Freedie Laker is persistent. He also appears to have taken Economics 101 or the equivalent. The combination of the two soon may result in a bargain for travelers to London and lots of money for Freedie Laker.

After a six-year quest, Laker, the ebullient head of Britain's Laker Airways, has won the endorsement of the Civil Aeronautics Board for at least a one-year trial of his proposal to provide low-fare Skytrain air service between New York and London. The board's recommendation awaits President Carter's expected approval.

Laker's proposal is based on a simple idea which is known as "full-plane economics." If he kept his operating costs to a minimum and flew large planes, he might be able to fill all the seats with customers by offering fares significantly lower than the current cartel-set rates, and he still could make more money than the regular scheduled carriers, which fly half-full aircraft, he reasoned. That would make both the customers - who perhaps cannot now afford to fly - and him happy, he decided.

As a result, his proposal Skytrain is a bare-bones, one-class operation. Travelers would not be able to purchase tickets more than six hours in advance. There would be no extensive network of ticket offices and computer reservations systems. It would be strictly first come, first served. When the available seats on each flights are sold - 345 during the peak summer season and 189 during the rest of the year - that's it. The only meals provided would have to be paid for when the traveler bought the ticket - all of it in cash, no credit cards.

Laker plans to carry no cargo and no mail operations - just people.

Under the license issued to him by the British government, the number of people he can carry is limited. He is being restricted to 11 flights a week during the peak travel season, and to 1 flight a day, with half the plane roped off, during the rest of the year.

The price tug: $135 to London, and currently about $101 back. It is expected that the fare each way will be $135 by the time service is initiated. The cause of the disparity is the change in the value of the British currency because Laker's early 1975 application to the British authorities suggested a fare of 59 British pounds each way. Under the current exchange rate, 59 pounds is about $101.48.

The current coach fare between New York and London is $367 each way during the current peak summer season and $323 each way the rest of the year. The lowest fare currently available from the scheduled airlines across the Atlantic and back is $440, if the passenger is able and willing to make reservations and pay for the ticket 45 days in advance of the flight and can stay 22 to 45 days.

Laker always has contended that his Skytrain will not appeal to all travelers. Most who can afford it will want to continue to fly the scheduled carriers, he says, and families and others who want to be assured of seats and who can plan their vacations more than a month ahead of time probably still will want to take advantage of charter flights which offer significant savings over the scheduled fares. Laker's flights are for "the forgotten man and the forgotten woman," he says, for the travelers who may not otherwise be able to go to Europe.

The flights may also make the United States more of a tourist attraction for foreign visitors. And if the experiment is a success, other countries, particularly France, will be bidding to start similar service.

Only a small fraction of the large numbers of people who fly between the United States and the United Kingdom each year - almost 3 million last year - can be accommodated on the Skytrain: just 255,408 in the first year of operation under the capacity limitations the British have imposed. Laker estimates he will be carrying 111,337 eastbound and 113,169 westbound, thus filling 87.5 per cent of its available seats.

The other carriers argued before the CAB that Laker couldn't possibly make money - he thinks he will make a profit of $4 million in the first year - even with a 100 per cent load factor at the fares he plans to charge, but the CAB rejected their contentions. "There seems little doubt that Laker is an efficient, low-cost operator," the board said. "Laker is not a subsidized public corporation, but a strictly private enterprise which is in business to make a profit and apparently, has been quite successful in doing so heretofore."

Robert M. Beckman, Laker's Washington attorney, said Laker's operations have shown a profit each year for the 30 he has been in business. Laker currently is limited to charter operations. His flights carry about 1 million passengers a year - 400,000 between England and North American (half to Canada and half to the United States), and 600,000 to European cities.

Laker's efforts on behalf of his innovative idea have pitted him against the notorious delays of the American regulatory agencies as well as the opposition of his own government at times. He first applied for Skytrain authority from the British on June 15, 1971. That came through and the started his quest for the American okay in December 1972.When the British government was on his side then, however, the CAB wasn't, thanks to what Laker complained of as an overly protective attitude of the U.S. flag carriers and their "high fare" service, an attitude he called "PanAmania."

Then, while his application here was proceeding at the snail's pace the CAB had become famous for, the British government turned against him - it was being overly protective of the government-owned British Airways and the high fares it charged, he argued - and he had to sue Her Majesty's Government. He won, and in February the British asked the U.S. to resume processing the Laker application because it once again had designated the carrier to serve the London-New York route under the terms of the U.S.-U.K. bilateral agreement.

No one really knows how successful the Skytrain will be, or if it really will be successful, but the vigor with which the other carriers - both scheduled and charter - fought it suggests that they fear it will be very successful. And the CAB has gone to great lengths in its Laker decision to give the U.S. carriers the opportunity to respond competitively if the want to. And both Pan American World Airways and Trans World Airlines, which have argued so strenuously over the years that they cannot possibly drop fares across the Atlantic, have said they would do so.

The board's approval of Laker's operations is conditioned on the ability of the U.S. carriers to take part in the one-year low-fare experiment on a fair and equal basis. Built into the approval is a broadly worded clause that would allow the U.S. to suspend Laker's Skytrain service if it was found that the British government had restricted properly authorized U.S. carriers from instituting service competitive with Laker's at fares no lower than Laker's and under rules acceptable to the U.S. government. The CAB thinks, for instance, that the U.S. carriers may want to experiment by using the low far in other ways, such as with standbys on regularly scheduled flights, and doesn't want to foreclose those possibilities.

"We would hope, of course, that with a measure of good will and restraint on both sides, it will never be necessary to invoke the clause at all," the board said, but it said it had reason to be careful. Both governments are trying to negotiate a new bilateral agreement governing scheduled air services between the two to replace the one the British government denounced a year ago. Under the abandoned Bermuda Agreement, the carriers of each nation were afforded equal opportunity, but the British essentially felt their carriers are not earning enough money on the transatlantic flights - they are carrying something more than one-third of the traffic. They are seeking an agreement where they get exactly half. Because dividing up the market into arbitrary shares is inimical to American economic policy at home and abroad, the negotiations have not been going well.

The CAB also noted that the British government recently sought to limit unilaterally the capacity offered by U.S. carriers over the objections of the U.S. government, notwithstanding the provisions of the still-in-effect agreement precluding unilateral restrictions.

Besides the broad new agreement between the two countries, there are some thorny issues left to resolve in the more narrow Laker situation. For instance, the CAB is insisting that Britian give equal access to low-fare equal access to low-far competitive service to both U.S. carriers flying between New York and London, not just one of them. In addition, it wants the British to allow the low-fare experiment by the American carriers at Heathrow Airport - the place they now fly - and not the farther-away Stansted Airport near London that the British have insisted Laker's Skytrain use. Afer all, the CAB said, the U.S. is allowing Laker to use J.F. Kennedy Airport in New York.

The remaining problems aside, Beckman, Laker's attorney here, said he and Laker have "no doubt" that Skytrain will be in the air sometime soon. He says they always expected that intergovernmental discussions would have to resolve some issues. Noting that the Carter administration is committed to more offering the public the lowest air fares possible, he said similar views are being expressed by British officials, notably Edmund Dell, the U.K.'s secretary of state for trade."We're riding the tide of consumerism on both sides of the Atlantic," he crows.