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PORTLAND, Maine — The rail authority that runs the Downeaster is proposing a new fare system that would increase ticket prices on the most crowded trains and drop prices on runs that usually have many empty seats, the Morning Sentinel reported.

Overall, fares would increase more than 4 percent. It would be the first increase since the service began a year ago, and is modeled after the way airlines do business.

The maximum increase on a Portland-to-Boston ticket would be $2, from $21 to $23. Fares also would change with the seasons, rising in the summer on many trains but then dropping after Labor Day.

The proposal calls for slashing fares for commuters traveling within Maine but increasing fares by 7 percent to 15 percent for passengers departing from stations in New Hampshire. Passengers departing from Haverhill, Mass. would also see an increase. Maine is the only state that subsidizes the service, and rail authority officials say they want to show the Maine Legislature that they are making every reasonable attempt to minimize the state’s subsidy.

That state subsidy is only $400,000 this year, but the rail authority projects it will grow to $1.3 million when federal start-up money dries up in two years.

The proposed change in fares is part of a strategy to collect the maximum amount of revenue the market can bear while filling the trains with the greatest number of people. The board of directors for the Northern New England Rail Authority voted on Dec. 13 to present the plan to the public for discussion.

“This is not done out of the desire to raise money for the heck of it,” said John Englert, the rail authority’s executive director, “but a matter of trying to eke as much from our existing infrastructure as we possibly can. It is simply smart business. That’s all.”

The authority is attempting to address the uneven way the service is being used. While some weekend trains are so crowded that people are turned away, many weekday trains have a surplus of empty seats. The Downeaster has a lot of occasional riders but not many regular riders, and there are very few people using the train to travel within Maine.

The proposal would leave unchanged the cost of commuter passes and 10-trip tickets. In fact, to encourage public transportation, the authority and Concord Trailways have agreed on a pilot project that would allow the holders of 10-trip tickets to travel either by train or bus without a reservation.

Under the new rate structure, the 10-ride pass, which is valid for 10 one-way trips between two cities within a 45-day period, would provide frequent travelers a 20 percent discount.

The authority hopes businesses will buy such tickets for employees because they offer a hassle-free way travel, Englert said.

“We have to get a lot smarter,” Englert said, “and look at the service from the customer point of view rather than our point of view.”

The proposal continues the popular $35 round-trip fare, but passengers would have to travel in off-peak periods to use it. While the current round-trip fare requires purchasers to return on the same day, the new fare would allow travel over multiple days.

The proposal gives people options, said Barbara Whitten, who sits on the rail authority board and also serves as president of Portland’s Convention and Visitors Bureau. Those concerned about the cost of a ticket could travel on the cheaper trains, while those who want to travel on the most popular trains won’t have to worry about finding seat, she said.

“It’s really a supply-and-demand situation,” she said. Wayne Davis, head of Train Riders/Northeast, a citizen lobby group, declined to comment on the proposal until he had a chance to study it.

Englert said the Downeaster’s costs are rising because of scheduled union wage increases and a sharp rise in insurance costs. The service cost an estimated $6.9 million this year, and the cost is projected to rise to $7.1 million next year. The service this year took in $4.7 million in revenues.

Because the fare plan is designed to change according to advanced bookings, the authority has not provided a list of which trains would see higher or lower prices. However, Englert said the fares of some trains will be easy to predict.

The fare for the train that departs from Boston at the unpopular time of 11 p.m., for example, would certainly decrease from $21 to 17.50, a 17 percent reduction, he said. The fare for the train that departs Portland at 8:45 a.m. would be unchanged for most weekdays, but on weekends would increase to $23, a 10 percent increase.

Also, the fare for the train that departs Boston at 6:15 p.m. —the service’s most popular train — would increase on most days from $21 to $23.

The rail authority’s board of directors plans to vote on the plan when it meets on Jan. 10. People can comment on the plan on the authority’s Web site, www.thedowneaster.com. The plan can be found by clicking on “News and Releases.”

Also, the rail authority and Concord Trailways have agreed on a pilot project that would allow holders of 10-trip tickets to travel either by train or by bus without a reservation.