(FORTUNE Magazine) – The golden goose may not be as fecund as she once was. Theme and amusement parks, those incredible cash machines, reported record attendance of 249 million and gross receipts of over $4 billion in 1988. But so far this summer, overall attendance is only just holding even. Managers blame rain. Others worry that customers may be getting sick of ever-increasing price hikes. Just getting a family of four past the turnstiles of some parks costs upward of $100. Says Bob Whittaker, manager of Nashville's Opryland USA (admission: $18.95, up $1 from last year): ''All of us in the industry are a little bit concerned about a point of resistance.'' Larry Cochran, president of Six Flags of Texas (the largest operator next to Disney), puts the problem more baldly: ''Pricing is stretched as high as we can stretch it. We're on the outer edge.'' Admission to Six Flags' seven parks averages $18.50. Attendance, about even with 1988, is 4% below projections. Six Flags may still see 17 million visitors by summer's end, and Cochran insists that all the parks are bargains: eight hours of high divers, dolphins, clowns, music, touchable cartoon characters, and Russian acrobats -- not to mention rides such as the awesome Scream Machine at Great Adventure in Jackson, New Jersey. Randy Baker, manager of Anheuser-Busch's four theme parks, says surveys show that 90% of Busch's customers think they're getting good value, even at up to $22.50. One of the parks is down 14%, the others holding even. Busch, whose parks appeal mainly to middle-income families, is interested in buying Harcourt Brace Jovanovich's Sea World, which draws from the same audience. MCA also is said to be eyeing Sea World. Disneyworld and Disneyland, meanwhile, continue to flourish. Despite a 4% price increase, attendance is up over 10% at Disneyworld, partly on the strength of Pleasure Island, which includes shops and a seven-nightclub complex. A.F.