One night, in a bar in Zanzibar, I saw two sex workers chatting up a couple of Germans. The men were in their 50s, paunchy and balding - the women were young and pretty. It was a painful sight, the Germans plying the women with drinks and single entendre; the women laughing as though their lives depended on it, which in a way they did.

But after a while the true pathos became apparent: the men actually thought that these young women were interested in them because of who they were rather than what they had - money. That their dazzling personalities and dashing good looks had magically transformed them into irresistible specimens of manhood. Mistaking the possibility of a commercial transaction for the unlikelihood of sexual attraction, their eyes lingered on the mirror behind the bar as they started preening themselves, as though their looks mattered.

Power, whether you wield it or not, has a way of shading our sense of selves and others. In The Audacity of Hope, Barack Obama recalls a businessman seeing Al Gore shortly after the 2000 election. "During the campaign I would take his calls any time of day," the executive said. "But suddenly, after the election, I couldn't help feeling that the meeting was a chore. At some level he wasn't Al Gore, former vice-president. He was just one of the hundred guys a day who are coming to me looking for money. It made me realise what a big steep cliff you guys are on."

The US may be perched on the edge of a similar precipice. The degree to which it commands its hegemony through wealth and might (hard power) as opposed to culture and democratic example (soft power) has long been an open question. The personal aspiration, individual liberty and social meritocracy that are central to its national brand has an almost universal appeal. But how much that ethos makes sense without wealth and power is another matter. People need a social ladder worth climbing and something to do with their freedoms when they get to the top.

Have Caribbean kids been ditching cricket for basketball because it is faster and slicker, or because it offers the possibility of university scholarships, riches and fame? Was Obama's victory any more miraculous than Evo Morales's - he was the first indigenous Bolivian to rule his country - or do we just know and care more about it because of America's impact on our lives? What is Sex and the City without the shopping and the skyline? By almost any count Sweden has greater gender equality and liberated sexual mores than the US. Yet would the escapades of four single women in Stockholm stand a chance of becoming an international blockbuster, even if it were in English? Unlikely.

The truth is that American economic and cultural power are so inextricably woven that to separate them would be to see the whole thing unravel before your eyes. Both are fundamental to how the rest of the world views the US and how Americans view themselves.

And yet, with the simultaneous transition of Obama's ascent to the White House and the national economy's descent into long-term decline, countervailing pressures are pushing those two factors in contradictory directions. Abroad, American political leadership has never been so popular or so impotent. At home, Americans have never felt so excited about what their country might become or so apprehensive about where it might be heading. The next few months are shaping up to be truly Dickensian: the best of times, and the worst of times.

On the one hand, almost three weeks after the election, Obama still peers out from posters and badges. The warm glow of his victory still radiates and few seem keen to snuff out the flame. On the subway in New York last weekend an African-American woman in her 50s asked me what I thought of "our new president". We talked politics until my stop, exchanged a handshake and a hug. I dare say I'll never see her again.

The disappointing composition of his transition team (if he was going to appoint half the Clinton cabinet, why not just let Hillary have the nomination?) has done nothing to blunt the enthusiasm. Two months before he takes office Obama enjoys a 61% approval rating. If the rest of the world were polled, it would be even higher. As his triumph was announced, public celebrations erupted in almost every time zone. It is difficult to think of a moment when there has been more global goodwill towards an American leader, let alone such a dramatic reversal of attitude towards US leadership.

On the other hand, it is difficult to think of a moment when Americans felt more depressed about the state of their country or were less able to enforce their will on the world. Just one in six believe that the country is heading in the right direction, and consumer confidence is at a historic low. A country wedded to the notion that every year will be better than the last, and every generation more prosperous, has seen social mobility stall and the past look more promising than the future. Meanwhile, thanks to Iraq and Afghanistan, the nation's military is hopelessly overstretched and its reputation for invincibility lies shattered. Diplomatically, it is out of moral capital. Economically, it is out of plain old capital.

While these two trends coincide, they are not moving in lockstep. The presidential transition is hostage to a definite time period - Obama will not take the oath for another 57 days. Meanwhile, the scale and pace of the economic decline is indefinite. Less than two months ago, Citigroup was one vulture swooping in to feed from the carcass of the failed Wachovia bank. With its shares now in freefall and its chief executive in peril, Citigroup now looks set to become carrion itself. Obama wants to try and save the big three car manufacturers; it remains to be seen how many will be left by his inauguration.

So Obama's win may have been a lesson for the rest of the world, as claimed by the secretary of state, Condoleezza Rice. "Electing a black president says around the world that you can overcome old wounds," she told the New York Times last weekend. "I've said in our case, we have a birth defect, but it can be overcome."

The trouble is the rest of the world no longer needs to attend the lectures. "Owing to the relative decline of its economic and, to a lesser extent, military power, the US will no longer have the same flexibility in choosing among as many policy options," concluded the National Intelligence Council (which coordinates analysis from all US intelligence agencies) last week. The report acknowledged that, while the US would remain the single most powerful force in the world, its relative strength and potential leverage are in decline.

It doesn't take a genius to work this out. Which is just as well, since there are clearly few geniuses in the NIC. Its last forecast, in December 2004, predicted "continued US dominance", and oil and gas supplies "sufficient to meet global demand".

It can take time for perception to catch up with reality. By the time those Germans figured out their true aesthetic value, they may well have been broke.

g.younge@theguardian.com