LetEbe the exterior algebra of a finite dimensional vector space over a fieldK. Hilbert functions and Betti numbers of graded idealsi⊂Eare studied. It is shown that there exists a unique graded idealJ⊂Esuch that for all graded idealsI⊂Egenerated in degree ≥ 2 such thatone hasfor alli. Hereis thei-th Betti number of a gradedE-moduleM. The unique idealJwith the above property has “maximal” Hiibert function. Our result is the analogue of a theorem of Valla [10] which he proved for graded ideals in the polynomial ring. We further prove a similar inequality for the Bass numbers ofE/I, and give a combinatorial application.