The idea behind this illustration is Hell on Earth, with the patriarch of the family, "Gramps," being the ruler of hell.
The story is set in 2185 A.D., 102 years after the invention of a medicine called anti-gerasone. This wonder drug halts the aging process and prevents people from dying of old age as long as they keep taking it. Anti-gerasone is cheap and plentiful, made from mud and dandelions. As a result, the world now suffers from severe overpopulation and shortages of food and resources. With the exception of the wealthy, most of the population survives on a diet of food made from processed seaweed and sawdust.
The Schwartz family, headed by 172-year-old Harold ("Gramps"), inhabits a three-room apartment in New York City. The city has grown so large due to overpopulation that it now spills into the state of Connecticut. Gramps' grandson Louis, his wife Emerald, and 20 other descendants are crowded into the space, perpetually jockeying for Gramps' favor. Gramps gets the best food and the only private bedroom. He controls everyone's life by constantly revising his will to disinherit anyone who earns his displeasure.
This story is part of Kurt Vonnegut's collection of short stories "Welcome to the Monkey House".