Prince George's County Executive Lawrence J. Hogan yesterday recommended $2 million in cuts in the county's budget for the suburban Maryland park and planning agency. The cuts would transform a proposed 3.9-cent increase in the park and planning tax rate into a one-cent tax cut.

This tax, currently set at 39.97 cents per $100 of assessed valuation, is added to property owner's real estate tax bills. If the County Council accepts Hogan's recommendations, the owner of a $50,000 home will pay $87.68 for parks and recreation, $11.02 less than under the proposed budget of the Parks and Recreation Department and $2.25 less than what he paid in this fiscal year.

In exchange for that tax break, however, county residents would lose some recreation programs, both new and old, and probably would notice longer grass and more cracked pavement in playgrounds and parking lots in their parks, a department official said yesterday.

Many of the cuts in the proposed $26.9 million budget "don't look all that bad, but if it's your parking lot that ends up having potholes, they will be bad," said Doug Sherwood, budget director of the bicounty Maryland-National Capital Park and Planning Commission.

Under Hogan's suggested cuts in the Prince George's recreation budget, three programs for teen-agers would be reduced in length to save money. One program, a summer day camp in Seat Pleasant for 900 economically disadvantaged youths, would be shortened to six weeks from eight.

In addition, a parks bus program used to transport youngsters to and from parks and to special recreational events in the summer would be cut back 45 percent, parks department officials said yesterday. Normally, the program sends 60 buses a day to 180 playgrounds during the summer.

New maintenance equipment and additional maintenance staff positions budgeted by the parks department have been cut out of the budget entirely. In all, Hogan suggested new programs, equipment and staff be taken out of the fiscal 1980 budget.

A total of about $500,000 is cut out of the commission's administrative budget under Hogan's plan, while $1 million would be cut out of the parks fund and more than $500,000 out of the recreation fund.

He also suggested a few new programs, including a summer day camp for handicapped children, and hiring two more park naturalists and a new recreation specialist for senior citizens.

Unlike other county departments, the county parks department, which is part of the bicounty commission, is not subject to the property tax restrictions of TRIM, the voter-approved county charter amendment. The tax cut recommended by Hogan is not mandated by law, as it is for the general county budget.

But in a letter to County Council Chairman Willaim B. Amonett, Hogan argued that the commission's proposed spending increase of 16 percent over this year was "not responsive to our citizens' mandate to reduce government spending."

In contrast, Montgomery County Executive Charles Gilchrist yesterday recommended no reductions in the Montgomery portion of the parks and planning commission spending plan, saying that the $16.5 million Montgomery park and planning budget was the "tightest" submitted by any of his county's agencies.