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Light Rail Demand and Social Welfare

You are head of the Transportation Department in Kingston evaluating the operation of a light rail line that was previously built (probably in 2050) across Lake Mali. It has operated for long enough to pay back capital costs, but you still have to worry about operating costs. You are considering several options:
- Don't operate the light rail
- Privatize the system and let the market sort things out
- Continue to operate the light rail yourself
Problem Parameters
? There are two income classes of commuters, each with 5 members. One group earns $20 per hour. The other group earns $60 per hour.
? Time individuals spend commuting is considered to be an opportunity cost for the leisure or work they could otherwise pursue.
? Commuters have the option of taking either the Smith Bridge or the light rail
? Smith Bridge slows with additional cars (i.e. it is rivalrous)
? The light rail can carry any capacity of ridership w/ no slowing
? Individuals care only about their own financial well-being.
? Net daily individual income equals 8 * wages - the cost of two commutes
? Net societal income is the sum of individual net incomes plus any light rail profits.
? When all else is equal (when costs of riding light rail equal cost of commuting via car), commuters will choose to ride the light rail

(See attached)

You may wish to fill in the table above to help you answer the questions below.

1. If the one-way light rail fare is $2.00, and there is no cost to driving, how many commuters will choose to ride the light rail?
2. If there is no light rail fare, and the cost of driving is $7.00 each way (tough gas prices!), how many commuters will ride the light rail?

3. What number of light rail riders would minimize the total commute time for society?
4. In the $2.00 light rail fare case, will the majority of light rail riders be from the high- or low-income group? Explain.
5. Assume no variable cost of riding the light rail, but a $7 one-way cost of driving (gas usage + wear & tear on your car). Is it the best outcome for society to encourage light rail ridership level such that it minimizes the total commute time for society? If yes, explain. If no, explain and state the optimum level of ridership.
Now imagine there is no light rail and that driving has a wear and tear cost of $1.00 per one-way trip. Assume the $1.00 wear and tear cost for all questions that follow.

6. What would be the total societal commute time?
7. What would be the total net societal income?
Now imagine a private operator runs the light rail, and it has an operating cost of $0.25 per rider. Remember, when costs of riding monorail equal cost of commuting via car, commuters will choose to ride the light rail.

8. Fill in the demand for light rail ridership at each fare?

(see attached)

9. What is the equilibrium fare?
hint: you may wish to fill in the rest of the table to answer this question.
10. What is the equilibrium number of riders?
hint: use the information on demand and think about monopoly pricing.
11. Does the private company make a profit or loss? What is the profit or loss?
12. What is net societal income?

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Solution Preview

See the attached file.

In the first table the total time in the rail is fixed 25, but in the total time you are showing different time.

In the eighth ...

Solution Summary

Light rail demand and social welfare are articulated and discussed in the solution.