he city of Metropolita added a new subway station in a neighborhood between two existing stations. After the station was built, the average house price increased by $10,000 (in the current year) and the average commute time fell by 15 minutes per day (starting in the next year). Suppose that there is one commuter per household, that the average commuter works 5 days a week, 50 weeks a year, and that the benefits of reduced commuting time apply in perpetuity. Assume a discount rate of 5%. Produce an estimate of the average value of time for commuters based on this information.

Question

Mathematics

Madeline

21 February, 15:27

he city of Metropolita added a new subway station in a neighborhood between two existing stations. After the station was built, the average house price increased by $10,000 (in the current year) and the average commute time fell by 15 minutes per day (starting in the next year). Suppose that there is one commuter per household, that the average commuter works 5 days a week, 50 weeks a year, and that the benefits of reduced commuting time apply in perpetuity. Assume a discount rate of 5%. Produce an estimate of the average value of time for commuters based on this information.

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Bentley · Answer 1

V = $8

Step-by-step explanation:

Letting V denote the value of an hour,

the annual value of the time savings from the change can be written as

= (5 days/week * 50 weeks/year *.25 hours/day) * V, or 62.5 V per year.

The present value of 62.5 V per year, forever, at a 5% discount rate, is

= 62.5 V / 0.05.

The implication of the change in house prices is that households were willing to pay $10,000 to gain 15 minutes per commuting day, i. e., that the present value of the time savings is $10,000.

Setting 62.5 V / 0.05 = $10,000 and solving gives V = $8