When William Penn Mott Jr. became chief of the California park system in 1967, he faced a challenging mandate: Gov. Ronald Reagan ordered him to increase income from the system without raising entrance fees for park visitors.

"At first it didn't seem possible, but we found a way," Mott recalled with a large grin. Mott imposed a 50-cent-a-head fee on dogs brought into the parks. "We took in $250,000 the first year and nobody complained," he said.

Two weeks ago Mott, 75, took over as chief of the National Park Service, and immediately faced a similar mandate from the same boss. In his fiscal 1986 budget, President Reagan has called for a sharp increase in user fees from national parks and recreation areas.

Mott, in his optimistic, can-do way, says he'll meet that mandate.

The administration's budget calls for a cut of nearly 30 percent in Park Service funding -- from an estimated $911 million this fiscal year to $670 million in 1986 -- and proposes that some of the difference be made up through increased fees.

The White House says the Park Service should take in 25 percent of its operating costs through user fees; those fees now defray 7 percent of costs. The argument for the increase is part finances, part fairness: the current fee structure represents a large subsidy to a relatively small group of park users.

In an interview here during his first inspection tour as Park Service director, Mott said that "25 percent seems pretty reasonable. We could probably do better than that."

Raising fees at the national parks is a well-worn issue in Washington, popping up every other year or so and generally being swatted down in short order by Congress.

Entrance fees have been frozen by statute since 1979. User fees -- for campgrounds, fishing licenses, etc. -- are not controlled by law, but Congress has resisted proposals to raise them in recent years.

Consequently, a visit to a national park remains one of the country's great bargains.

Here at Yellowstone, the world's most famous park, the cost of admission for a whole family (actually, one carful) is $2 for seven days, and admission to the equally spectacular Grand Teton National Park is included in that price.

"Two bucks -- that's almost absurd," said park superintendent Robert Bardee. "It barely pays for the cost of having somebody at the entrance station to collect the money."

Mott said he was "startled" during his visit here last week to learn that a fishing license in Yellowstone Park is free. By contrast, in the three states just outside the park boundaries, a nonresident may pay more than $30 for the right to fish the same rivers that run through the park.

"I can't believe that anybody would complain about paying something like $5 for a fishing license in this wonderful park," Mott said. "If people are getting a quality experience, they're not going to rant and rave about a modest fee for that."

A $5 fishing license fee here would bring in $2 million annually, said Barbee, the park superintendent. "But you have to remember it's going to cost us something to collect that money," he added.

Mott insisted that park fees will not be increased merely to help the Office of Management and Budget reduce the federal deficit. "We will raise our fees where it's reasonable, but some of that money has to come right back to our parks for improvements," he said.

It is this connection -- using increased fees to help sustain the park system in an era of decreasing budgets -- that Mott hopes to use to overcome congressional opposition to changes in the fee structure.

The increase in fees would also fit nicely with Mott's belief that the number of visits to some major parks must be controlled to reduce human impact on the parks' natural inhabitants. The new Park Service chief says he wants to determine a "carrying capacity" for each big national park and keep the number of visitors at or below that figure -- an idea that has won strong support from environmental organizations. CAPTION: Picture, A family now pays $2 to enter Yellowstone National Park for a visit of up to seven days, but President Reagan has called for a sharp increase in such user fees. By Christian Science Monitor