The effect of the Reagan admninistration's proposed cuts in Social Security benefits on the private pension system would be unwelcome and burdensome, according to one of the country's largest pension consulting firms.

Rodger Patrick, senior partner of Hewitt Associates, said that reducing Social Security's share of the average worker's retirement benefits from the current 41 percent to 38 percent could raise an employer's pension costs by about 7 percent.

According to Reagan administration estimates, the savings to the Treasury from reducing this "replacement ratio" by three percentage points would be between $4.2 billion and $4.7 billion from 1982 to 1986. Private pension plans could be expected to make up about half of the percentage reduction by increasing the benefits they pay, Patrick said. This would increase private employers' pension costs by an average of 7 percent.

Patrick said many employers would try to avoid the extra burdensome costs. But other changes proposed by the administration probably will make that effort unecessary.

By reducing early-retirement Social Security payments from 80 percent to 55 percent of benefits and eliminating the earnings test, the government hopes to induce more workers to stay on the job until age 65 and after. This will reduce employers' pension costs by an estimated 12 percent to 15 percent, according to Hewitt's calculations.

Patrick gave the example of a retirement-age worker earnings $12,000. If the government will pay him $8,000 a year in Social Security benefits and allow him to continue earning as much as he can, there is no reason for him to quit working when his pay has been effectively increased to $20,000 overnight, Patrick said.

However much they may save on pensions, employers cannot but look unfavorably on a program that keeps many older workers on the payroll and thereby cuts their productivity, he continued. He also questioned the effect large numbers of older workers remaining on the job would have on youth unemployment.

Therefore, Patrick predicted that employers still would continue to encourage early retirement. He said this could be done by restructuring retirement benefits on a front-loaded basis. Businesses will pay more benefits to workers between age 62 and 65 and fewer to those over 65. Thus, although the cost of buyouts would increase, the employers' overall pension costs would not.

The Employee Benefits Research Institute estimates the private pension system pays out somewhere between $10 billion and $15 billion in retirement benefits annually