Cab drivers, lawyers, artists and other self-employed taxpayers would have to bear a higher share of the Social Security tax burden under the plan to rescue the national retirement system proposed by a bipartisan commission last weekend. The proposed increase would be greater for entrepreneurs in lower tax brackets than those in the top tax brackets according to Congressional estimates.

This proposal, part of the recommendations agreed to by the National Commission on Social Security Reform and endorsed by President Reagan and Congressional leaders, would raise an estimated $18 billion in new revenues between 1983 and 1989.

The tax on the self-employed would grow from three-quarters of the combined rate paid by employer and employe to the full amount. However, half of the total payment would be deductible on the entrepreneur's income taxes.

Under current tax law the 1984 rate on Social Security contributions for self-employed persons would be 9.35 percent. The commission would raise that to 14 percent. Some 8.9 million self-employed would be affected.

The deduction proposed by the commission would favor higher-income taxpayers. For example, because of the deduction, a single person with a taxable income of $20,000 would have a greater net tax increase than another single taxpayer with an $81,800 income, counting the changes in Social Security and income taxes, according to Congressional sources.

A typical taxpayer with a $20,000 income and a marginal tax rate of 31 percent now pays an $1,870 Social Security contribution. The proposed reform would raise that to $2,800. But half of that, or $1,400, could be claimed as a deduction, which would lower the federal income tax by $434 for someone in that tax bracket. This person would wind up paying $2,366, or a net increase of $496 in additional taxes--the Social Security tax increase minus the reduction in federal income taxes.

Meanwhile, a person earning $81,800 would pay a Social Security contribution of $3,506 in 1984 under the current rate. The proposed higher rate would raise the tax to $5,250. But of that amount, half would be deductible on the federal tax return. Since this person is in the 50 percent tax bracket, this new deduction would lower the federal income tax by $1,312.50. As a result, the net tax increase--income and Social Security--would be $431.50, according to Congressional staff estimates..

Thus the net tax increase for the person with the smaller income would be 26.5 percent, while that for the maximum earner would be just 12.3 percent under the commission's plan.

When asked what the self-employed could do to counter such an increase, should it be approved by Congress, Alex Zakupowsky, a partner in Deloitte, Haskins & Sells, replied, "very little." A self-employed person could incorporate, thus becoming an employe of a corporation. However, this would not materially benefit a person of modest income, he said. He suggested that a fairer way to impose the new Social Security tax would be to allow a tax credit, rather than a deduction, for one half the tax increase.