See PBS.org's section on the show American Experience for this article: The Works Progress Administration (WPA).
Under the direction of Harry Hopkins, an enthusiastic ex-social worker
who had come from modest means, the WPA would spend more than $11
million in employment relief before it was canceled in 1943. The work
relief program was more expensive than direct relief payments, but
worth the added cost, Hopkins believed. “Give a man a dole,” he
observed, “and you save his body and destroy his spirit. Give him a
job and you save both body and spirit”.
The article answers the question 'why support art?':
When federal support of artists was questioned, Hopkins answered,
“Hell! They’ve got to eat just like other people.” The WPA supported
tens of thousands of artists, by funding creation of 2,566 murals and
17,744 pieces of sculpture that decorate public buildings nationwide.
The federal art, theater, music, and writing programs, while not
changing American culture as much as their adherents had hoped, did
bring more art to more Americans than ever before or since. The WPA
program in the arts led to the creation of the National Foundation for
the Arts and the National Endowment for the Humanities.
For primary source material at the National Archives, see NARA's entry page,
Records of the Work Projects Administration.