If millennials and members of Generation Z have developed a reputation for finding trauma and injustice wherever they look, then 37-year-old playwright Martyna Majok is one artist — and there are others, rest assured — who can apply the courage of her compassion with a grownup’s sense of perspective. The Polish-born Ms. Majok’s characters, prominent among them immigrants, confront genuinely harrowing circumstances, but self-pity is as foreign a strategy for them as sentimentality is for their creator. 

“Cost of Living,” the play that marks Ms. Majok’s Broadway debut, arrives six years after its premiere at Williamstown Theatre Festival, following productions downtown and at Los Angeles and London; it received a Pulitzer Prize for drama in 2018. Its subject is timeless — the fragility of life, explored through two very different relationships with one common factor: A person in each is physically disabled.

If you’re at all familiar with Ms. Majok’s work, it won’t surprise you that neither John, a graduate student at Princeton suffering from cerebral palsy, nor Ani, a middle-aged woman confined to a wheelchair after severing her spinal cord in an accident, is romanticized, or defined by illness or injury. For all of her empathy, the playwright is most interested in the emotional and external factors that challenge all of her characters.

That would include Ani’s estranged husband, an out-of-work truck driver, and Jess, the young woman John hires as a caretaker. Jess, who attended Princeton herself, would appear overqualified for the job, or for the bar gigs she also juggles to make ends meet; but Ms. Majok quickly establishes — without inserting obvious politics or pedantry — that John has been more fortunate in other respects than the person now tasked with cleaning and dressing him.

Under Jo Bonney’s beautifully measured direction, Kara Young — fresh from a sparkling Broadway debut in Lynn Nottage’s “Clyde’s” last season — captures the grit and humor that have sustained Jess and the damage that has nonetheless been wrought, particularly after a crucial misunderstanding with John precipitates a downward spiral. Gregg Mozgala, who has cerebral palsy himself, reveals John’s entitlement without undercutting our sympathy; we sense how, for someone in his condition, privilege can be a double-edged sword.

David Zayas and Katy Sullivan are even more moving as, respectively, Eddie and Ani, in part because these characters are older, with less time left for a change in course, or luck — though as Ms. Majok repeatedly suggests here, age can be measured in terms of experience as well as years. This couple also gets the most gorgeously lyrical, and piercing, scene in the play, in which Eddie bathes Ani, and a new tenderness unfolds between them.

Even here, “Cost of Living” never threatens to become maudlin. The dialogue, between Eddie and Ani especially, is wonderfully salty; in her stage directions, Ms. Majok explains, “For the Jersey mouth” — the characters are based in that state, though some action takes place in Brooklyn — “the word ‘f—in’ is often used as a comma, or a vocalized pause.” Ms. Sullivan, herself a double amputee who competed in the 2010 Paralympics, channels Ani’s resentment, despair, pride, and lingering resolve into a blazingly human, and humane, performance.

Mr. Zayas’s heartbreaking Eddie is an ideal foil, physically imposing but nursing a palpably broken spirit. He, too, has known loss and seen hope dissolve, and just as Ms. Majok doesn’t patronize any of her characters by writing them off as victims, she recognizes all of their suffering, and its power to both unify and divide them.

It is through Eddie and Jess that the two stories in “Cost of Living” ultimately intersect, at a very low point for both. “It’s just unfortunate that some people have already lived a lot of life before they meet other people,” she tells him. Yet part of the beauty of “Cost of Living” is something else these disparate characters share: a determination to press on — no matter the price.