A view of two works by Takashi Murakami, ‘Giant Magical Princess! She’s Walking Down the Streets of Akihabara!’ (2009) and ‘The Simple Things’ (2009)

Leaning forward to greet you as you enter Tate Modern’s new Pop Life exhibition is Takashi Murakami’s “Hiropon”, a life-size fibreglass cartoon schoolgirl poised to jump, while milk spurting from her enormous breasts circles her naked body like a skipping rope. Her partner, “Lonesome Cowboy”, a punky masturbating youth twirling a lasso of his own semen, sold last year at Sotheby’s for £9m.

Murakami endorsed that sale by attending it, watching in polite amazement as the work quadrupled its estimate. “Few people come to museums,” he explained. “The museum is kind of old-style media, like opera. I’m really interested in making merchandise for ordinary people.” These range from millionaires who collect his sculptures inspired by Japanese animation to kids buying his smiling flower stickers (£1.96) in Tate’s shop.

When artists enter the material world, can and should a museum try to keep up? Forty years ago, Warhol blew the lid off the art world soup can and called it by its real name – a business selling luxury goods to the highest bidder. Then he cannibalised his own work as a marketing/aesthetic strategy, because “good business is the best art”. Pop Life’s five Warhol rooms include the monumental 1978-1979 “Retrospective” and “Black on Black Retrospective” canvases, where Warhol revisits and reverses in a darker key his iconic Campbell’s Soup, Marilyn, and flower paintings, and the double celebrity portraits – Mick Jagger, David Hockney – with which he set out to make “a big painting called Portrait of Society”. Overshadowing the entire exhibition as memory and portent is Warhol’s own image: Andy in his fright wig, kissing John Lennon in 1978; standing pale and vampish alongside Jean-Michel Basquiat in 1982; staring out of the hollows in the deadly, brilliant self-portraits of 1986.

Gavin Turk’s ‘Pop’ (1993)

Within a year, Warhol was dead but his descendants, rather than merely commenting on mass media, now began cannibalising their own lives into performances. Throughout the 1990s, artists infiltrated the publicity machine, harnessed the power of celebrity to expand their reach beyond museums, and became global brands. This, Tate argues in a brave yet uncertain, difficult show, is pop art’s big legacy. It is a phenomenon inextricable from the end-of-history triumph of capitalism that has played out since the late 1980s, and is most tellingly explored in three careers born in capitalism’s heartlands: Jeff Koons in New York, Damien Hirst in London, Murakami in Tokyo.

Tate valiantly tries to give voice to other artists and does include a marvellous working reconstruction of Keith Haring’s 1987 “Pop Shop” (T-shirts: £25) fizzing with nostalgic disco innocence, but the Alpha Male trio of Koons-Hirst-Murakami inevitably dominates, just as their prices lead the market. None matches Warhol’s creepy grandeur, but their vain, showy, macho vocabulary offers a ghastly, parodic coda to it: the outsize penises, dildos and rippling muscles in Koons’ “Made in Heaven”, hardcore photographs and marble and blown-glass sculptures depicting his sexual relations with porn star La Cicciolina; Hirst’s calf in formaldehyde, “False Idol”, and hard, diamond-encrusted butterfly painting “The Kiss of Midas”; Murakami’s digital prints of himself in a harem of grinning schoolgirls, “The Majokko Eight”, sweetly perverse as “Hiropon”, and his illuminated cabinets of Louis Vuitton sneakers marching from shop floor to icon.

Money talks. For two decades, this cock-and-bull language has mirrored the credit bubble, creating value out of nothing for a breed of new super-rich collectors in search of tokens of glamour and prestige, and delivering back to them images of their own greed and emptiness. That is why Hirst’s “False Idol”, Koons’ shiny, stainless-steel inflated balloon “Rabbit”, and Murakami’s “superflat” characters are emblematic of our times, and why it is Tate’s role to show them.

Fearful, rightly, of either judging or colluding, Pop Life goes for an archival stance, contextualising, juxtaposing, historicising. This is not altogether successful because the show’s intellectual grit is thin, and many of its excavations look merely dated, academic, irrelevant: Martin Kippenberger’s prankster ego; Piotr Uklanski’s Nazi jokes; Tracey Emin’s minuscule memorabilia from her first White Cube show “My Major Retrospective”; worst of all, dreary, dim pornography-as-documentary such as Cosey Fanni Tutti’s photographs recording her ventures as a sleaze model, or Andrea Fraser’s film of her hour as a prostitute, paid $20,000 to have sex with an anonymous collector.

‘Untitled’(2009) by Maurizio Cattelan

The undercurrent of sexual politics is the saddest thing about this show, for it wholly divides the male and female artists in it and suggests that the sexual revolution worked only in men’s favour. Thus the baroque exaggerations of Koons and Murakami are banal but gleeful, comic and – despite the artists’ protestations of sincerity – they invite ironic, detached readings. By contrast, the life-as-art interventions of the women are pathetic, and witless, serving only to emphasise the triumphalism of male sexual fantasy that goes hand-in-hand with celebrity here.

In this context, Murakami (“colourfulness, cuteness, simplicity – that’s my aesthetic”) and Koons (“I am trying to make art be competitive in a competitive society”) are both beneficiaries of the democratisation of taste in the 1960s, when critical hegemony disappeared and low/high art boundaries evaporated. Koons developed this to an extreme in his “Made in Heaven” (1991) and “Banality” (1988) series, telling audiences, “Don’t divorce yourself from your true being. Embrace it. That’s the only way you can move on to become a new upper class.” The shamelessness of his pornographic pictures, of course, is not that they are sexually explicit – films such as Emmanuelle had been seen by millions in mainstream cinemas a decade earlier – but that Koons was so openly on the make in devising and manipulating them to propel himself to tabloid fame.

Hirst, represented by a selection from his Beautiful Inside My Head show-sale-performance at Sotheby’s last year, soars above such works as unquestionably the most important artist here after Warhol. Inventor of a fresh way of making art, he uses a new repertoire of materials – animals in formaldehyde, pharmaceutical cabinets – which, though lately co-opted to play an art market game, were always about more than that. Hirst is Warhol’s descendant not only as businessman but in his obsession with death, in the nuances of melancholy and romance coursing through his oeuvre. Indebted to the purity of minimalism, his works say confidently, “I am what I am”. Koons and Murakami’s works say, “I am what I am worth”, which, when the music stops, will not be very much at all.

‘Pop Life: Art in a Material World’, Tate Modern, London SE1, to January 17. Tel: +44 (0)20-7887 8888; www.tate.org.uk Hamburger Kunsthalle, February 15-May 9 2010; National Gallery of Canada, Ottawa, June 11-September 19 2010