The homology of infinite-dimensional Lie algebras in connection with Macdonald identity

D. Fuchs' monograph devoted to the cohomology of infinite-dimensional Lie algebras contains an error in calculating the homology of graded affine Kac–Moody algebra of type $A_n^{(1)}$, so that the proof of the corresponding Macdonald identity which is based on that calculation appears to be incorrect. In the present paper the corrected proof is suggested.