The chairman of the House Social Security subcommittee yesterday laid down for study a plan to solve the system's financing problems, both long range and short, in part by raising the retirement age starting in the year 2000.

Chairman J.J. Pickle (D-Tex.) said the proposals represented the most promising among hundreds that have been suggested. The provisions include:

Funding half of Medicare from the income tax rather than the Social Security tax, thereby freeing more Social Security revenues to shore up the old age insurance fund.

Raising the normal retirement age from 65 to 68 stages from 2000 to 2012.

Eliminating the earnings limitation for persons 65 and over, as promised by President Reagan. This provision would cost the system money but the costs would be offset by other changes.

Providing that the annual automatic increase in benefits be based on increases in wages paid in the economy, instead of on increases in prices in years of high inflation when wages lag behind price increases.

Shifting the date of payment of automatic increases to Oct. 3 from July 3 beginning in 1982.

Phasing out the so-called students benefit, eliminating the $122 minimum benefit but only for future beneficiaries, and installing a "cap" on the total that can be received in public disability benefits -- all proposals made in somewhat different form by Reagan.