I am struggling with the following question. Could someone please explain how to do it?
People are trying to go to the city centre. A bus takes 1 hour and will always take 1 hour, unaffected by traffic. If there is just one car on the road, it will take 20 minutes. Each additional car adds 15 seconds to all car journeys. A bus ticket costs £2.50 and petrol for a car costs £5.00 (independent of the time). The opportunity cost of time is £15 an hour.
a) What is the equilibrium number of cars?
b) What is the socially optimum number of cars?
Here is my attempt at part a:
- I found the cost of taking the bus to be £17.50 (£15 in time and £2.50 for the ticket).
- I also found the cost of using a car to be £15*(time in hours) + 5 (for fuel). I found the time in hours as (20 + 0.25(n+1))/60 so the costs of using a car to be 5 + (20 + 0.25(n+1))/4.
- I found the equilibrium number of cars by setting these equal to each other and solving for n to get 119. Is this correct?
I have not attempted part b yet as I have no clue what to do!
Any help will be appreciated!
Thanks in advance