America’s best-known investor, Warren E. Buffett, is making his biggest bet yet on the nation’s economic future by buying, of all things, a railroad.

Warren E. Buffett

Railroads were once the engines of the U.S. economy. What role do they play now?

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After deftly capitalizing on the financial crisis with a series of bold deals, Mr. Buffett on Tuesday agreed to buy the 131-year-old Burlington Northern Santa Fe Corporation.

A railroad might strike many people as a bit old-fashioned — more 19th century than 21st. But Mr. Buffett is wagering that as the economy revives, so will the demand for goods to be shipped by train. Burlington Northern carries coal and timber from the West,...