How does the new train affect the welfare of residents

Suppose that we have two cities in a larger system of cities. Call these cities San Francisco and Sacramento. San Francisco has a higher producer amenity that allows firms in that city to pay higher wages.

(a) Draw the housing price curves in these two cities.

(b) Now suppose that a high-speed bullet train is constructed between the CBD in San Francisco and the CBD in Sacramento. This train allows people to work in San Francisco while living in Sacramento, so now no one has to work for the lower productivity Sacramento firms. Riders only have to pay a small fee f to ride the train (which includes both monetary and time cost). Ignore for now where the money comes from to build the project. Describe graphically how this affects the housing price curves in the two cities. How does the price of housing at the CBD in Sacramento compare to the price of housing at the CBD in San Francisco?

(c) How does the new train affect the welfare of residents that originally lived in San Francisco? How does the new train affect the welfare of residents that originally lived in Sacramento?

(d) Suppose there is a vote at the state level about whether to let San Francisco and Sacramento build a bullet train (which they will pay for).

How should we expect residents of a third city, call it Bakersfield, which will not be connected to the bullet train, to vote, assuming they are rational?

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