Question

Within certain limits, a bus company has a demand function connecting patronage (Q) and price per ride (P) as follows: Q = 2150 − 1000P where Q is person-trips/day and P is the price (dollars/ride). Suppose the manager has the following options to increase the total revenue: (1) attracting additional riders by rescheduling and rerouting the service and thus changing the demand function to Q = 2175 − 1000P, or (2) encouraging more riders onto the system by reducing the fare from $1.30 to $1.00. (a) What option would you advise the manager to adopt, giving good reasons for doing so? (b) What is the change of the consumer surplus if (1) is adopted? And if (2) is adopted?

Answer 1

Question :

Answer : Q = 2150 - 1000P

P = $1.30; Q = 2150 - 1000*1.3 = 850

Total Revenue = P * Q = $1.3 * 850 = $1105

Part a : Option 1 :

New Q = 2175 -1000P; P = $1.30

New Q = 2175 - 1000*1.30 = 2175 - 1300

New Q = 875

Total Revenue = P * New Q = $1.30 * 875 = $ 1137.5

Option 2 : Q = 2150 - 1000P

New P = $1; Q = 2150 - 1000 * $1 = 1150

total Revenue = New P * Q = $1 * 1150 = $1150

Here, the objective of manager was to increase total revenue, so, option 2 is giving the manager larger total revenue than the prevailing condition and option 2.

i.e. with Q = 1150 and P = $1

Part b : Consumer surplus in existing condition = $361.25

Consumer surplus in Option 1 = $382.81, therefore change = $382.81 - $361.25 = $21.56

Consumer surplus in option 2 = $ 661.25, therefore change = $661.25 - $361.25 = $300