Pseudocompactness of hyperspaces

We consider the following question of Ginsburg: Is there any relationship between the pseudocompactness of Xω and that of the hyperspace X2? We do that first in the context of Mrówka–Isbell spaces Ψ(A) associated with a maximal almost disjoint (MAD) family A on ω answering a question of J. Cao and T. Nogura. The space Ψω(A) is pseudocompact for every MAD family A. We show that(1)(p=c) 2Ψ(A) is pseudocompact for every MAD family A.(2)(h