Making forecasts for some fifty years is a dicey business but it's useful for building possible scenarios. The OECD has come out with forecasts up to 2060. The good news is that the OECD think the world economy will regain the average growth rate of the past decade and a half over the period 2011-30. The forecasts for India don't look good. India overtakes the US in GDP in PPP terms only in 2060; China does this in the middle of this decade itself.
I found this strange. Goldman Sachs, in its BRICS report of 2007, saw India overtaking the US in GDP at the market exchange rate of 2006 in 2050 itself. This implies that catch up in PPP terms should happen sooner since India's GDP gets inflated by a factor of about 3 when you use PPP. Arvind Virmani, writing in 2006, thought India would overtake the US in GDP in PPP terms by 2037, which would broadly accord with the Goldman forecast.
How come the OECD is so pessimistic? The answer is to be found in the implied growth rate. The OECD sees India growing at just 6.7% in 2011-30. Goldman had thought the growth rate would be 8.4% in 2007-20. If you accept that the world economy will get back to its pre-crisis decadal average growth, then India should be able to bounce back to growth rate of 7-8% over the next 20 years. So, the catch up with US would happen faster than OECD thinks.
More in my ET column, Post-Crisis, Is India a loser?