The Commissioner of Social Security may enter into an agreement with any State which wishes to do so under which the Commissioner will determine eligibility for medical assistance in the case of aged, blind, or disabled individuals under such State’s plan approved under subchapter XIX. Any such agreement shall provide for payments by the State, for use by the Commissioner of Social Security in carrying out the agreement, of an amount equal to one-half of the cost of carrying out the agreement, but in computing such cost with respect to individuals eligible for benefits under this subchapter, the Commissioner of Social Security shall include only those costs which are additional to the costs incurred in carrying out this subchapter.