Local telephone rates went up Thursday, and AT&T's long-distance prices are going down, soon to be followed by those of rivals US Sprint Communications Co. and MCI Communications Corp.

This script has been replayed several times in recent years as part of an effort by federal regulators to shift the costs of the local phone network to local customers.For about half of all customers, long-distance price cuts of 38 percent since 1984 have more than offset the rise in local rates, according to the Federal Communications Commission. Those in the other half, however, don't call long-distance enough to benefit. Instead, their overall bill is higher.

Beginning Thursday, customers will see another 60 cents added to their monthly local phone bills, and American Telephone & Telegraph Co. will drop its basic interstate long-distance rates an average of 3.8 percent.

US Sprint said it will drop its rates Jan. 1 an average 3.85 percent, about the same for business as for residential customers. MCI expects to announce details of a price cut next month.

AT&T is able to make its $697 million annual reduction, and US Sprint and MCI theirs, because costs of connecting to the local network are being reduced by the corresponding increase in customers' monthly bills.

With Thursday's 60-cent increase, the subscriber line charge has risen to $3.20. The federal charge, imposed in 1985, is designed to reduce the subsidy long-distance companies pay to maintain the local network.

A customer who makes about $5.20 per month in direct-dialed long-distance calls saves enough to offset the effects of the line charge, according to James L. Lande in the FCC's industry analysis division.

"About half the people are at least breaking even," he said.

AT&T will cut its basic long-distance rates for calls traveling more than 124 miles by 3.8 percent. It will make smaller cuts in rates for interstate calls of shorter distances, which account for about one-quarter of AT&T interstate calls.

The largest among the price cuts will go to large volume users, both residential and business.

Rates for Reach Out America, AT&T's long-distance calling plan for residential customers, will be cut 4.9 percent.

AT&T WATS rates will drop 4 percent and the company will restructure the service to bill calls individually based on time and distance, rather than by the current hourly pricing method. This price reduction is to take effect Jan. 1, a month later than the others.