You have to admire Simon Godwin’s nerve. He assumes the leadership of one of the best-known Shakespeare companies in the country, and the first production he directs is not “Othello” or “Richard II” or even “Love’s Labour’s Lost.” No, it’s “Timon of Athens.”

What is that one about again? Well, exactly. The precise authorship of poor, only occasionally seen “Timon” isn’t clear; it’s commonly attributed to Shakespeare and Thomas Middleton, and whether it’s even a finished work is a matter of conjecture for professional literary decoders. The truth of it is lost to time. The silence of the iambs.

We can, however, deduce what Godwin, a devoted Bardolator, is up to. With this smartly conceived “Timon” — featuring sparrowlike but mighty British American actress Kathryn Hunter in the title role — he’s letting Shakespeare Theatre Company audiences know the entire canon can run, and cannot hide. We’re embarking with Godwin on an elite level of classical investigation, with forthcoming course diversions into more popular fare, such as the modern media world “Much Ado About Nothing” he’s planned for the spring.

It so happens, too, that Godwin has cut an incisive path through “Timon,” showing us the manner in which a play about money can fuse an Elizabethan vision with a contemporary one. In the divisive age of the 1 percent against the other 99, this cautionary fable unravels the tyrannical hypocrisy of the haves and the embittered outrage of the have-nots. As a nation mulls the implications of lopsided tax cuts for the rich, and billionaires offloading fortunes into campaign ads, “Timon of Athens” seems to burst with thought minted for the moment.

At a glittering dinner party, with guests costumed by Soutra Gilmour as if they were gilded baubles at a Tiffany counter, Timon entertains the well-heeled, self-infatuated sycophants of Athens. They’re only too happy to accept the lavish gifts Timon bestows, and she’s all too ready to bask in their fawning thanks. Only the house cynic, Arnie Burton’s splendidly vexed Apemantus — a sort of Grecian Fran Lebowitz — appears to grasp the unholy nature of Timon’s bargain. “I am wealthy in my friends,” Timon declares, and of course, when the money runs out and the gifts stop coming, so does the affection for her. Desolation follows adoration.

There’s a Brechtian, polemical clarity to “Timon” that makes it ideal for the church pulpit and the editorial page but rather dry and plodding for the stage. The play seems minor because it’s better at instruction than revelation; Timon’s ascetic exile in the forest, under a looming leafless tree, portrays her as wiser, and sadder. But her refusal to rejoin the world when beckoned back to mediate between the Athenian swells and an advancing army of the dispossessed feels like the completion of a lesson for the audience. She’s a paragon, not a person — too good for the world the rest of us must face.

Still, the gimlet eye that Shakespeare (and Middleton) train on the perfidious rich gives “Timon” an enjoyable edge. Shirine Babb and Dave Quay are appealingly duplicitous as supercilious social backstabbers, and John Rothman, Adam Langdon and Helen Cespedes form a compelling triptych of loyalty as the servants in Timon’s debt-ridden household. For comic relief, the team of Zachary Fine and Yonatan Gebeyehu, as talentless, arty hangers-on, has an audience-pleasing moment. Having heard Timon may still have gold, they seek her out in the woods to again beseech her patronage. Their comeuppance has, let’s say, an amusingly unappetizing flavor.

Hunter — in a role typically played by a man — radiates effortless theatricality whether in a gown of gold lamé or a dirty sackcloth; you could imagine Samuel Beckett seeing a production of “Timon of Athens” and jotting a few notes for Vladi­mir and Estragon in “Waiting for Godot,” or Winnie in “Happy Days.” Her voice may be gravelly and the countenance may come across as severe, but the delivery is riveting and the line readings redolent of pathos and regret. She takes us rewardingly on Timon’s downward slope, until, at last, she’s raised up by her enlightened resolve.

Godwin, too, provides many interesting perspectives from which to appreciate the play, including Gilmour’s stunning sets and costumes and Donald Holder’s handsome lighting. Michael Bruce’s music, played by an onstage band and sung by Kristen Misthopoulos, ushers a Mediterranean sound in through the doors of the Michael R. Klein (formerly the Lansburgh) Theatre. One perspective, though, could still use tweaking: the production was directed earlier this year by Godwin, with the same cast, at Brooklyn’s Theater for a New Audience, where the sightlines around the thrust stage were better. With actors deployed as inadvertent obstacles downstage, Godwin’s blocking isn’t uniformly well adapted for the Klein’s proscenium.

But this is Godwin's first turn in the trenches of the Klein. On the basis of this thoughtful, robust embrace of material so hard to get right, his education about how to use the company’s spaces promises to put Shakespeare lovers on a pleasurable learning curve.

Timon of Athens, by William Shakespeare and Thomas Middleton. Directed by Simon Godwin. Sound, Christopher Shutt; music, Michael Bruce; fight direction, Lisa Kopitsky. With Shirine Babb, Helen Cespedes, Yonatan Gebeyehu, Zachary Fine, David Quay, John Rothman. About 2½ hours. $35-$120. Through March 22 at Michael R. Klein Theatre, 450 Seventh St. NW. 202-547-1122.