The World Bank defines extreme poverty as living on less than $1.25 a day. A recent study by David Woodward published in the World Economics Review claims that if we assuming pre-crisis levels of growth (1993-2008) continue indefinitely it will take 100 years to bring the world’s population out of extreme poverty and 200 years to bring everyone to the modest income of $5 a day at 2005 purchasing power parity. Global GDP would have to reach 15 times its 2010 levels by 2115 and 173 times its 2010 levels by 2222.
Closing the poverty gap by increasing the income of the 63.2% of the world’s population living beneath $5-a-day to above this line would require an increase of $4.5 trillion to their incomes. Achieving this through our current growth pattern would involve increasing global GDP by more than $11,500 trillion and reaching a GDP per capita of $1.3 million. Attempting to eliminate poverty by this means would thus entail increasing production and consumption by more than 2,000 times the income we are seeking to generate, and still taking two centuries to do this. A process Woodward describes as “at best grotesquely inefficient”.
Woodward’s claim isn’t that global income is too low to alleviate poverty but rather that it is too unequally distributed. For example the poorest 30% the world population received just 1.2% of the additional income generated by global GDP growth between 1999 and 2008, the poorest 60% received 5.0% but the richest 40% accrued 95% of additional income.
Consider a more proportional scenario in which the income of the poorest decile rises at the same rate as global GDP per capita, whilst maintaining growth at the 1993-2008 rate. Everyone will be brought above the $1.25-a-day poverty line by 2068 and above the $5-a-day poverty line by 2076, this path would only necessitate increasing GDP by a factor of 3 and then 9. If we go even further and assume a pro-poor bias in global growth changing the ratio of income growth for the poorest decile to that of global GDP per capita to 1.82 (i.e. incomes of the poorest rise faster than World GDP) the results are even more impressive. Extreme poverty is eliminated by 2042, the entire population is brought over the $5-a-day line by 2076 and the scale of GDP growth required to achieve this is reduced by a factor of more than 28 than on our current projection.
The idea that economic growth on the current model will not eradicate extreme poverty over acceptable time horizons is lent support by other recent literature. A recent study that looked at the relation between increases in GDP per capita and childhood undernutrition between 1970 and 1996 across 36 low and middle-income countries found a very small to non-existent association between increases in GDP per capita and undernutrition. Even those that contested the findings of this study argued only that there was a marginal decrease in undernutrition associated with GDP per capita growth. These findings are echoed in a recent study which looked at the link between GDP per capita growth in Indian states and found no consistent evidence for the relationship between growth and undernutrition. One plausible mechanism for this effect is that many of those groups presently at risk of undernutrition receive such a small share of the rewards of economic growth that they are not able to increase the quality and quantity of the food they consume.
Another recent study claims that on current projections it will take until 2111 for sub-Saharan Africa to reach 100% lower-secondary school completion and at least 100 years for the average scores for students in the developing world to begin to match the average scores of students from developed countries in 2015. Another study indicates that at current rates it will take 96 countries beyond 2040 to achieve the 2015 Millennium Development Goals relating to significant reductions in maternal mortality and providing universal access to reproductive healthcare. This study also claims that it will take 23 sub-saharan African countries beyond 2040 to achieve the 2015 Millennium Goal of reducing child mortality by two thirds.
Given how pessimistic Woodward’s conclusions regarding the current model of economic growth are it is worth asking whether there are any reasons to doubt his reasoning.
Woodward excludes China from his projection of current economic growth and poverty alleviation. If China were included the resulting numbers would be more optimistic. China is obviously an outlier but one might hope that other countries could follow China’s enormous rates of growth and poverty reduction. However, there is good reason to suppose China’s economic rise is exceptional. Chinese growth is broadly attributable to economic reforms begun in the 1970s. Huge gains in productivity were gained by moving away from collectivised agriculture, relaxing price controls, and easing restrictions on the migration of farmers to cities. Other aspects of the economy were gradually reformed to introduce more private industry and greater competitive pressure on state owned industries.  The model of huge economic growth through gradual liberalisation of a centrally planned command economy is clearly not directly applicable to most countries today.
Additionally, even on the very optimistic projections of global growth (an average of 4% growth in GDP per capita per annum), the time horizons for poverty elimination are still extremely unsatisfactory, with extreme poverty elimination only projected to occur by 2072.
One might think that as economic growth occurs the share of this growth amongst the population will eventually become more equal. The economist Simon Kuznets hypothesised that as an economy develops market forces lead to an increase in inequality, increased investment opportunities cause the rich to become richer whilst influxes of labour into the cities keep down wages amongst the working class. Eventually processes associated with the development of industrialisation and the welfare state lead to an increase in equality. This hypothesis can be captured by an inverted U-shaped curve in which income per capita is plotted on the horizontal x axis and inequality on the Y axis. However whether this hypothesis is borne out in reality is highly controversial.   
One might be concerned that the line of $1.25 a day adjusted for purchasing power parity might not be the best way to measure poverty. However other indicators do not give a more cheerful prognosis. The Multiple Poverty Indicator which measures material deprivation through questions about housing, healthcare and diet places almost 1.7 billion people in “acute poverty” as opposed to the 1 billion people who live in “extreme poverty” according to the $1.25-a-day metric of the World Bank.  There is no reason to think continued economic growth along current lines is any more likely to impact this measure of poverty than the $1.25 dollar a day metric. In any case the number of people who need to be lifted from this form of poverty is even greater to begin with.
Finally there are reasons to think that Woodward’s projections might actually be too optimistic. One such reason cited by Woodward himself is that the growth in income for the poorest decile between 1993-2008 probably reflects a number of favourable shifts for the poor in this period such as increased debt cancellation and more focus on poverty reduction rather than structural adjustment, the adoption of the Millennium Development Goals and a doubling of per capita aid receipts between 2001-2008. Extrapolating income growth rates from this period implicitly assumes a continuation of this pro-poor shift at a similar rate for the indefinite future. And there is no reason to think this will necessarily be the case.
Another issue is that when we consider the increasing carbon and environmental constraints facing the global community it is plausible that this enormous level of growth may not even be viable. On current projections we will need to increase the size of the global economy by a factor of 173 times it’s 2010 size. Even if we expect future growth to be much less carbon and resource intensive the sheer size of the economic growth required may be beyond what carbon and resource constraints allow. This is not just a question of not wanting to pursue economic growth at such a cost to global warming and the environment, but also a question of whether such growth is even possible. Global warming and resource depletion will have a highly negative impact on standards of living, particularly harming the poorest in the world. These factors might be absolute constraints on what levels of economic growth and poverty alleviation can be achieved. 
An assessment of the literature indicates that we should be sceptical that “business as usual” economic growth will lead to eradication of extreme poverty over anything approaching an acceptable time horizon. Environmental and carbon constraints may even make it the case that eradicating extreme poverty will be impossible on our current trajectory. To eradicate poverty over a time-period of decades rather than centuries, the world’s poorest people need to receive a much greater share of global income. It may be necessary to radically change our entire approach to economic development to achieve this, but exactly what radical changes would be required and whether such changes would be tractable is unclear. Certainly one means to attempt to achieve this is to encourage many more people living in wealthy countries to give a significant portion of their income to charities operating in low-income countries.