gokhle model paper

[lipsa]

section B: Q.5
You are an analyst for a metropolitan transportation authority. You are asked if it would
improve efficiency to buy more buses, and if so, how many more should be bought. The
operating cost of a bus is 30 during the day and 60 during the night, when higher wages
must be paid to drivers and other workers. The daily capital cost of a bus, whether or not
it is used, is 10. The demand for buses aggregated over persons and stops during the 12
hours of day and night, respectively D and N, are
Qd= 160-Pd
Qn= 80-Pn

what prices should be charged to induce efficient ridership?
a) Pd=45 , Pn=55
b) Pd=40 , Pn=60
c) Pd=70 , Pn=80
d) Pd=60 , Pn=40

[Amit Goyal]

Maximize the following objective with respect to d and n, where d denotes total number of buses used during day-time and n denotes total number of buses used during night-time:

Total surplus generated during day time by using d buses + Total surplus generated during night time by using n buses-Cost
= (1/2)d^2 + d(160-d) + (1/2)n^2 + n(80-n) -(30d + 60n + 10d)
and you will get d = 120 and n = 20.
Hence Pd = 40 , Pn = 60