400/n

n/100-2400/n=4

After solving

n~729