The rental car industry has buckled itself into the nation's economy.

With business travelers accounting for between 80 percent and 85 percent of their customers, Avis, Hertz and National Car Rentals have been among the first to feel any slowdown in the nation's economic pulse.

"We can be a harbinger of things to come," said Frank Lonano, vice president and general manager of Avis Rent-A-Car.

So far, the industry reports it still is putting a lot of people in the driver's seat. Hertz says its business is up between 16 percent and 20 percent and it hasn't seen any sign of an economic showdown. Avis and National both agree.

Still, Frank A. Olson, president and chief executive officer of Hertz, expects upward-racheting interest rates to take a toll on the economy. "We expect a downturn in the first quarter of next year," he said.

However, this time Olson thinks the rental car industry will not suffer as much as the general economy. "The rental car business has become part of the transportation network of the country," he said, and as such it is a prime candidate to benefit from many of the structural changes that have taken place in the country.

He said among these changes are the shift of companies to suburban locations, requiring the use of an automobile to visit them; the rising number of families with both husband and wife working, resulting in increased leisure travel; and the advent of low cross-country air fares.

Lonano said he is cautiously optimistic about the prospects for the industry in 1980. "We can't see interest rates getting much higher, and if they come down, we'll get some more opportunities to grow as the economy recovers," he said.

Lonano also noted that business psychology about traveling has changed somewhat over the last serveral years. In the past, advertising and travel were among the first items cut during a recession. Now, however, he said, some managers take the position, "Let's get out and sell more. If we get out there personally, we can make the sale."

Additional impetus for the industry will come with the Winter Olympics in Lake Placid, N.Y., and the election campaign. Both the political parties and the media rent a large number of automobiles during election years. And the Super Bowl always is a big stimulant to car renting.

Another source of strength has been the strong travel market to Florida. With the deregulation of the airline industry, more airlines are flying to Florida, and the rental car business is booming. Olson said Hertz's Florida business has grown by between 40 percent and 50 percent this year. The California market also has been strong.

The industry isn't without problems. The gasoline shortage this summer changed driving patterns. Thus renters in Los Angeles, for example, would fly to San Francisco and rent a car rather than drive there. Rental periods were shortened. "Intercity business was off," said Lonano.

Higher gasoline prices also have cut into profit somewhat. For example, Hertz now is sitting on top of 10 million gallons of unleaded gasoline that was bought at about $1.30 a gallon. The gasoline, sitting in storage tanks, is "looking for a home," said Olson, "not at today's lower spot gasoline prices."

The companies' latest foray had led them to go after the leisure travel market. Hertz, with a large fleet that sits unused during the weekends, decided to stimulate the leisure travel market with what is considered competitive pricing. The pricing included a flat rate and unlimited mileage.

Immediately, Budget Rent-A-Car lowered its rates. Because 60 percent of Budget's business is in the weekend-traveler category, it felt as if Hertz was going after its share of the market.

Morris Belzberg, Budget president, began an aggressive advertising campaign, claiming Budget's rates are $10 a day cheaper than Hertz's. Olson tried to get the television networks to take the ad off the air, claiming it is wrong. The networks have refused so far, and Olson is appealing the decision to the National Advertising Review Board.

Although Olson refuses to admit he is in a price war with Belzberg, he is keeping his rates competitive.