Who owns the right to reproduce your painting?

You, the artist, do. If a buyer copies it without your consent, he’s liable for damages.

The Monarch of the Glen, 1851, Sir Edwin Landseer, has been used for everything from the Hartford Insurance Company’s stag logo to biscuit tins and butter wrappers. You can read its history here
“A previous customer wants to use the painting they purchased as part of an advertising image. Anyone with experience in this?” an artist asked on Facebook. It’s a confusing subject.
The fact that her client approached her first indicates he knows that royalties are due. The artist needs to research royalties in her discipline before she can negotiate. I don’t envy her; it’s a difficult thing to pin down. 
Copyright law in the United States is different than in other countries. We have some treaty protection for our work, but nothing really protects artists from international freebooters. What I’m about to say is applicable only here. And of course I’m not a lawyer, so my advice is worth exactly what you’re paying for it.
You don’t need to register your copyright with the government for it to be protected. Copyright exists naturally once the work of art comes into existence. For something to be copyrighted, however, you actually have to make it in a tangible form. “I had that idea first!” is not a valid copyright argument, unless you can demonstrate that you actually acted on the idea.
Copyright gives you, the artist, the sole right to reproduce, create derivative works from, make prints from, and display the work publicly. It doesn’t matter if you sell the physical painting or sculpture; the rights to its image remain with you.
The Associated Press sued artist Shepard Fairey for copyright infringement for his Obama poster. The parties settled out of court in 2011, with details remaining confidential.
‘Work for hire’ is an exception to the general copyright rule. It happens when an employee creates art as part of his job or is specifically commissioned as part of a collaborative work. Advertising art done by either a salaried artist or a contracting artist is an example of the former. An example of the latter might be the artists who draw the illustrations in a medical dictionary for a commercial publisher.
An agreement that the work is for hire isn’t sufficient; the project must meet the courts’ narrow definition. Whether or not the artist is attributed makes absolutely no difference to its legal status.
String of Puppies, 1988. Jeff Koons.
Another exception is the fair-use exemption. This permits limited use of copyrighted material without the copyright holder’s permission. Fair use exemptions include research, scholarship, commentary, criticism, news reporting, parody, and search engines. Without it, artistic commentary (including mine) would grind to a halt. 
The fair use exemption doesn’t allow unlimited copying of artwork by other artists, even for self-styled ‘appropriation artists’ like Jeff Koons.
Puppies, 1985, Art Rogers. Rogers successfully sued Jeff Koons for copyright infringement, one of several times the artist has been sued.
Copyright currently lasts through the life of the author plus 70 years. If the work was produced under corporate authorship it may last 120 years after creation or 95 years after publication, whichever comes first.
What should you do if you find your painting gracing a wine label or a set of plastic dishes—or worse, badly reproduced? Consult a lawyer specializing in intellectual property. That’s theft.

Of course, anyone involved in an intellectual exchange should have a lawyer. The law is extremely complex, and expert advice is worth every penny you pay for it.

Sneering and sniggering to the bank

Naked, 1988, by Jeff Koons

Jeff Koons has been found guilty of plagiarizing the work of a popular French photographer. A French court has ruled that Koons’ Naked (1988) ripped off a black-and-white photograph by the late Jean-François Bauret (1932-2014). Although unknown here in the United States, Bauret was successful enough to have earned the Ministry of Culture’s Chevalier de l’ordre des Arts et des Lettres. His 1975 postcard picture, Enfants, was a popular seller in France.

Bauret’s widow was awarded a penalty payment of €44,000. That translates into US $46,937.88. Half of it, roughly, will cover her legal fees. That doesn’t compensate for seeing her husband’s endearing portrait of children turned into a sniggering, sexualized bit of American camp culture.
Enfants, 1975, by Jean-Francois Bauret
Ten months ago, Naked sold (or didn’t sell, to be more precise) for $5.7 million at Phillips’ 20th century and contemporary art sale in New York. When pressed on the subject, Phillips’ CEO Edward Dolman admitted that the porcelain sculpture went to the artwork’s third party guarantor. The fact that vast sums of money are exchanged for works nobody wants is the first hint that what we’re talking about here is fungibility, not creativity.
This is the fifth time Koons has been taken to court over his Banality series, which purports to show the dullness of the objects of our modern life by making equally dull, but really pricey, copies. In fact, the whole point is to sneer at the working and middle classes, who can’t afford to surround themselves with exquisite objects.
String of Puppies, 1988, by Jeff Koons
In 1989, photographer Art Rogers sued Koons for stealing an image for his sculpture “String of Puppies.” Koons was sued over the sculpture Wild Boy and Puppy, which was clearly a rip-off of Odie from Garfield.
Both times Koons claimed the fair use exemption by parody. Both times, he lost. The court held that he could have made his general statements about parody without copying those artists’ specific work.
String of Puppies, by Art Rogers
Fashion photographer Andrea Blanch sued Koonsfor using an image entitled Silk Sandals by Gucci, published in Allure in 2000. There, Blanch lost because the courts held that he did not own the image copyright to the sandals themselves. The resulting work, Niagara, is also substantially different from the original photo.
French adman Franck Davidovici filed a counterfeiting lawsuit over the artist’s 1988 work Fait d’Hiver. According to Le Monde, the penalties, if Davidovici prevails, will be quite a bit higher than in the Buaret case. The plaintiff demands the sculpture itself, along with an additional €271,000 in damages. “Even if that the claim is only brought against the edition of Fait d’Hiver currently in France for the Pompidou show—there are three other copies—the total requested damages could theoretically stretch well into the millions,” wroteAlexander Forbes. He then went on to mention the issue that bedevils this all: that the works in question are no longer owned by Koons himself, but are being hustled on the aftermarket. They’re commodities.
Fait d’Hiver, 1988, by Jeff Koons
Koons is an appropriation artist, so naturally he takes the broadest possible view of the fair use exemption. And appropriation art sells, which is why Koons gets millions for work of dubious intellectual and technical quality.
There is no consistent answer to the question of where artistic appropriation becomes copyright infringement. It sometimes seems to have mainly to do with which end of the stick you’re holding.

The original ad by Franck Davidovici. The penguin makes all the difference.
In 2011 Koons sent a cease-and-desist letter to a San Francisco store and gallery for selling balloon dog bookends. Attorney Jedediah Wakefield responded, “As virtually any clown can attest, no one owns the idea of making a balloon dog, and the shape created by twisting a balloon into a dog-like form is part of the public domain.” He then went on to skewer Koons as, “a retired stockbroker whose sculptures and other works are well-known for copying pre-existing forms and images from popular culture.”

Meanwhile, it is still unwise to appropriate another person’s photograph for your reference material. The Bauret case reinforces that. But if you’re thinking that the rich and famous get richer and more famous by flouting the law, I can’t argue with you.