[ $YBa_2Cu_3O_{7-y}$ ](123) powders were synthesized by the solid state reaction method using two different purity $BaCO_3$ powders (99.75% and 99.7% purity) and $Y_2O_3$ (99.9%) and CuO (99.9%) powders. The effect of $BaCO_3$ purity on the formation of a 123 phase and the superconducting properties were investigated. The mixtures of raw powders were calcined at temperature ranges of $800^{circ}C-880^{circ}C$ in air and finally made into a single grain samples by a melt processing with top seeding. It was found that a 123 phase was well formed at temperature above $870^{circ}C$, but the purity effect on the 123 formation was negligible. The single-grain 123 samples prepared from the different $BaCO_3$ powders showed the same $T_c$ value of 90.5 K and similar $J_c$ values about $10^4;A/cm^2$ at 0 T and 77 K, and $10^3;A/cm^2$ at 2 T and 77 K. This result indicates that the low purity, cheap price $BaCO_3$ powder can be used as a raw material for the fabrication of single-grain, high-$J_c$ superconducting levitator.